Combining different models is a widely used paradigm in machine learning applications. While the most common approach is to form an ensemble of models and average their individual predictions, this approach is often rendered infeasible by given resource constraints in terms of memory and computation, which grow linearly with the number of models. We present a layer-wise model fusion algorithm for neural networks that utilizes optimal transport to (soft-) align neurons across the models before averaging their associated parameters.

We show that this can successfully yield "one-shot" knowledge transfer (i.e, without requiring any retraining) between neural networks trained on heterogeneous non-i.i.d. data. In both i.i.d. and non-i.i.d. settings, we illustrate that our approach significantly outperforms vanilla averaging, as well as how it can serve as an efficient replacement for the ensemble with moderate fine-tuning, for standard convolutional networks (like VGG11), residual networks (like ResNet18), and multi-layer perceptrons on CIFAR10, CIFAR100, and MNIST. Finally, our approach also provides a principled way to combine the parameters of neural networks with different widths, and we explore its application for model compression.

The code is available at the following link, https://github.com/sidak/otfusion.

Various Neural Networks employ time-consuming matrix operations like matrix inversion. Many such matrix operations are faster to compute given the Singular Value Decomposition (SVD). Techniques from (Zhang et al., 2018; Mhammedi et al., 2017) allow using the SVD in Neural Networks without computing it. In theory, the techniques can speed up matrix operations, however, in practice, they are not fast enough. We present an algorithm that is fast enough to speed up several matrix operations. The algorithm increases the degree of parallelism of an underlying matrix multiplication H*X where H is an orthogonal matrix represented by a product of Householder matrices.

A recent line of work focused on making adversarial training computationally efficient for deep learning models. In particular, Wong et al. (2020) showed that $\ell_\infty$-adversarial training with fast gradient sign method (FGSM) can fail due to a phenomenon called catastrophic overfitting, when the model quickly loses its robustness over a single epoch of training. We show that adding a random step to FGSM, as proposed in Wong et al. (2020), does not prevent catastrophic overfitting, and that randomness is not important per se --- its main role being simply to reduce the magnitude of the perturbation. Moreover, we show that catastrophic overfitting is not inherent to deep and overparametrized networks, but can occur in a single-layer convolutional network with a few filters. In an extreme case, even a single filter can make the network highly non-linear locally, which is the main reason why FGSM training fails. Based on this observation, we propose a new regularization method, GradAlign, that prevents catastrophic overfitting by explicitly maximizing the gradient alignment inside the perturbation set and improves the quality of the FGSM solution. As a result, GradAlign allows to successfully apply FGSM training also for larger $\ell_\infty$-perturbations and reduce the gap to multi-step adversarial training. The code of our experiments is available at https://github.com/tml-epfl/understanding-fast-adv-training.

Neural Networks can perform poorly when the training label distribution is heavily imbalanced, as well as when the testing data differs from the training distribution. In order to deal with shift in the testing label distribution, which imbalance causes, we motivate the problem from the perspective of an optimal Bayes classifier and derive a prior rebalancing technique that can be solved through a KL-divergence based optimization. This method allows a flexible post-training hyper-parameter to be efficiently tuned on a validation set and effectively modify the classifier margin to deal with this imbalance. We further combine this method with existing likelihood shift methods, re-interpreting them from the same Bayesian perspective, and demonstrating that our method can deal with both problems in a unified way. The resulting algorithm can be conveniently used on probabilistic classification problems agnostic to underlying architectures. Our results on six different datasets and five different architectures show state of art accuracy, including on large-scale imbalanced datasets such as iNaturalist for classification and Synthia for semantic segmentation. Please see https://github.com/GT-RIPL/UNO-IC.git for implementation.

The vast majority of deep models use multiple gradient signals, typically corresponding to a sum of multiple loss terms, to update a shared set of trainable weights. However, these multiple updates can impede optimal training by pulling the model in conflicting directions. We present Gradient Sign Dropout (GradDrop), a probabilistic masking procedure which samples gradients at an activation layer based on their level of consistency. GradDrop is implemented as a simple deep layer that can be used in any deep net and synergizes with other gradient balancing approaches. We show that GradDrop outperforms the state-of-the-art multiloss methods within traditional multitask and transfer learning settings, and we discuss how GradDrop reveals links between optimal multiloss training and gradient stochasticity.

Sampling-based methods promise scalability improvements when paired with stochastic gradient descent in training Graph Convolutional Networks (GCNs). While effective in alleviating the neighborhood explosion, due to bandwidth and memory bottlenecks, these methods lead to computational overheads in preprocessing and loading new samples in heterogeneous systems, which significantly deteriorate the sampling performance. By decoupling the frequency of sampling from the sampling strategy, we propose LazyGCN, a general yet effective framework that can be integrated with any sampling strategy to substantially improve the training time. The basic idea behind LazyGCN is to perform sampling periodically and effectively recycle the sampled nodes to mitigate data preparation overhead. We theoretically analyze the proposed algorithm and show that under a mild condition on the recycling size, by reducing the variance of inner layers, we are able to obtain the same convergence rate as the underlying sampling method. We also give corroborating empirical evidence on large real-world graphs, demonstrating that the proposed schema can significantly reduce the number of sampling steps and yield superior speedup without compromising the accuracy.

Obtaining reliable and accurate quantification of uncertainty estimates from deep neural networks is important in safety-critical applications. A well-calibrated model should be accurate when it is certain about its prediction and indicate high uncertainty when it is likely to be inaccurate. Uncertainty calibration is a challenging problem as there is no ground truth available for uncertainty estimates. We propose an optimization method that leverages the relationship between accuracy and uncertainty as an anchor for uncertainty calibration. We introduce a differentiable accuracy versus uncertainty calibration (AvUC) loss function that allows a model to learn to provide well-calibrated uncertainties, in addition to improved accuracy. We also demonstrate the same methodology can be extended to post-hoc uncertainty calibration on pretrained models. We illustrate our approach with mean-field stochastic variational inference and compare with state-of-the-art methods. Extensive experiments demonstrate our approach yields better model calibration than existing methods on large-scale image classification tasks under distributional shift.

Deterministic neural networks (NNs) are increasingly being deployed in safety critical domains, where calibrated, robust, and efficient measures of uncertainty are crucial. In this paper, we propose a novel method for training non-Bayesian NNs to estimate a continuous target as well as its associated evidence in order to learn both aleatoric and epistemic uncertainty. We accomplish this by placing evidential priors over the original Gaussian likelihood function and training the NN to infer the hyperparameters of the evidential distribution. We additionally impose priors during training such that the model is regularized when its predicted evidence is not aligned with the correct output. Our method does not rely on sampling during inference or on out-of-distribution (OOD) examples for training, thus enabling efficient and scalable uncertainty learning. We demonstrate learning well-calibrated measures of uncertainty on various benchmarks, scaling to complex computer vision tasks, as well as robustness to adversarial and OOD test samples.

We consider the development of practical stochastic quasi-Newton, and in particular Kronecker-factored block diagonal BFGS and L-BFGS methods, for training deep neural networks (DNNs). In DNN training, the number of variables and components of the gradient n is often of the order of tens of millions and the Hessian has n^2 elements. Consequently, computing and storing a full n times n BFGS approximation or storing a modest number of (step, change in gradient) vector pairs for use in an L-BFGS implementation is out of the question. In our proposed methods, we approximate the Hessian by a block-diagonal matrix and use the structure of the gradient and Hessian to further approximate these blocks, each of which corresponds to a layer, as the Kronecker product of two much smaller matrices. This is analogous to the approach in KFAC , which computes a Kronecker-factored block diagonal approximation to the Fisher matrix in a stochastic natural gradient method. Because the indefinite and highly variable nature of the Hessian in a DNN, we also propose a new damping approach to keep the upper as well as the lower bounds of the BFGS and L-BFGS approximations bounded. In tests on autoencoder feed-forward network models with either nine or thirteen layers applied to three datasets, our methods outperformed or performed comparably to KFAC and state-of-the-art first-order stochastic methods.

In this paper, we propose a number of novel techniques and numerical representation formats that enable, for the very first time, the precision of training systems to be aggressively scaled from 8-bits to 4-bits. To enable this advance, we explore a novel adaptive Gradient Scaling technique (Gradscale) that addresses the challenges of insufficient range and resolution in quantized gradients as well as explores the impact of quantization errors observed during model training. We theoretically analyze the role of bias in gradient quantization and propose solutions that mitigate the impact of this bias on model convergence. Finally, we examine our techniques on a spectrum of deep learning models in computer vision, speech, and NLP. In combination with previously proposed solutions for 4-bit quantization of weight and activation tensors, 4-bit training shows a non-significant loss in accuracy across application domains while enabling significant hardware acceleration (> 7X over state-of-the-art FP16 systems).

Stochastic Gradient Descent (SGD) has proven to be remarkably effective in optimizing deep neural networks that employ ever-larger numbers of parameters. Yet, improving the efficiency of large-scale optimization remains a vital and highly active area of research. Recent work has shown that deep neural networks can be optimized in randomly-projected subspaces of much smaller dimensionality than their native parameter space. While such training is promising for more efficient and scalable optimization schemes, its practical application is limited by inferior optimization performance. Here, we improve on recent random subspace approaches as follows. We show that keeping the random projection fixed throughout training is detrimental to optimization. We propose re-drawing the random subspace at each step, which yields significantly better performance. We realize further improvements by applying independent projections to different parts of the network, making the approximation more efficient as network dimensionality grows. To implement these experiments, we leverage hardware-accelerated pseudo-random number generation to construct the random projections on-demand at every optimization step, allowing us to distribute the computation of independent random directions across multiple workers with shared random seeds. This yields significant reductions in memory and is up to 10x faster for the workloads in question.

Several sampling algorithms with variance reduction have been proposed for accelerating the training of Graph Convolution Networks (GCNs). However, due to the intractable computation of optimal sampling distribution, these sampling algorithms are suboptimal for GCNs and are not applicable to more general graph neural networks (GNNs) where the message aggregator contains learned weights rather than fixed weights, such as Graph Attention Networks (GAT). The fundamental reason is that the embeddings of the neighbors or learned weights involved in the optimal sampling distribution are \emph{changing} during the training and \emph{not known a priori}, but only \emph{partially observed} when sampled, thus making the derivation of an optimal variance reduced samplers non-trivial. In this paper, we formulate the optimization of the sampling variance as an adversary bandit problem, where the rewards are related to the node embeddings and learned weights, and can vary constantly. Thus a good sampler needs to acquire variance information about more neighbors (exploration) while at the same time optimizing the immediate sampling variance (exploit). We theoretically show that our algorithm asymptotically approaches the optimal variance within a factor of 3. We show the efficiency and effectiveness of our approach on multiple datasets.

Large-scale distributed training of Deep Neural Networks (DNNs) on state-of-the-art platforms are expected to be severely communication constrained. To overcome this limitation, numerous gradient compression techniques have been proposed and have demonstrated high compression ratios. However, most existing compression methods do not scale well to large scale distributed systems (due to gradient build-up) and / or lack evaluations in large datasets. To mitigate these issues, we propose a new compression technique, Scalable Sparsified Gradient Compression (ScaleComp), that (i) leverages similarity in the gradient distribution amongst learners to provide a commutative compressor and keep communication cost constant to worker number and (ii) includes low-pass filter in local gradient accumulations to mitigate the impacts of large batch size training and significantly improve scalability. Using theoretical analysis, we show that ScaleComp provides favorable convergence guarantees and is compatible with gradient all-reduce techniques. Furthermore, we experimentally demonstrate that ScaleComp has small overheads, directly reduces gradient traffic and provides high compression rates (70-150X) and excellent scalability (up to 64-80 learners and 10X larger batch sizes over normal training) across a wide range of applications (image, language, and speech) without significant accuracy loss.

Optimal Transport (OT) distances such as Wasserstein have been used in several areas such as GANs and domain adaptation. OT, however, is very sensitive to outliers (samples with large noise) in the data since in its objective function, every sample, including outliers, is weighed similarly due to the marginal constraints. To remedy this issue, robust formulations of OT with unbalanced marginal constraints have previously been proposed. However, employing these methods in deep learning problems such as GANs and domain adaptation is challenging due to the instability of their dual optimization solvers. In this paper, we resolve these issues by deriving a computationally-efficient dual form of the robust OT optimization that is amenable to modern deep learning applications. We demonstrate the effectiveness of our formulation in two applications of GANs and domain adaptation. Our approach can train state-of-the-art GAN models on noisy datasets corrupted with outlier distributions. In particular, the proposed optimization method computes weights for training samples reflecting how difficult it is for those samples to be generated in the model. In domain adaptation, our robust OT formulation leads to improved accuracy compared to the standard adversarial adaptation methods. Our code is available at https://github.com/yogeshbalaji/robustOT.

We formulate the problem of neural network optimization as Bayesian filtering, where the observations are backpropagated gradients. While neural network optimization has previously been studied using natural gradient methods which are closely related to Bayesian inference, they were unable to recover standard optimizers such as Adam and RMSprop with a root-mean-square gradient normalizer, instead getting a mean-square normalizer. To recover the root-mean-square normalizer, we find it necessary to account for the temporal dynamics of all the other parameters as they are optimized. The resulting optimizer, AdaBayes, adaptively transitions between SGD-like and Adam-like behaviour, automatically recovers AdamW, a state of the art variant of Adam with decoupled weight decay, and has generalisation performance competitive with SGD.

Designing deep neural networks is an art that often involves an expensive search over candidate architectures. To overcome this for recurrent neural nets (RNNs), we establish a connection between the hidden state dynamics in an RNN and gradient descent (GD). We then integrate momentum into this framework and propose a new family of RNNs, called {\em MomentumRNNs}. We theoretically prove and numerically demonstrate that MomentumRNNs alleviate the vanishing gradient issue in training RNNs. We study the momentum long-short term memory (MomentumLSTM) and verify its advantages in convergence speed and accuracy over its LSTM counterpart across a variety of benchmarks. We also demonstrate that MomentumRNN is applicable to many types of recurrent cells, including those in the state-of-the-art orthogonal RNNs. Finally, we show that other advanced momentum-based optimization methods, such as Adam and Nesterov accelerated gradients with a restart, can be easily incorporated into the MomentumRNN framework for designing new recurrent cells with even better performance.

While stochastic gradient descent (SGD) is still the de facto algorithm in deep learning, adaptive methods like Clipped SGD/Adam have been observed to outperform SGD across important tasks, such as attention models. The settings under which SGD performs poorly in comparison to adaptive methods are not well understood yet. In this paper, we provide empirical and theoretical evidence that a heavy-tailed distribution of the noise in stochastic gradients is one cause of SGD's poor performance. We provide the first tight upper and lower convergence bounds for adaptive gradient methods under heavy-tailed noise. Further, we demonstrate how gradient clipping plays a key role in addressing heavy-tailed gradient noise. Subsequently, we show how clipping can be applied in practice by developing an adaptive coordinate-wise clipping algorithm (ACClip) and demonstrate its superior performance on BERT pretraining and finetuning tasks.

Imbalanced learning (IL), i.e., learning unbiased models from class-imbalanced data, is a challenging problem. Typical IL methods including resampling and reweighting were designed based on some heuristic assumptions. They often suffer from unstable performance, poor applicability, and high computational cost in complex tasks where their assumptions do not hold. In this paper, we introduce a novel ensemble IL framework named MESA. It adaptively resamples the training set in iterations to get multiple classifiers and forms a cascade ensemble model. MESA directly learns the sampling strategy from data to optimize the final metric beyond following random heuristics. Moreover, unlike prevailing meta-learning-based IL solutions, we decouple the model-training and meta-training in MESA by independently train the meta-sampler over task-agnostic meta-data. This makes MESA generally applicable to most of the existing learning models and the meta-sampler can be efficiently applied to new tasks. Extensive experiments on both synthetic and real-world tasks demonstrate the effectiveness, robustness, and transferability of MESA. Our code is available at https://github.com/ZhiningLiu1998/mesa.

Continual Learning has inspired a plethora of approaches and evaluation settings; however, the majority of them overlooks the properties of a practical scenario, where the data stream cannot be shaped as a sequence of tasks and offline training is not viable. We work towards General Continual Learning (GCL), where task boundaries blur and the domain and class distributions shift either gradually or suddenly. We address it through mixing rehearsal with knowledge distillation and regularization; our simple baseline, Dark Experience Replay, matches the network's logits sampled throughout the optimization trajectory, thus promoting consistency with its past. By conducting an extensive analysis on both standard benchmarks and a novel GCL evaluation setting (MNIST-360), we show that such a seemingly simple baseline outperforms consolidated approaches and leverages limited resources. We further explore the generalization capabilities of our objective, showing its regularization being beneficial beyond mere performance.

Research on continual learning has led to a variety of approaches to mitigating catastrophic forgetting in feed-forward classification networks. Until now surprisingly little attention has been focused on continual learning of recurrent models applied to problems like image captioning. In this paper we take a systematic look at continual learning of LSTM-based models for image captioning. We propose an attention-based approach that explicitly accommodates the transient nature of vocabularies in continual image captioning tasks -- i.e. that task vocabularies are not disjoint. We call our method Recurrent Attention to Transient Tasks (RATT), and also show how to adapt continual learning approaches based on weight regularization and knowledge distillation to recurrent continual learning problems. We apply our approaches to incremental image captioning problem on two new continual learning benchmarks we define using the MS-COCO and Flickr30 datasets. Our results demonstrate that RATT is able to sequentially learn five captioning tasks while incurring no forgetting of previously learned ones.

Existing research on continual learning of a sequence of tasks focused on dealing with catastrophic forgetting, where the tasks are assumed to be dissimilar and have little shared knowledge. Some work has also been done to transfer previously learned knowledge to the new task when the tasks are similar and have shared knowledge. %However, in the most general case, a CL system not only should have the above two capabilities, but also the \textit{backward knowledge transfer} capability so that future tasks may help improve the past models whenever possible. To the best of our knowledge, no technique has been proposed to learn a sequence of mixed similar and dissimilar tasks that can deal with forgetting and also transfer knowledge forward and backward. This paper proposes such a technique to learn both types of tasks in the same network. For dissimilar tasks, the algorithm focuses on dealing with forgetting, and for similar tasks, the algorithm focuses on selectively transferring the knowledge learned from some similar previous tasks to improve the new task learning. Additionally, the algorithm automatically detects whether a new task is similar to any previous tasks. Empirical evaluation using sequences of mixed tasks demonstrates the effectiveness of the proposed model.

Continually learning new skills is important for intelligent systems, yet standard deep learning methods suffer from catastrophic forgetting of the past. Recent works address this with weight regularisation. Functional regularisation, although computationally expensive, is expected to perform better, but rarely does so in practice. In this paper, we fix this issue by using a new functional-regularisation approach that utilises a few memorable past examples crucial to avoid forgetting. By using a Gaussian Process formulation of deep networks, our approach enables training in weight-space while identifying both the memorable past and a functional prior. Our method achieves state-of-the-art performance on standard benchmarks and opens a new direction for life-long learning where regularisation and memory-based methods are naturally combined.

The continual learning problem involves training models with limited capacity to perform well on a set of an unknown number of sequentially arriving tasks. While meta-learning shows great potential for reducing interference between old and new tasks, the current training procedures tend to be either slow or offline, and sensitive to many hyper-parameters. In this work, we propose Look-ahead MAML (La-MAML), a fast optimisation-based meta-learning algorithm for online-continual learning, aided by a small episodic memory. By incorporating the modulation of per-parameter learning rates in our meta-learning update, our approach also allows us to draw connections to and exploit prior work on hypergradients and meta-descent. This provides a more flexible and efficient way to mitigate catastrophic forgetting compared to conventional prior-based methods. La-MAML achieves performance superior to other replay-based, prior-based and meta-learning based approaches for continual learning on real-world visual classification benchmarks.

Human intelligence is characterized not only by the capacity to learn complex skills, but the ability to rapidly adapt and acquire new skills within an ever-changing environment. In this work we study how the learning of modular solutions can allow for effective generalization to both unseen and potentially differently distributed data. Our main postulate is that the combination of task segmentation, modular learning and memory-based ensembling can give rise to generalization on an exponentially growing number of unseen tasks. We provide a concrete instantiation of this idea using a combination of: (1) the Forget-Me-Not Process, for task segmentation and memory based ensembling; and (2) Gated Linear Networks, which in contrast to contemporary deep learning techniques use a modular and local learning mechanism. We demonstrate that this system exhibits a number of desirable continual learning properties: robustness to catastrophic forgetting, no negative transfer and increasing levels of positive transfer as more tasks are seen. We show competitive performance against both offline and online methods on standard continual learning benchmarks.

In continual learning (CL), a learner is faced with a sequence of tasks, arriving one after the other, and the goal is to remember all the tasks once the continual learning experience is finished. The prior art in CL uses episodic memory, parameter regularization or extensible network structures to reduce interference among tasks, but in the end, all the approaches learn different tasks in a joint vector space. We believe this invariably leads to interference among different tasks. We propose to learn tasks in different (low-rank) vector subspaces that are kept orthogonal to each other in order to minimize interference. Further, to keep the gradients of different tasks coming from these subspaces orthogonal to each other, we learn isometric mappings by posing network training as an optimization problem over the Stiefel manifold. To the best of our understanding, we report, for the first time, strong results over experience-replay baseline with and without memory on standard classification benchmarks in continual learning.

Online continual learning is a challenging scenario where a model needs to learn from a continuous stream of data without revisiting any previously encountered data instances. The phenomenon of catastrophic forgetting is worsened since the model should not only address the forgetting at the task-level but also at the data instance-level within the same task. To mitigate this, we leverage the concept of "instance awareness" in the neural network, where each data instance is classified by a path in the network searched by the controller from a meta-graph. To preserve the knowledge we learn from previous instances, we proposed a method to protect the path by restricting the gradient updates of one instance from overriding past updates calculated from previous instances if these instances are not similar. On the other hand, it also encourages fine-tuning the path if the incoming instance shares the similarity with previous instances. The mechanism of selecting paths according to instances similarity is naturally determined by the controller, which is compact and online updated. Experimental results show that the proposed method outperforms state-of-the-arts in online continual learning. Furthermore, the proposed method is evaluated against a realistic setting where the boundaries between tasks are blurred. Experimental results confirm that the proposed method outperforms the state-of-the-arts on CIFAR-10, CIFAR-100, and Tiny-ImageNet.

Continual learning agents experience a stream of (related) tasks. The main challenge is that the agent must not forget previous tasks and also adapt to novel tasks in the stream. We are interested in the intersection of two recent continual-learning scenarios. In meta-continual learning, the model is pre-trained using meta-learning to minimize catastrophic forgetting of previous tasks. In continual-meta learning, the aim is to train agents for faster remembering of previous tasks through adaptation. In their original formulations, both methods have limitations. We stand on their shoulders to propose a more general scenario, OSAKA, where an agent must quickly solve new (out-of-distribution) tasks, while also requiring fast remembering. We show that current continual learning, meta-learning, meta-continual learning, and continual-meta learning techniques fail in this new scenario. We propose Continual-MAML, an online extension of the popular MAML algorithm as a strong baseline for this scenario. We show in an empirical study that Continual-MAML is better suited to the new scenario than the aforementioned methodologies including standard continual learning and meta-learning approaches.

Recently, different machine learning methods have been introduced to tackle the challenging few-shot learning scenario that is, learning from a small labeled dataset related to a specific task. Common approaches have taken the form of meta-learning: learning to learn on the new problem given the old. Following the recognition that meta-learning is implementing learning in a multi-level model, we present a Bayesian treatment for the meta-learning inner loop through the use of deep kernels. As a result we can learn a kernel that transfers to new tasks; we call this Deep Kernel Transfer (DKT). This approach has many advantages: is straightforward to implement as a single optimizer, provides uncertainty quantification, and does not require estimation of task-specific parameters. We empirically demonstrate that DKT outperforms several state-of-the-art algorithms in few-shot classification, and is the state of the art for cross-domain adaptation and regression. We conclude that complex meta-learning routines can be replaced by a simpler Bayesian model without loss of accuracy.

Meta-learning methods have shown an impressive ability to train models that rapidly learn new tasks. However, these methods only aim to perform well in expectation over tasks coming from some particular distribution that is typically equivalent across meta-training and meta-testing, rather than considering worst-case task performance. In this work we introduce the notion of ``task-robustness'' by reformulating the popular Model-Agnostic Meta-Learning (MAML) objective \citep{finn2017model} such that the goal is to minimize the maximum loss over the observed meta-training tasks. The solution to this novel formulation is task-robust in the sense that it places equal importance on even the most difficult and/or rare tasks. This also means that it performs well over all distributions of the observed tasks, making it robust to shifts in the task distribution between meta-training and meta-testing. We present an algorithm to solve the proposed min-max problem, and show that it converges to an $\epsilon$-accurate point at the optimal rate of $\mathcal{O}(1/\epsilon^2)$ in the convex setting and to an $(\epsilon, \delta)$-stationary point at the rate of $\mathcal{O}(\max\{1/\epsilon^5, 1/\delta^5\})$ in nonconvex settings. We also provide an upper bound on the new task generalization error that captures the advantage of minimizing the worst-case task loss, and demonstrate this advantage in sinusoid regression and image classification experiments.

In this paper, we introduce variational semantic memory into meta-learning to acquire long-term knowledge for few-shot learning. The variational semantic memory accrues and stores semantic information for the probabilistic inference of class prototypes in a hierarchical Bayesian framework. The semantic memory is grown from scratch and gradually consolidated by absorbing information from tasks it experiences. By doing so, it is able to accumulate long-term, general knowledge that enables it to learn new concepts of objects. We formulate memory recall as the variational inference of a latent memory variable from addressed contents, which offers a principled way to adapt the knowledge to individual tasks. Our variational semantic memory, as a new long-term memory module, confers principled recall and update mechanisms that enable semantic information to be efficiently accrued and adapted for few-shot learning. Experiments demonstrate that the probabilistic modelling of prototypes achieves a more informative representation of object classes compared to deterministic vectors. The consistent new state-of-the-art performance on four benchmarks shows the benefit of variational semantic memory in boosting few-shot recognition.

Meta-learning is a promising strategy for learning to efficiently learn using data gathered from a distribution of tasks. However, the meta-learning literature thus far has focused on the task segmented setting, where at train-time, offline data is assumed to be split according to the underlying task, and at test-time, the algorithms are optimized to learn in a single task. In this work, we enable the application of generic meta-learning algorithms to settings where this task segmentation is unavailable, such as continual online learning with unsegmented time series data. We present meta-learning via online changepoint analysis (MOCA), an approach which augments a meta-learning algorithm with a differentiable Bayesian changepoint detection scheme. The framework allows both training and testing directly on time series data without segmenting it into discrete tasks. We demonstrate the utility of this approach on three nonlinear meta-regression benchmarks as well as two meta-image-classification benchmarks.

Supervised learning requires a large amount of training data, limiting its application where labeled data is scarce. To compensate for data scarcity, one possible method is to utilize auxiliary tasks to provide additional supervision for the main task. Assigning and optimizing the importance weights for different auxiliary tasks remains an crucial and largely understudied research question. In this work, we propose a method to automatically reweight auxiliary tasks in order to reduce the data requirement on the main task. Specifically, we formulate the weighted likelihood function of auxiliary tasks as a surrogate prior for the main task. By adjusting the auxiliary task weights to minimize the divergence between the surrogate prior and the true prior of the main task, we obtain a more accurate prior estimation, achieving the goal of minimizing the required amount of training data for the main task and avoiding a costly grid search. In multiple experimental settings (e.g. semi-supervised learning, multi-label classification), we demonstrate that our algorithm can effectively utilize limited labeled data of the main task with the benefit of auxiliary tasks compared with previous task reweighting methods. We also show that under extreme cases with only a few extra examples (e.g. few-shot domain adaptation), our algorithm results in significant improvement over the baseline. Our code and video is available at https://sites.google.com/view/auxiliary-task-reweighting.

Self-organization of complex morphological patterns from local interactions is a fascinating phenomenon in many natural and artificial systems. In the artificial world, typical examples of such morphogenetic systems are cellular automata. Yet, their mechanisms are often very hard to grasp and so far scientific discoveries of novel patterns have primarily been relying on manual tuning and ad hoc exploratory search. The problem of automated diversity-driven discovery in these systems was recently introduced [26, 62], highlighting that two key ingredients are autonomous exploration and unsupervised representation learning to describe “relevant” degrees of variations in the patterns. In this paper, we motivate the need for what we call Meta-diversity search, arguing that there is not a unique ground truth interesting diversity as it strongly depends on the final observer and its motives. Using a continuous game-of-life system for experiments, we provide empirical evidences that relying on monolithic architectures for the behavioral embedding design tends to bias the final discoveries (both for hand-defined and unsupervisedly-learned features) which are unlikely to be aligned with the interest of a final end-user. To address these issues, we introduce a novel dynamic and modular architecture that enables unsupervised learning of a hierarchy of diverse representations. Combined with intrinsically motivated goal exploration algorithms, we show that this system forms a discovery assistant that can efficiently adapt its diversity search towards preferences of a user using only a very small amount of user feedback.

Missing Not At Random (MNAR) values where the probability of having missing data may depend on the missing value itself, are notoriously difficult to account for in analyses, although very frequent in the data. One solution to handle MNAR data is to specify a model for the missing data mechanism, which makes inference or imputation tasks more complex. Furthermore, this implies a strong \textit{a priori} on the parametric form of the distribution. However, some works have obtained guarantees on the estimation of parameters in the presence of MNAR data, without specifying the distribution of missing data \citep{mohan2018estimation, tang2003analysis}. This is very useful in practice, but is limited to simple cases such as few self-masked MNAR variables in data generated according to linear regression models. We continue this line of research, but extend it to a more general MNAR mechanism, in a more general model of the probabilistic principal component analysis (PPCA), \textit{i.e.}, a low-rank model with random effects. We prove identifiability of the PPCA parameters. We then propose an estimation of the loading coefficients, and a data imputation method. Both are based on estimators of means, variances and covariances of missing variables, for which consistency is discussed. These estimators have the great advantage of being calculated using only the observed information, leveraging the underlying low-rank structure of the data. We illustrate the relevance of the method with numerical experiments on synthetic data and also on two datasets, one collected from a medical register and the other one from a recommendation system.

Recent years have seen the rise of statistical program learning based on neural models as an alternative to traditional rule-based systems for programming by example. Rule-based approaches offer correctness guarantees in an unsupervised way as they inherently capture logical rules, while neural models are more realistically scalable to raw, high-dimensional input, and provide resistance to noisy I/O specifications. We introduce PLANS (Program LeArning from Neurally inferred Specifications), a hybrid model for program synthesis from visual observations that gets the best of both worlds, relying on (i) a neural architecture trained to extract abstract, high-level information from each raw individual input (ii) a rule-based system using the extracted information as I/O specifications to synthesize a program capturing the different observations. In order to address the key challenge of making PLANS resistant to noise in the network's output, we introduce a dynamic filtering algorithm for I/O specifications based on selective classification techniques. We obtain state-of-the-art performance at program synthesis from diverse demonstration videos in the Karel and ViZDoom environments, while requiring no ground-truth program for training.

Linear systems are the bedrock of virtually all numerical computation. Machine learning poses specific challenges for the solution of such systems due to their scale, characteristic structure, stochasticity and the central role of uncertainty in the field. Unifying earlier work we propose a class of probabilistic linear solvers which jointly infer the matrix, its inverse and the solution from matrix-vector product observations. This class emerges from a fundamental set of desiderata which constrains the space of possible algorithms and recovers the method of conjugate gradients under certain conditions. We demonstrate how to incorporate prior spectral information in order to calibrate uncertainty and experimentally showcase the potential of such solvers for machine learning.

Design of experiments and estimation of treatment effects in large-scale networks, in the presence of strong interference, is a challenging and important problem. Most existing methods' performance deteriorates as the density of the network increases. In this paper, we present a novel strategy for accurately estimating the causal effects of a class of treatments in a dense large-scale network. First, we design an approximate randomized controlled experiment by solving an optimization problem to allocate treatments in the presence of competition among neighboring nodes. Then we apply an importance sampling adjustment to correct for any leftover bias (from the approximation) in estimating average treatment effects. We provide theoretical guarantees, verify robustness in a simulation study, and validate the scalability and usefulness of our procedure in a real-world experiment on a large social network.

We present a novel algorithm for non-linear instrumental variable (IV) regression, DualIV, which simplifies traditional two-stage methods via a dual formulation. Inspired by problems in stochastic programming, we show that two-stage procedures for non-linear IV regression can be reformulated as a convex-concave saddle-point problem. Our formulation enables us to circumvent the first-stage regression which is a potential bottleneck in real-world applications. We develop a simple kernel-based algorithm with an analytic solution based on this formulation. Empirical results show that we are competitive to existing, more complicated algorithms for non-linear instrumental variable regression.

While much attention has been given to the problem of estimating the effect of discrete interventions from observational data, relatively little work has been done in the setting of continuous-valued interventions, such as treatments associated with a dosage parameter. In this paper, we tackle this problem by building on a modification of the generative adversarial networks (GANs) framework. Our model, SCIGAN, is flexible and capable of simultaneously estimating counterfactual outcomes for several different continuous interventions. The key idea is to use a significantly modified GAN model to learn to generate counterfactual outcomes, which can then be used to learn an inference model, using standard supervised methods, capable of estimating these counterfactuals for a new sample. To address the challenges presented by shifting to continuous interventions, we propose a novel architecture for our discriminator - we build a hierarchical discriminator that leverages the structure of the continuous intervention setting. Moreover, we provide theoretical results to support our use of the GAN framework and of the hierarchical discriminator. In the experiments section, we introduce a new semi-synthetic data simulation for use in the continuous intervention setting and demonstrate improvements over the existing benchmark models.

Deciding how to optimally treat a patient, including how to select treatments over time among the multiple available treatments, represents one of the most important issues that need to be addressed in medicine today. A dynamic treatment regime (DTR) is a sequence of treatment rules indicating how to individualize treatments for a patient based on the previously assigned treatments and the evolving covariate history. However, DTR evaluation and learning based on offline data remain challenging problems due to the bias introduced by time-varying confounders that affect treatment assignment over time; this may lead to suboptimal treatment rules being used in practice. In this paper, we introduce Gradient Regularized V-learning (GRV), a novel method for estimating the value function of a DTR. GRV regularizes the underlying outcome and propensity score models with respect to the optimality condition in semiparametric estimation theory. On the basis of this design, we construct estimators that are efficient and stable in finite samples regime. Using multiple simulation studies and one real-world medical dataset, we demonstrate that our method is superior in DTR evaluation and learning, thereby providing improved treatment options over time for patients.

Recommending the best course of action for an individual is a major application of individual-level causal effect estimation. This application is often needed in safety-critical domains such as healthcare, where estimating and communicating uncertainty to decision-makers is crucial. We introduce a practical approach for integrating uncertainty estimation into a class of state-of-the-art neural network methods used for individual-level causal estimates. We show that our methods enable us to deal gracefully with situations of "no-overlap", common in high-dimensional data, where standard applications of causal effect approaches fail. Further, our methods allow us to handle covariate shift, where the train and test distributions differ, common when systems are deployed in practice. We show that when such a covariate shift occurs, correctly modeling uncertainty can keep us from giving overconfident and potentially harmful recommendations. We demonstrate our methodology with a range of state-of-the-art models. Under both covariate shift and lack of overlap, our uncertainty-equipped methods can alert decision makers when predictions are not to be trusted while outperforming standard methods that use the propensity score to identify lack of overlap.

Causal inference relies on two fundamental assumptions: ignorability and positivity. We study causal inference when the true confounder value can be expressed as a function of the observed data; we call this setting estimation with functional confounders (EFC). In this setting ignorability is satisfied, however positivity is violated, and causal inference is impossible in general. We consider two scenarios where causal effects are estimable. First, we discuss interventions on a part of the treatment called functional interventions and a sufficient condition for effect estimation of these interventions called functional positivity. Second, we develop conditions for nonparametric effect estimation based on the gradient fields of the functional confounder and the true outcome function. To estimate effects under these conditions, we develop Level-set Orthogonal Descent Estimation (LODE). Further, we prove error bounds on LODE’s effect estimates, evaluate our methods on simulated and real data, and empirically demonstrate the value of EFC.

Estimating counterfactual outcome of different treatments from observational data is an important problem to assist decision making in a variety of fields. Among the various forms of treatment specification, bundle treatment has been widely adopted in many scenarios, such as recommendation systems and online marketing. The bundle treatment usually can be abstracted as a high dimensional binary vector, which makes it more challenging for researchers to remove the confounding bias in observational data. In this work, we assume the existence of low dimensional latent structure underlying bundle treatment. Via the learned latent representations of treatments, we propose a novel variational sample re-weighting (VSR) method to eliminate confounding bias by decorrelating the treatments and confounders. Finally, we conduct extensive experiments to demonstrate that the predictive model trained on this re-weighted dataset can achieve more accurate counterfactual outcome prediction.

We develop an approach for estimating models described via conditional moment restrictions, with a prototypical application being non-parametric instrumental variable regression. We introduce a min-max criterion function, under which the estimation problem can be thought of as solving a zero-sum game between a modeler who is optimizing over the hypothesis space of the target model and an adversary who identifies violating moments over a test function space. We analyze the statistical estimation rate of the resulting estimator for arbitrary hypothesis spaces, with respect to an appropriate analogue of the mean squared error metric, for ill-posed inverse problems. We show that when the minimax criterion is regularized with a second moment penalty on the test function and the test function space is sufficiently rich, then the estimation rate scales with the critical radius of the hypothesis and test function spaces, a quantity which typically gives tight fast rates. Our main result follows from a novel localized Rademacher analysis of statistical learning problems defined via minimax objectives. We provide applications of our main results for several hypothesis spaces used in practice such as: reproducing kernel Hilbert spaces, high dimensional sparse linear functions, spaces defined via shape constraints, ensemble estimators such as random forests, and neural networks. For each of these applications we provide computationally efficient optimization methods for solving the corresponding minimax problem (e.g. stochastic first-order heuristics for neural networks). In several applications, we show how our modified mean squared error rate, combined with conditions that bound the ill-posedness of the inverse problem, lead to mean squared error rates. We conclude with an extensive experimental analysis of the proposed methods.

We consider the evaluation and training of a new policy for the evaluation data by using the historical data obtained from a different policy. The goal of off-policy evaluation (OPE) is to estimate the expected reward of a new policy over the evaluation data, and that of off-policy learning (OPL) is to find a new policy that maximizes the expected reward over the evaluation data. Although the standard OPE and OPL assume the same distribution of covariate between the historical and evaluation data, there often exists a problem of a covariate shift,i.e., the distribution of the covariate of the historical data is different from that of the evaluation data. In this paper, we derive the efficiency bound of OPE under a covariate shift. Then, we propose doubly robust and efficient estimators for OPE and OPL under a covariate shift by using an estimator of the density ratio between the distributions of the historical and evaluation data. We also discuss other possible estimators and compare their theoretical properties. Finally, we confirm the effectiveness of the proposed estimators through experiments.

It is a truth universally acknowledged that an observed association without known mechanism must be in want of a causal estimate. Causal estimates from observational data will be biased in the presence of ‘unobserved confounding’. However, we might hope that the influence of unobserved confounders is weak relative to a ‘large’ estimated effect. The purpose of this paper is to develop Austen plots, a sensitivity analysis tool to aid such judgments by making it easier to reason about potential bias induced by unobserved confounding. We formalize confounding strength in terms of how strongly the unobserved confounding influences treatment assignment and outcome. For a target level of bias, an Austen plot shows the minimum values of treatment and outcome influence required to induce that level of bias. Austen plots generalize the classic sensitivity analysis approach of Imbens [Imb03]. Critically, Austen plots allow any approach for modeling the observed data. We illustrate the tool by assessing biases for several real causal inference problems, using a variety of machine learning approaches for the initial data analysis. Code, demo data, and a tutorial are available at github.com/anishazaveri/austen_plots.

This paper studies the problem of learning the correlation structure of a set of intervention functions defined on the directed acyclic graph (DAG) of a causal model. This is useful when we are interested in jointly learning the causal effects of interventions on different subsets of variables in a DAG, which is common in field such as healthcare or operations research. We propose the first multi-task causal Gaussian process (GP) model, which we call DAG-GP, that allows for information sharing across continuous interventions and across experiments on different variables. DAG-GP accommodates different assumptions in terms of data availability and captures the correlation between functions lying in input spaces of different dimensionality via a well-defined integral operator. We give theoretical results detailing when and how the DAG-GP model can be formulated depending on the DAG. We test both the quality of its predictions and its calibrated uncertainties. Compared to single-task models, DAG-GP achieves the best fitting performance in a variety of real and synthetic settings. In addition, it helps to select optimal interventions faster than competing approaches when used within sequential decision making frameworks, like active learning or Bayesian optimization.

Shapley values underlie one of the most popular model-agnostic methods within explainable artificial intelligence. These values are designed to attribute the difference between a model's prediction and an average baseline to the different features used as input to the model. Being based on solid game-theoretic principles, Shapley values uniquely satisfy several desirable properties, which is why they are increasingly used to explain the predictions of possibly complex and highly non-linear machine learning models. Shapley values are well calibrated to a user’s intuition when features are independent, but may lead to undesirable, counterintuitive explanations when the independence assumption is violated.

In this paper, we propose a novel framework for computing Shapley values that generalizes recent work that aims to circumvent the independence assumption. By employing Pearl's do-calculus, we show how these `causal' Shapley values can be derived for general causal graphs without sacrificing any of their desirable properties. Moreover, causal Shapley values enable us to separate the contribution of direct and indirect effects. We provide a practical implementation for computing causal Shapley values based on causal chain graphs when only partial information is available and illustrate their utility on a real-world example.

Recent work has discussed the limitations of counterfactual explanations to recommend actions for algorithmic recourse, and argued for the need of taking causal relationships between features into consideration. Unfortunately, in practice, the true underlying structural causal model is generally unknown. In this work, we first show that it is impossible to guarantee recourse without access to the true structural equations. To address this limitation, we propose two probabilistic approaches to select optimal actions that achieve recourse with high probability given limited causal knowledge (e.g., only the causal graph). The first captures uncertainty over structural equations under additive Gaussian noise, and uses Bayesian model averaging to estimate the counterfactual distribution. The second removes any assumptions on the structural equations by instead computing the average effect of recourse actions on individuals similar to the person who seeks recourse, leading to a novel subpopulation-based interventional notion of recourse. We then derive a gradient-based procedure for selecting optimal recourse actions, and empirically show that the proposed approaches lead to more reliable recommendations under imperfect causal knowledge than non-probabilistic baselines.

Despite achieving tremendous success, existing deep learning models have exposed limitations in compositional generalization, the capability to learn compositional rules and apply them to unseen cases in a systematic manner. To tackle this issue, we propose the Neural-Symbolic Stack Machine (NeSS). It contains a neural network to generate traces, which are then executed by a symbolic stack machine enhanced with sequence manipulation operations. NeSS combines the expressive power of neural sequence models with the recursion supported by the symbolic stack machine. Without training supervision on execution traces, NeSS achieves 100% generalization performance in four domains: the SCAN benchmark of language-driven navigation tasks, the task of few-shot learning of compositional instructions, the compositional machine translation benchmark, and context-free grammar parsing tasks.

Human reasoning involves recognising common underlying principles across many examples. The by-products of such reasoning are invariants that capture patterns such as "if someone went somewhere then they are there", expressed using variables "someone" and "somewhere" instead of mentioning specific people or places. Humans learn what variables are and how to use them at a young age. This paper explores whether machines can also learn and use variables solely from examples without requiring human pre-engineering. We propose Unification Networks, an end-to-end differentiable neural network approach capable of lifting examples into invariants and using those invariants to solve a given task. The core characteristic of our architecture is soft unification between examples that enables the network to generalise parts of the input into variables, thereby learning invariants. We evaluate our approach on five datasets to demonstrate that learning invariants captures patterns in the data and can improve performance over baselines.

Disentangled representation learning has seen a surge in interest over recent times, generally focusing on new models which optimise one of many disparate disentanglement metrics. Symmetry Based Disentangled Representation learning introduced a robust mathematical framework that defined precisely what is meant by a ``linear disentangled representation''. This framework determined that such representations would depend on a particular decomposition of the symmetry group acting on the data, showing that actions would manifest through irreducible group representations acting on independent representational subspaces. Caselles-Dupré et al. [2019] subsequently proposed the first model to induce and demonstrate a linear disentangled representation in a VAE model. In this work we empirically show that linear disentangled representations are not generally present in standard VAE models and that they instead require altering the loss landscape to induce them. We proceed to show that such representations are a desirable property with regard to classical disentanglement metrics. Finally we propose a method to induce irreducible representations which forgoes the need for labelled action sequences, as was required by prior work. We explore a number of properties of this method, including the ability to learn from action sequences without knowledge of intermediate states and robustness under visual noise. We also demonstrate that it can successfully learn 4 independent symmetries directly from pixels.

Not all data in a typical training set help with generalization; some samples can be overly ambiguous or outrightly mislabeled. This paper introduces a new method to identify such samples and mitigate their impact when training neural networks. At the heart of our algorithm is the Area Under the Margin (AUM) statistic, which exploits differences in the training dynamics of clean and mislabeled samples. A simple procedure - adding an extra class populated with purposefully mislabeled threshold samples - learns a AUM upper bound that isolates mislabeled data. This approach consistently improves upon prior work on synthetic and real-world datasets. On the WebVision50 classification task our method removes 17% of training data, yielding a 1.6% (absolute) improvement in test error. On CIFAR100 removing 13% of the data leads to a 1.2% drop in error.

We investigate neural network representations from a probabilistic perspective. Specifically, we leverage Bayesian nonparametrics to construct models of neural activations in Convolutional Neural Networks (CNNs) and latent representations in Variational Autoencoders (VAEs). This allows us to formulate a tractable complexity measure for distributions of neural activations and to explore global structure of latent spaces learned by VAEs. We use this machinery to uncover how memorization and two common forms of regularization, i.e. dropout and input augmentation, influence representational complexity in CNNs. We demonstrate that networks that can exploit patterns in data learn vastly less complex representations than networks forced to memorize. We also show marked differences between effects of input augmentation and dropout, with the latter strongly depending on network width. Next, we investigate latent representations learned by standard $\beta$-VAEs and Maximum Mean Discrepancy (MMD) $\beta$-VAEs. We show that aggregated posterior in standard VAEs quickly collapses to the diagonal prior when regularization strength increases. MMD-VAEs, on the other hand, learn more complex posterior distributions, even with strong regularization. While this gives a richer sample space, MMD-VAEs do not exhibit independence of latent dimensions. Finally, we leverage our probabilistic models as an effective sampling strategy for latent codes, improving quality of samples in VAEs with rich posteriors.

Invariances to translations have imbued convolutional neural networks with powerful generalization properties. However, we often do not know a priori what invariances are present in the data, or to what extent a model should be invariant to a given augmentation. We show how to learn invariances by parameterizing a distribution over augmentations and optimizing the training loss simultaneously with respect to the network parameters and augmentation parameters. With this simple procedure we can recover the correct set and extent of invariances on image classification, regression, segmentation, and molecular property prediction from a large space of augmentations, on training data alone. We show our approach is competitive with methods that are specialized to each task with the appropriate hard-coded invariances, without providing any prior knowledge of which invariance is needed.

Symmetry transformations induce invariances and are a crucial building block of modern machine learning algorithms. In many complex domains, such as the chemical space, invariances can be observed, yet the corresponding symmetry transformation cannot be formulated analytically. We propose to learn the symmetry transformation with a model consisting of two latent subspaces, where the first subspace captures the target and the second subspace the remaining invariant information. Our approach is based on the deep information bottleneck in combination with a continuous mutual information regulariser. Unlike previous methods, we focus on the challenging task of minimising mutual information in continuous domains. To this end, we base the calculation of mutual information on correlation matrices in combination with a bijective variable transformation. Extensive experiments demonstrate that our model outperforms state-of-the-art methods on artificial and molecular datasets.

In this paper, we propose a new iterative hierarchical data augmentation (IHDA) method to fine-tune trained deep neural networks to improve their generalization performance. The IHDA is motivated by three key insights: (1) Deep networks (DNs) are good at learning multi-level representations from data. (2) Performing data augmentation (DA) in the learned feature spaces of DNs can significantly improve their performance. (3) Implementing DA in hard-to-learn regions of a feature space can effectively augment the dataset to improve generalization. Accordingly, the IHDA performs DA in a deep feature space, at level l, by transforming it into a distribution space and synthesizing new samples using the learned distributions for data points that lie in hard-to-classify regions, which is estimated by analyzing the neighborhood characteristics of each data point. The synthesized samples are used to fine-tune the parameters of the subsequent layers. The same procedure is then repeated for the feature space at level l+1. To avoid overfitting, the concept of dropout probability is employed, which is gradually relaxed as the IHDA works towards high-level feature spaces. IHDA provided a state-of-the-art performance on CIFAR-10, CIFAR-100, and ImageNet for several DNs, and beat the performance of existing state-of-the-art DA approaches for the same networks on these datasets. Finally, to demonstrate its domain-agnostic properties, we show the significant improvements that IHDA provided for a deep neural network on a non-image wearable sensor-based activity recognition benchmark.

We introduce Exemplar VAEs, a family of generative models that bridge the gap between parametric and non-parametric, exemplar based generative models. Exemplar VAE is a variant of VAE with a non-parametric latent prior based on a Parzen window estimator. To sample from it, one first draws a random exemplar from a training set, then stochastically transforms that exemplar into a latent code and a new observation. We propose retrieval augmented training (RAT) as a way to speed up Exemplar VAE training by using approximate nearest neighbor search in the latent space to define a lower bound on log marginal likelihood. To enhance generalization, model parameters are learned using exemplar leave-one-out and subsampling. Experiments demonstrate the effectiveness of Exemplar VAEs on density estimation and representation learning. Importantly, generative data augmentation using Exemplar VAEs on permutation invariant MNIST and Fashion MNIST reduces classification error from 1.17% to 0.69% and from 8.56% to 8.16%.

Despite recent advances, goal-directed generation of structured discrete data remains challenging. For problems such as program synthesis (generating source code) and materials design (generating molecules), finding examples which satisfy desired constraints or exhibit desired properties is difficult. In practice, expensive heuristic search or reinforcement learning algorithms are often employed. In this paper, we investigate the use of conditional generative models which directly attack this inverse problem, by modeling the distribution of discrete structures given properties of interest. Unfortunately, the maximum likelihood training of such models often fails with the samples from the generative model inadequately respecting the input properties. To address this, we introduce a novel approach to directly optimize a reinforcement learning objective, maximizing an expected reward. We avoid high-variance score-function estimators that would otherwise be required by sampling from an approximation to the normalized rewards, allowing simple Monte Carlo estimation of model gradients. We test our methodology on two tasks: generating molecules with user-defined properties and identifying short python expressions which evaluate to a given target value. In both cases, we find improvements over maximum likelihood estimation and other baselines.

We present a generative model for stroke-based drawing tasks which is able to model complex free-form structures. While previous approaches rely on sequence-based models for drawings of basic objects or handwritten text, we propose a model that treats drawings as a collection of strokes that can be composed into complex structures such as diagrams (e.g., flow-charts). At the core of the approach lies a novel auto-encoder that projects variable-length strokes into a latent space of fixed dimension. This representation space allows a relational model, operating in latent space, to better capture the relationship between strokes and to predict subsequent strokes. We demonstrate qualitatively and quantitatively that our proposed approach is able to model the appearance of individual strokes, as well as the compositional structure of larger diagram drawings. Our approach is suitable for interactive use cases such as auto-completing diagrams. We make code and models publicly available at https://eth-ait.github.io/cose.

We present a causal view on the robustness of neural networks against input manipulations, which applies not only to traditional classification tasks but also to general measurement data. Based on this view, we design a deep causal manipulation augmented model (deep CAMA) which explicitly models possible manipulations on certain causes leading to changes in the observed effect. We further develop data augmentation and test-time fine-tuning methods to improve deep CAMA's robustness. When compared with discriminative deep neural networks, our proposed model shows superior robustness against unseen manipulations. As a by-product, our model achieves disentangled representation which separates the representation of manipulations from those of other latent causes.

In many machine learning problems the output should not depend on the order of the inputs. Such ``permutation invariant'' functions have been studied extensively recently. Here we argue that temporal architectures such as RNNs are highly relevant for such problems, despite the inherent dependence of RNNs on order. We show that RNNs can be regularized towards permutation invariance, and that this can result in compact models, as compared to non-recursive architectures. Existing solutions (e.g., DeepSets) mostly suggest restricting the learning problem to hypothesis classes which are permutation invariant by design. Our approach of enforcing permutation invariance via regularization gives rise to learning functions which are "semi permutation invariant", e.g. invariant to some permutations and not to others. Our approach relies on a novel form of stochastic regularization. We demonstrate that our method is beneficial compared to existing permutation invariant methods on synthetic and real world datasets.

Recurrent Neural Networks (RNNs) have made great achievements for sequential prediction tasks. In practice, the target sequence often follows certain model properties or patterns (e.g., reasonable ranges, consecutive changes, resource constraint, temporal correlations between multiple variables, existence, unusual cases, etc.). However, RNNs cannot guarantee their learned distributions satisfy these model properties. It is even more challenging for predicting large-scale and complex Cyber-Physical Systems. Failure to produce outcomes that meet these model properties will result in inaccurate and even meaningless results. In this paper, we develop a new temporal logic-based learning framework, STLnet, which guides the RNN learning process with auxiliary knowledge of model properties, and produces a more robust model for improved future predictions. Our framework can be applied to general sequential deep learning models, and trained in an end-to-end manner with back-propagation. We evaluate the performance of STLnet using large-scale real-world city data. The experimental results show STLnet not only improves the accuracy of predictions, but importantly also guarantees the satisfaction of model properties and increases the robustness of RNNs.

We develop a method for generating causal post-hoc explanations of black-box classifiers based on a learned low-dimensional representation of the data. The explanation is causal in the sense that changing learned latent factors produces a change in the classifier output statistics. To construct these explanations, we design a learning framework that leverages a generative model and information-theoretic measures of causal influence. Our objective function encourages both the generative model to faithfully represent the data distribution and the latent factors to have a large causal influence on the classifier output. Our method learns both global and local explanations, is compatible with any classifier that admits class probabilities and a gradient, and does not require labeled attributes or knowledge of causal structure. Using carefully controlled test cases, we provide intuition that illuminates the function of our causal objective. We then demonstrate the practical utility of our method on image recognition tasks.

SATNet is an award-winning MAXSAT solver that can be used to infer logical rules and integrated as a differentiable layer in a deep neural network. It had been shown to solve Sudoku puzzles visually from examples of puzzle digit images, and was heralded as an impressive achievement towards the longstanding AI goal of combining pattern recognition with logical reasoning. In this paper, we clarify SATNet's capabilities by showing that in the absence of intermediate labels that identify individual Sudoku digit images with their logical representations, SATNet completely fails at visual Sudoku (0% test accuracy). More generally, the failure can be pinpointed to its inability to learn to assign symbols to perceptual phenomena, also known as the symbol grounding problem, which has long been thought to be a prerequisite for intelligent agents to perform real-world logical reasoning. We propose an MNIST based test as an easy instance of the symbol grounding problem that can serve as a sanity check for differentiable symbolic solvers in general. Naive applications of SATNet on this test lead to performance worse than that of models without logical reasoning capabilities. We report on the causes of SATNet’s failure and how to prevent them.

Adaptive gradient methods such as AdaGrad, RMSprop and Adam have been optimizers of choice for deep learning due to their fast training speed. However, it was recently observed that their generalization performance is often worse than that of SGD for over-parameterized neural networks. While new algorithms such as AdaBound, SWAT, and Padam were proposed to improve the situation, the provided analyses are only committed to optimization bounds for the training objective, leaving critical generalization capacity unexplored. To close this gap, we propose \textit{\textbf{S}table \textbf{A}daptive \textbf{G}radient \textbf{D}escent} (\textsc{SAGD}) for nonconvex optimization which leverages differential privacy to boost the generalization performance of adaptive gradient methods. Theoretical analyses show that \textsc{SAGD} has high-probability convergence to a population stationary point. We further conduct experiments on various popular deep learning tasks and models. Experimental results illustrate that \textsc{SAGD} is empirically competitive and often better than baselines.

Adam is a widely used optimization method for training deep learning models. It computes individual adaptive learning rates for different parameters. In this paper, we propose a generalization of Adam, called Adambs, that allows us to also adapt to different training examples based on their importance in the model's convergence. To achieve this, we maintain a distribution over all examples, selecting a mini-batch in each iteration by sampling according to this distribution, which we update using a multi-armed bandit algorithm. This ensures that examples that are more beneficial to the model training are sampled with higher probabilities. We theoretically show that Adambs improves the convergence rate of Adam---$O(\sqrt{\frac{\log n}{T} })$ instead of $O(\sqrt{\frac{n}{T}})$ in some cases. Experiments on various models and datasets demonstrate Adambs's fast convergence in practice.

Random Reshuffling (RR) is an algorithm for minimizing finite-sum functions that utilizes iterative gradient descent steps in conjunction with data reshuffling. Often contrasted with its sibling Stochastic Gradient Descent (SGD), RR is usually faster in practice and enjoys significant popularity in convex and non-convex optimization. The convergence rate of RR has attracted substantial attention recently and, for strongly convex and smooth functions, it was shown to converge faster than SGD if 1) the stepsize is small, 2) the gradients are bounded, and 3) the number of epochs is large. We remove these 3 assumptions, improve the dependence on the condition number from $\kappa^2$ to $\kappa$ (resp.\ from $\kappa$ to $\sqrt{\kappa}$) and, in addition, show that RR has a different type of variance. We argue through theory and experiments that the new variance type gives an additional justification of the superior performance of RR. To go beyond strong convexity, we present several results for non-strongly convex and non-convex objectives. We show that in all cases, our theory improves upon existing literature. Finally, we prove fast convergence of the Shuffle-Once (SO) algorithm, which shuffles the data only once, at the beginning of the optimization process. Our theory for strongly convex objectives tightly matches the known lower bounds for both RR and SO and substantiates the common practical heuristic of shuffling once or only a few times. As a byproduct of our analysis, we also get new results for the Incremental Gradient algorithm (IG), which does not shuffle the data at all.

Owing to their stability and convergence speed, extragradient methods have become a staple for solving large-scale saddle-point problems in machine learning. The basic premise of these algorithms is the use of an extrapolation step before performing an update; thanks to this exploration step, extra-gradient methods overcome many of the non-convergence issues that plague gradient descent/ascent schemes. On the other hand, as we show in this paper, running vanilla extragradient with stochastic gradients may jeopardize its convergence, even in simple bilinear models. To overcome this failure, we investigate a double stepsize extragradient algorithm where the exploration step evolves at a more aggressive time-scale compared to the update step. We show that this modification allows the method to converge even with stochastic gradients, and we derive sharp convergence rates under an error bound condition.

We propose a new methodology to design first-order methods for unconstrained strongly convex problems. Specifically, instead of tackling the original objective directly, we construct a shifted objective function that has the same minimizer as the original objective and encodes both the smoothness and strong convexity of the original objective in an interpolation condition. We then propose an algorithmic template for tackling the shifted objective, which can exploit such a condition. Following this template, we derive several new accelerated schemes for problems that are equipped with various first-order oracles and show that the interpolation condition allows us to vastly simplify and tighten the analysis of the derived methods. In particular, all the derived methods have faster worst-case convergence rates than their existing counterparts. Experiments on machine learning tasks are conducted to evaluate the new methods.

We introduce a generic \emph{two-loop} scheme for smooth minimax optimization with strongly-convex-concave objectives. Our approach applies the accelerated proximal point framework (or Catalyst) to the associated \emph{dual problem} and takes full advantage of existing gradient-based algorithms to solve a sequence of well-balanced strongly-convex-strongly-concave minimax problems. Despite its simplicity, this leads to a family of near-optimal algorithms with improved complexity over all existing methods designed for strongly-convex-concave minimax problems. Additionally, we obtain the first variance-reduced algorithms for this class of minimax problems with finite-sum structure and establish even faster convergence rate. Furthermore, when extended to the nonconvex-concave minimax optimization, our algorithm again achieves the state-of-the-art complexity for finding a stationary point. We carry out several numerical experiments showcasing the superiority of the Catalyst framework in practice.

Nonconvex minimax problems appear frequently in emerging machine learning applications, such as generative adversarial networks and adversarial learning. Simple algorithms such as the gradient descent ascent (GDA) are the common practice for solving these nonconvex games and receive lots of empirical success. Yet, it is known that these vanilla GDA algorithms with constant stepsize can potentially diverge even in the convex setting. In this work, we show that for a subclass of nonconvex-nonconcave objectives satisfying a so-called two-sided Polyak-{\L}ojasiewicz inequality, the alternating gradient descent ascent (AGDA) algorithm converges globally at a linear rate and the stochastic AGDA achieves a sublinear rate. We further develop a variance reduced algorithm that attains a provably faster rate than AGDA when the problem has the finite-sum structure.

In this paper, we analyze the trajectories of stochastic gradient descent (SGD) with the aim of understanding their convergence properties in non-convex problems. We first show that the sequence of iterates generated by SGD remains bounded and converges with probability $1$ under a very broad range of step-size schedules. Subsequently, we prove that the algorithm's rate of convergence to local minimizers with a positive-definite Hessian is $O(1/n^p)$ if the method is run with a $Θ(1/n^p)$ step-size. This provides an important guideline for tuning the algorithm's step-size as it suggests that a cool-down phase with a vanishing step-size could lead to significant performance gains; we demonstrate this heuristic using ResNet architectures on CIFAR. Finally, going beyond existing positive probability guarantees, we show that SGD avoids strict saddle points/manifolds with probability $1$ for the entire spectrum of step-size policies considered.

We develop a novel and single-loop variance-reduced algorithm to solve a class of stochastic nonconvex-convex minimax problems involving a nonconvex-linear objective function, which has various applications in different fields such as ma- chine learning and robust optimization. This problem class has several compu- tational challenges due to its nonsmoothness, nonconvexity, nonlinearity, and non-separability of the objective functions. Our approach relies on a new combi- nation of recent ideas, including smoothing and hybrid biased variance-reduced techniques. Our algorithm and its variants can achieve $\mathcal{O}(T^{-2/3})$-convergence rate and the best-known oracle complexity under standard assumptions, where T is the iteration counter. They have several computational advantages compared to exist- ing methods such as simple to implement and less parameter tuning requirements. They can also work with both single sample or mini-batch on derivative estimators, and with constant or diminishing step-sizes. We demonstrate the benefits of our algorithms over existing methods through two numerical examples, including a nonsmooth and nonconvex-non-strongly concave minimax model.

SGD with momentum (SGDM) has been widely applied in many machine learning tasks, and it is often applied with dynamic stepsizes and momentum weights tuned in a stagewise manner. Despite of its empirical advantage over SGD, the role of momentum is still unclear in general since previous analyses on SGDM either provide worse convergence bounds than those of SGD, or assume Lipschitz or quadratic objectives, which fail to hold in practice. Furthermore, the role of dynamic parameters has not been addressed. In this work, we show that SGDM converges as fast as SGD for smooth objectives under both strongly convex and nonconvex settings. We also prove that multistage strategy is beneficial for SGDM compared to using fixed parameters. Finally, we verify these theoretical claims by numerical experiments.

This work proposes a novel analysis of stochastic gradient descent (SGD) for non-convex and smooth optimization. Our analysis sheds light on the impact of the probability distribution of the gradient noise on the convergence rate of the norm of the gradient. In the case of sub-Gaussian and centered noise, we prove that, with probability $1-\delta$, the number of iterations to reach a precision $\varepsilon$ for the squared gradient norm is $O(\varepsilon^{-2}\ln(1/\delta))$. In the case of centered and integrable heavy-tailed noise, we show that, while the expectation of the iterates may be infinite, the squared gradient norm still converges with probability $1-\delta$ in $O(\varepsilon^{-p}\delta^{-q})$ iterations, where $p,q > 2$. This result shows that heavy-tailed noise on the gradient slows down the convergence of SGD without preventing it, proving that SGD is robust to gradient noise with unbounded variance, a setting of interest for Deep Learning. In addition, it indicates that choosing a step size proportional to $T^{-1/b}$ where $b$ is the tail-parameter of the noise and $T$ is the number of iterations leads to the best convergence rates. Both results are simple corollaries of a unified analysis using the novel concept of biased expectations, a simple and intuitive mathematical tool to obtain concentration inequalities. Using this concept, we propose a new quantity to measure the amount of noise added to the gradient, and discuss its value in multiple scenarios.

We consider the robust linear regression problem in the online setting where we have access to the data in a streaming manner, one data point after the other. More specifically, for a true parameter $ \theta^* $, we consider the corrupted Gaussian linear model $y = + \varepsilon + b$ where the adversarial noise $b$ can take any value with probability $\eta$ and equals zero otherwise. We consider this adversary to be oblivious (i.e., $b$ independent of the data) since this is the only contamination model under which consistency is possible. Current algorithms rely on having the whole data at hand in order to identify and remove the outliers. In contrast, we show in this work that stochastic gradient descent on the l1 loss converges to the true parameter vector at a $\tilde{O}( 1 / (1 - \eta)^2 n )$ rate which is independent of the values of the contaminated measurements. Our proof relies on the elegant smoothing of the l1 loss by the Gaussian data and a classical non-asymptotic analysis of Polyak-Ruppert averaged SGD. In addition, we provide experimental evidence of the efficiency of this simple and highly scalable algorithm.

In this paper, we propose a new accelerated stochastic first-order method called clipped-SSTM for smooth convex stochastic optimization with heavy-tailed distributed noise in stochastic gradients and derive the first high-probability complexity bounds for this method closing the gap in the theory of stochastic optimization with heavy-tailed noise. Our method is based on a special variant of accelerated Stochastic Gradient Descent (SGD) and clipping of stochastic gradients. We extend our method to the strongly convex case and prove new complexity bounds that outperform state-of-the-art results in this case. Finally, we extend our proof technique and derive the first non-trivial high-probability complexity bounds for SGD with clipping without light-tails assumption on the noise.

We propose and analyze algorithms for distributionally robust optimization of convex losses with conditional value at risk (CVaR) and $\chi^2$ divergence uncertainty sets. We prove that our algorithms require a number of gradient evaluations independent of training set size and number of parameters, making them suitable for large-scale applications. For $\chi^2$ uncertainty sets these are the first such guarantees in the literature, and for CVaR our guarantees scale linearly in the uncertainty level rather than quadratically as in previous work. We also provide lower bounds proving the worst-case optimality of our algorithms for CVaR and a penalized version of the $\chi^2$ problem. Our primary technical contributions are novel bounds on the bias of batch robust risk estimation and the variance of a multilevel Monte Carlo gradient estimator due to [Blanchet & Glynn, 2015]. Experiments on MNIST and ImageNet confirm the theoretical scaling of our algorithms, which are 9-36 times more efficient than full-batch methods.

We study the problem of least squares linear regression where the datapoints are dependent and are sampled from a Markov chain. We establish sharp information theoretic minimax lower bounds for this problem in terms of $\tmix$, the mixing time of the underlying Markov chain, under different noise settings. Our results establish that in general, optimization with Markovian data is strictly harder than optimization with independent data and a trivial algorithm (SGD-DD) that works with only one in every $\tmix$ samples, which are approximately independent, is minimax optimal. In fact, it is strictly better than the popular Stochastic Gradient Descent (SGD) method with constant step-size which is otherwise minimax optimal in the regression with independent data setting. Beyond a worst case analysis, we investigate whether structured datasets seen in practice such as Gaussian auto-regressive dynamics can admit more efficient optimization schemes. Surprisingly, even in this specific and natural setting, Stochastic Gradient Descent (SGD) with constant step-size is still no better than SGD-DD. Instead, we propose an algorithm based on experience replay--a popular reinforcement learning technique--that achieves a significantly better error rate. Our improved rate serves as one of the first results where an algorithm outperforms SGD-DD on an interesting Markov chain and also provides one of the first theoretical analyses to support the use of experience replay in practice.

We consider nonconvex-concave minimax optimization problems of the form $\min_{\bf x}\max_{\bf y\in{\mathcal Y}} f({\bf x},{\bf y})$, where $f$ is strongly-concave in $\bf y$ but possibly nonconvex in $\bf x$ and ${\mathcal Y}$ is a convex and compact set. We focus on the stochastic setting, where we can only access an unbiased stochastic gradient estimate of $f$ at each iteration. This formulation includes many machine learning applications as special cases such as robust optimization and adversary training. We are interested in finding an ${\mathcal O}(\varepsilon)$-stationary point of the function $\Phi(\cdot)=\max_{\bf y\in{\mathcal Y}} f(\cdot, {\bf y})$. The most popular algorithm to solve this problem is stochastic gradient decent ascent, which requires $\mathcal O(\kappa^3\varepsilon^{-4})$ stochastic gradient evaluations, where $\kappa$ is the condition number. In this paper, we propose a novel method called Stochastic Recursive gradiEnt Descent Ascent (SREDA), which estimates gradients more efficiently using variance reduction. This method achieves the best known stochastic gradient complexity of ${\mathcal O}(\kappa^3\varepsilon^{-3})$, and its dependency on $\varepsilon$ is optimal for this problem.

Community detection is a widely-studied unsupervised learning problem in which the task is to group similar entities together based on observed pairwise entity interactions. This problem has applications in diverse domains such as social network analysis and computational biology. There is a significant amount of literature studying this problem under the assumption that the communities do not overlap. When the communities are allowed to overlap, often a \textit{pure nodes} assumption is made, i.e. each community has a node that belongs exclusively to that community. This assumption, however, may not always be satisfied in practice. In this paper, we provide a provable method to detect overlapping communities in weighted graphs without explicitly making the pure nodes assumption. Moreover, contrary to most existing algorithms, our approach is based on convex optimization, for which many useful theoretical properties are already known. We demonstrate the success of our algorithm on artificial and real-world datasets.

We consider the problem of lossy image compression with deep latent variable models. State-of-the-art methods build on hierarchical variational autoencoders (VAEs) and learn inference networks to predict a compressible latent representation of each data point. Drawing on the variational inference perspective on compression, we identify three approximation gaps which limit performance in the conventional approach: an amortization gap, a discretization gap, and a marginalization gap. We propose remedies for each of these three limitations based on ideas related to iterative inference, stochastic annealing for discrete optimization, and bits-back coding, resulting in the first application of bits-back coding to lossy compression. In our experiments, which include extensive baseline comparisons and ablation studies, we achieve new state-of-the-art performance on lossy image compression using an established VAE architecture, by changing only the inference method.

Humans have an inherent ability to learn novel concepts from only a few samples and generalize these concepts to different situations. Even though today's machine learning models excel with a plethora of training data on standard recognition tasks, a considerable gap exists between machine-level pattern recognition and human-level concept learning. To narrow this gap, the Bongard problems (BPs) were introduced as an inspirational challenge for visual cognition in intelligent systems. Despite new advances in representation learning and learning to learn, BPs remain a daunting challenge for modern AI. Inspired by the original one hundred BPs, we propose a new benchmark Bongard-LOGO for human-level concept learning and reasoning. We develop a program-guided generation technique to produce a large set of human-interpretable visual cognition problems in action-oriented LOGO language. Our benchmark captures three core properties of human cognition: 1) context-dependent perception, in which the same object may have disparate interpretations given different contexts; 2) analogy-making perception, in which some meaningful concepts are traded off for other meaningful concepts; and 3) perception with a few samples but infinite vocabulary. In experiments, we show that the state-of-the-art deep learning methods perform substantially worse than human subjects, implying that they fail to capture core human cognition properties. Finally, we discuss research directions towards a general architecture for visual reasoning to tackle this benchmark.

Kernel methods provide an elegant and principled approach to nonparametric learning, but so far could hardly be used in large scale problems, since naïve implementations scale poorly with data size. Recent advances have shown the benefits of a number of algorithmic ideas, for example combining optimization, numerical linear algebra and random projections. Here, we push these efforts further to develop and test a solver that takes full advantage of GPU hardware. Towards this end, we designed a preconditioned gradient solver for kernel methods exploiting both GPU acceleration and parallelization with multiple GPUs, implementing out-of-core variants of common linear algebra operations to guarantee optimal hardware utilization. Further, we optimize the numerical precision of different operations and maximize efficiency of matrix-vector multiplications. As a result we can experimentally show dramatic speedups on datasets with billions of points, while still guaranteeing state of the art performance. Additionally, we make our software available as an easy to use library.

Signed networks are graphs where edges are annotated with a positive or negative sign, indicating whether an edge interaction is friendly or antagonistic. Signed networks can be used to study a variety of social phenomena, such as mining polarized discussions in social media, or modeling relations of trust and distrust in online review platforms. In this paper we study the problem of detecting $k$ conflicting groups in a signed network. Our premise is that each group is positively connected internally and negatively connected with the other $k-1$ groups. An important aspect of our formulation is that we are not searching for a complete partition of the signed network, instead, we allow other nodes to be neutral with respect to the conflict structure we are searching. As a result, the problem we tackle differs from previously studied problems, such as correlation clustering and $k$-way partitioning. To solve the conflicting-group discovery problem, we derive a novel formulation in which each conflicting group is naturally characterized by the solution to the maximum discrete Rayleigh's quotient (\maxdrq) problem. We present two spectral methods for finding approximate solutions to the \maxdrq problem, which we analyze theoretically. Our experimental evaluation shows that, compared to state-of-the-art baselines, our methods find solutions of higher quality, are faster, and recover ground truth conflicting groups with higher accuracy.

Given a combinatorial optimization problem taking an input, can we learn a strategy to solve it from the examples of input-solution pairs without knowing its objective function? In this paper, we consider such a setting and study the misinformation prevention problem. Given the examples of attacker-protector pairs, our goal is to learn a strategy to compute protectors against future attackers, without the need of knowing the underlying diffusion model. To this end, we design a structured prediction framework, where the main idea is to parameterize the scoring function using random features constructed through distance functions on randomly sampled subgraphs, which leads to a kernelized scoring function with weights learnable via the large margin method. Evidenced by experiments, our method can produce near-optimal protectors without using any information about the diffusion model, and it outperforms other possible graph-based and learning-based methods by an evident margin.

We study the problem of learning differentiable functions expressed as programs in a domain-specific language. Such programmatic models can offer benefits such as composability and interpretability; however, learning them requires optimizing over a combinatorial space of program "architectures". We frame this optimization problem as a search in a weighted graph whose paths encode top-down derivations of program syntax. Our key innovation is to view various classes of neural networks as continuous relaxations over the space of programs, which can then be used to complete any partial program. All the parameters of this relaxed program can be trained end-to-end, and the resulting training loss is an approximately admissible heuristic that can guide the combinatorial search. We instantiate our approach on top of the A* and Iterative Deepening Depth-First Search algorithms and use these algorithms to learn programmatic classifiers in three sequence classification tasks. Our experiments show that the algorithms outperform state-of-the-art methods for program learning, and that they discover programmatic classifiers that yield natural interpretations and achieve competitive accuracy.

A significant effort has been made to train neural networks that replicate algorithmic reasoning, but they often fail to learn the abstract concepts underlying these algorithms. This is evidenced by their inability to generalize to data distributions that are outside of their restricted training sets, namely larger inputs and unseen data. We study these generalization issues at the level of numerical subroutines that comprise common algorithms like sorting, shortest paths, and minimum spanning trees. First, we observe that transformer-based sequence-to-sequence models can learn subroutines like sorting a list of numbers, but their performance rapidly degrades as the length of lists grows beyond those found in the training set. We demonstrate that this is due to attention weights that lose fidelity with longer sequences, particularly when the input numbers are numerically similar. To address the issue, we propose a learned conditional masking mechanism, which enables the model to strongly generalize far outside of its training range with near-perfect accuracy on a variety of algorithms. Second, to generalize to unseen data, we show that encoding numbers with a binary representation leads to embeddings with rich structure once trained on downstream tasks like addition or multiplication. This allows the embedding to handle missing data by faithfully interpolating numbers not seen during training.

Compositional generalization is a key challenge in grounding natural language to visual perception. While deep learning models have achieved great success in multimodal tasks like visual question answering, recent studies have shown that they fail to generalize to new inputs that are simply an unseen combination of those seen in the training distribution. In this paper, we propose to tackle this challenge by employing neural factor graphs to induce a tighter coupling between concepts in different modalities (e.g. images and text). Graph representations are inherently compositional in nature and allow us to capture entities, attributes and relations in a scalable manner. Our model first creates a multimodal graph, processes it with a graph neural network to induce a factor correspondence matrix, and then outputs a symbolic program to predict answers to questions. Empirically, our model achieves close to perfect scores on a caption truth prediction problem and state-of-the-art results on the recently introduced CLOSURE dataset, improving on the mean overall accuracy across seven compositional templates by 4.77\% over previous approaches.

Offline methods for reinforcement learning have a potential to help bridge the gap between reinforcement learning research and real-world applications. They make it possible to learn policies from offline datasets, thus overcoming concerns associated with online data collection in the real-world, including cost, safety, or ethical concerns. In this paper, we propose a benchmark called RL Unplugged to evaluate and compare offline RL methods. RL Unplugged includes data from a diverse range of domains including games e.g., Atari benchmark) and simulated motor control problems (e.g., DM Control Suite). The datasets include domains that are partially or fully observable, use continuous or discrete actions, and have stochastic vs. deterministic dynamics. We propose detailed evaluation protocols for each domain in RL Unplugged and provide an extensive analysis of supervised learning and offline RL methods using these protocols. We will release data for all our tasks and open-source all algorithms presented in this paper. We hope that our suite of benchmarks will increase the reproducibility of experiments and make it possible to study challenging tasks with a limited computational budget, thus making RL research both more systematic and more accessible across the community. Moving forward, we view RL Unplugged as a living benchmark suite that will evolve and grow with datasets contributed by the research community and ourselves. Our project page is available on github.

Modern deep learning approaches have shown promising results in meteorological applications like precipitation nowcasting, synthetic radar generation, front detection and several others. In order to effectively train and validate these complex algorithms, large and diverse datasets containing high-resolution imagery are required. Petabytes of weather data, such as from the Geostationary Environmental Satellite System (GOES) and the Next-Generation Radar (NEXRAD) system, are available to the public; however, the size and complexity of these datasets is a hindrance to developing and training deep models. To help address this problem, we introduce the Storm EVent ImagRy (SEVIR) dataset - a single, rich dataset that combines spatially and temporally aligned data from multiple sensors, along with baseline implementations of deep learning models and evaluation metrics, to accelerate new algorithmic innovations. SEVIR is an annotated, curated and spatio-temporally aligned dataset containing over 10,000 weather events that each consist of 384 km x 384 km image sequences spanning 4 hours of time. Images in SEVIR were sampled and aligned across five different data types: three channels (C02, C09, C13) from the GOES-16 advanced baseline imager, NEXRAD vertically integrated liquid mosaics, and GOES-16 Geostationary Lightning Mapper (GLM) flashes. Many events in SEVIR were selected and matched to the NOAA Storm Events database so that additional descriptive information such as storm impacts and storm descriptions can be linked to the rich imagery provided by the sensors. We describe the data collection methodology and illustrate the applications of this dataset with two examples of deep learning in meteorology: precipitation nowcasting and synthetic weather radar generation. In addition, we also describe a set of metrics that can be used to evaluate the outputs of these models. The SEVIR dataset and baseline implementations of selected applications are available for download.

Applying differentiable programming techniques and machine learning algorithms to foreign programs requires developers to either rewrite their code in a machine learning framework, or otherwise provide derivatives of the foreign code. This paper presents Enzyme, a high-performance automatic differentiation (AD) compiler plugin for the LLVM compiler framework capable of synthesizing gradients of statically analyzable programs expressed in the LLVM intermediate representation (IR). Enzyme synthesizes gradients for programs written in any language whose compiler targets LLVM IR including C, C++, Fortran, Julia, Rust, Swift, MLIR, etc., thereby providing native AD capabilities in these languages. Unlike traditional source-to-source and operator-overloading tools, Enzyme performs AD on optimized IR. On a machine-learning focused benchmark suite including Microsoft's ADBench, AD on optimized IR achieves a geometric mean speedup of 4.2 times over AD on IR before optimization allowing Enzyme to achieve state-of-the-art performance. Packaging Enzyme for PyTorch and TensorFlow provides convenient access to gradients of foreign code with state-of-the-art performance, enabling foreign code to be directly incorporated into existing machine learning workflows.

Geometric methods rely on tensors that can be encoded using a symbolic formula and data arrays, such as kernel and distance matrices. We present an extension for standard machine learning frameworks that provides comprehensive support for this abstraction on CPUs and GPUs: our toolbox combines a versatile, transparent user interface with fast runtimes and low memory usage. Unlike general purpose acceleration frameworks such as XLA, our library turns generic Python code into binaries whose performances are competitive with state-of-the-art geometric libraries - such as FAISS for nearest neighbor search - with the added benefit of flexibility. We perform an extensive evaluation on a broad class of problems: Gaussian modelling, K-nearest neighbors search, geometric deep learning, non-Euclidean embeddings and optimal transport theory. In practice, for geometric problems that involve 1k to 1M samples in dimension 1 to 100, our library speeds up baseline GPU implementations by up to two orders of magnitude.

Progress in the field of machine learning has been fueled by the introduction of benchmark datasets pushing the limits of existing algorithms. Enabling the design of datasets to test specific properties and failure modes of learning algorithms is thus a problem of high interest, as it has a direct impact on innovation in the field. In this sense, we introduce Synbols — Synthetic Symbols — a tool for rapidly generating new datasets with a rich composition of latent features rendered in low resolution images. Synbols leverages the large amount of symbols available in the Unicode standard and the wide range of artistic font provided by the open font community. Our tool's high-level interface provides a language for rapidly generating new distributions on the latent features, including various types of textures and occlusions. To showcase the versatility of Synbols, we use it to dissect the limitations and flaws in standard learning algorithms in various learning setups including supervised learning, active learning, out of distribution generalization, unsupervised representation learning, and object counting.

Interpretability of machine learning models is critical to scientific understanding, AI safety, as well as debugging. Attribution is one approach to interpretability, which highlights input dimensions that are influential to a neural network’s prediction. Evaluation of these methods is largely qualitative for image and text models, because acquiring ground truth attributions requires expensive and unreliable human judgment. Attribution has been little studied for graph neural networks (GNNs), a model class of growing importance that makes predictions on arbitrarily-sized graphs. In this work we adapt commonly-used attribution methods for GNNs and quantitatively evaluate them using computable ground-truths that are objective and challenging to learn. We make concrete recommendations for which attribution methods to use, and provide the data and code for our benchmarking suite. Rigorous and open source benchmarking of attribution methods in graphs could enable new methods development and broader use of attribution in real-world ML tasks.

We introduce CuLE (CUDA Learning Environment), a CUDA port of the Atari Learning Environment (ALE) which is used for the development of deep reinforcement algorithms. CuLE overcomes many limitations of existing CPU-based emulators and scales naturally to multiple GPUs. It leverages GPU parallelization to run thousands of games simultaneously and it renders frames directly on the GPU, to avoid the bottleneck arising from the limited CPU-GPU communication bandwidth. CuLE generates up to 155M frames per hour on a single GPU, a finding previously achieved only through a cluster of CPUs. Beyond highlighting the differences between CPU and GPU emulators in the context of reinforcement learning, we show how to leverage the high throughput of CuLE by effective batching of the training data, and show accelerated convergence for A2C+V-trace. CuLE is available at https://github.com/NVlabs/cule.

Many communication-efficient variants of SGD use gradient quantization schemes. These schemes are often heuristic and fixed over the course of training. We empirically observe that the statistics of gradients of deep models change during the training. Motivated by this observation, we introduce two adaptive quantization schemes, ALQ and AMQ. In both schemes, processors update their compression schemes in parallel by efficiently computing sufficient statistics of a parametric distribution. We improve the validation accuracy by almost 2% on CIFAR-10 and 1% on ImageNet in challenging low-cost communication setups. Our adaptive methods are also significantly more robust to the choice of hyperparameters.

A popular approach to learning encoders for lossy compression is to use additive uniform noise during training as a differentiable approximation to test-time quantization. We demonstrate that a uniform noise channel can also be implemented at test time using universal quantization (Ziv, 1985). This allows us to eliminate the mismatch between training and test phases while maintaining a completely differentiable loss function. Implementing the uniform noise channel is a special case of the more general problem of communicating a sample, which we prove is computationally hard if we do not make assumptions about its distribution. However, the uniform special case is efficient as well as easy to implement and thus of great interest from a practical point of view. Finally, we show that quantization can be obtained as a limiting case of a soft quantizer applied to the uniform noise channel, bridging compression with and without quantization.

Quantized neural networks with low-bit weights and activations are attractive for developing AI accelerators. However, the quantization functions used in most conventional quantization methods are non-differentiable, which increases the optimization difficulty of quantized networks. Compared with full-precision parameters (\emph{i.e.}, 32-bit floating numbers), low-bit values are selected from a much smaller set. For example, there are only 16 possibilities in 4-bit space. Thus, we present to regard the discrete weights in an arbitrary quantized neural network as searchable variables, and utilize a differential method to search them accurately. In particular, each weight is represented as a probability distribution over the discrete value set. The probabilities are optimized during training and the values with the highest probability are selected to establish the desired quantized network. Experimental results on benchmarks demonstrate that the proposed method is able to produce quantized neural networks with higher performance over the state-of-the-arts on both image classification and super-resolution tasks.

We introduce Bayesian Bits, a practical method for joint mixed precision quantization and pruning through gradient based optimization. Bayesian Bits employs a novel decomposition of the quantization operation, which sequentially considers doubling the bit width. At each new bit width, the residual error between the full precision value and the previously rounded value is quantized. We then decide whether or not to add this quantized residual error for a higher effective bit width and lower quantization noise. By starting with a power-of-two bit width, this decomposition will always produce hardware-friendly configurations, and through an additional 0-bit option, serves as a unified view of pruning and quantization. Bayesian Bits then introduces learnable stochastic gates, which collectively control the bit width of the given tensor. As a result, we can obtain low bit solutions by performing approximate inference over the gates, with prior distributions that encourage most of them to be switched off. We experimentally validate our proposed method on several benchmark datasets and show that we can learn pruned, mixed precision networks that provide a better trade-off between accuracy and efficiency than their static bit width equivalents.

Quantization based on the binary codes is gaining attention because each quantized bit can be directly utilized for computations without dequantization using look-up tables. Previous attempts, however, only allow for integer numbers of quantization bits, which ends up restricting the search space for compression ratio and accuracy. In this paper, we propose an encryption algorithm/architecture to compress quantized weights so as to achieve fractional numbers of bits per weight. Decryption during inference is implemented by digital XOR-gate networks added into the neural network model while XOR gates are described by utilizing $\tanh(x)$ for backward propagation to enable gradient calculations. We perform experiments using MNIST, CIFAR-10, and ImageNet to show that inserting XOR gates learns quantization/encrypted bit decisions through training and obtains high accuracy even for fractional sub 1-bit weights. As a result, our proposed method yields smaller size and higher model accuracy compared to binary neural networks.

Neural network quantization methods often involve simulating the quantization process during training, making the trained model highly dependent on the target bit-width and precise way quantization is performed. Robust quantization offers an alternative approach with improved tolerance to different classes of data-types and quantization policies. It opens up new exciting applications where the quantization process is not static and can vary to meet different circumstances and implementations. To address this issue, we propose a method that provides intrinsic robustness to the model against a broad range of quantization processes. Our method is motivated by theoretical arguments and enables us to store a single generic model capable of operating at various bit-widths and quantization policies. We validate our method's effectiveness on different ImageNet Models. A reference implementation accompanies the paper.

Fully quantized training (FQT), which uses low-bitwidth hardware by quantizing the activations, weights, and gradients of a neural network model, is a promising approach to accelerate the training of deep neural networks. One major challenge with FQT is the lack of theoretical understanding, in particular of how gradient quantization impacts convergence properties. In this paper, we address this problem by presenting a statistical framework for analyzing FQT algorithms. We view the quantized gradient of FQT as a stochastic estimator of its full precision counterpart, a procedure known as quantization-aware training (QAT). We show that the FQT gradient is an unbiased estimator of the QAT gradient, and we discuss the impact of gradient quantization on its variance. Inspired by these theoretical results, we develop two novel gradient quantizers, and we show that these have smaller variance than the existing per-tensor quantizer. For training ResNet-50 on ImageNet, our 5-bit block Householder quantizer achieves only 0.5% validation accuracy loss relative to QAT, comparable to the existing INT8 baseline.

The Gumbel-Softmax is a continuous distribution over the simplex that is often used as a relaxation of discrete distributions. Because it can be readily interpreted and easily reparameterized, it enjoys widespread use. We propose a modular and more flexible family of reparameterizable distributions where Gaussian noise is transformed into a one-hot approximation through an invertible function. This invertible function is composed of a modified softmax and can incorporate diverse transformations that serve different specific purposes. For example, the stick-breaking procedure allows us to extend the reparameterization trick to distributions with countably infinite support, thus enabling the use of our distribution along nonparametric models, or normalizing flows let us increase the flexibility of the distribution. Our construction enjoys theoretical advantages over the Gumbel-Softmax, such as closed form KL, and significantly outperforms it in a variety of experiments. Our code is available at https://github.com/cunningham-lab/igr.

Training models with discrete latent variables is challenging due to the difficulty of estimating the gradients accurately. Much of the recent progress has been achieved by taking advantage of continuous relaxations of the system, which are not always available or even possible. The Augment-REINFORCE-Merge (ARM) estimator provides an alternative that, instead of relaxation, uses continuous augmentation. Applying antithetic sampling over the augmenting variables yields a relatively low-variance and unbiased estimator applicable to any model with binary latent variables. However, while antithetic sampling reduces variance, the augmentation process increases variance. We show that ARM can be improved by analytically integrating out the randomness introduced by the augmentation process, guaranteeing substantial variance reduction. Our estimator, DisARM, is simple to implement and has the same computational cost as ARM. We evaluate DisARM on several generative modeling benchmarks and show that it consistently outperforms ARM and a strong independent sample baseline in terms of both variance and log-likelihood. Furthermore, we propose a local version of DisARM designed for optimizing the multi-sample variational bound, and show that it outperforms VIMCO, the current state-of-the-art method.

Probabilistic inference in pairwise Markov Random Fields (MRFs), i.e. computing the partition function or computing a MAP estimate of the variables, is a foundational problem in probabilistic graphical models. Semidefinite programming relaxations have long been a theoretically powerful tool for analyzing properties of probabilistic inference, but have not been practical owing to the high computational cost of typical solvers for solving the resulting SDPs. In this paper, we propose an efficient method for computing the partition function or MAP estimate in a pairwise MRF by instead exploiting a recently proposed coordinate-descent-based fast semidefinite solver. We also extend semidefinite relaxations from the typical binary MRF to the full multi-class setting, and develop a compact semidefinite relaxation that can again be solved efficiently using the solver. We show that the method substantially outperforms (both in terms of solution quality and speed) the existing state of the art in approximate inference, on benchmark problems drawn from previous work. We also show that our approach can scale to large MRF domains such as fully-connected pairwise CRF models used in computer vision.

The Gumbel-Max trick is the basis of many relaxed gradient estimators. These estimators are easy to implement and low variance, but the goal of scaling them comprehensively to large combinatorial distributions is still outstanding. Working within the perturbation model framework, we introduce stochastic softmax tricks, which generalize the Gumbel-Softmax trick to combinatorial spaces. Our framework is a unified perspective on existing relaxed estimators for perturbation models, and it contains many novel relaxations. We design structured relaxations for subset selection, spanning trees, arborescences, and others. When compared to less structured baselines, we find that stochastic softmax tricks can be used to train latent variable models that perform better and discover more latent structure.

We present Quantized Variational Inference, a new algorithm for Evidence Lower Bound minimization. We show how Optimal Voronoi Tesselation produces variance free gradients for Evidence Lower Bound (ELBO) optimization at the cost of introducing asymptotically decaying bias. Subsequently, we propose a Richardson extrapolation type method to improve this bound. We show that using the Quantized Variational Inference framework leads to fast convergence for both score function and the reparametrized gradient estimator at a comparable computational cost. Finally, we propose several experiments to assess the performance of our method and its limitations.

Flexible variational distributions improve variational inference but are harder to optimize. In this work we present a control variate that is applicable for any reparameterizable distribution with known mean and covariance, e.g. Gaussians with any covariance structure. The control variate is based on a quadratic approximation of the model, and its parameters are set using a double-descent scheme. We empirically show that this control variate leads to large improvements in gradient variance and optimization convergence for inference with non-factorized variational distributions.

We analyse the properties of an unbiased gradient estimator of the ELBO for variational inference, based on the score function method with leave-one-out control variates. We show that this gradient estimator can be obtained using a new loss, defined as the variance of the log-ratio between the exact posterior and the variational approximation, which we call the log-variance loss. Under certain conditions, the gradient of the log-variance loss equals the gradient of the (negative) ELBO. We show theoretically that this gradient estimator, which we call VarGrad due to its connection to the log-variance loss, exhibits lower variance than the score function method in certain settings, and that the leave-one-out control variate coefficients are close to the optimal ones. We empirically demonstrate that VarGrad offers a favourable variance versus computation trade-off compared to other state-of-the-art estimators on a discrete VAE.

This paper introduces novel results for the score-function gradient estimator of the importance-weighted variational bound (IWAE). We prove that in the limit of large $K$ (number of importance samples) one can choose the control variate such that the Signal-to-Noise ratio (SNR) of the estimator grows as $\sqrt{K}$. This is in contrast to the standard pathwise gradient estimator where the SNR decreases as $1/\sqrt{K}$. Based on our theoretical findings we develop a novel control variate that extends on VIMCO. Empirically, for the training of both continuous and discrete generative models, the proposed method yields superior variance reduction, resulting in an SNR for IWAE that increases with $K$ without relying on the reparameterization trick. The novel estimator is competitive with state-of-the-art reparameterization-free gradient estimators such as Reweighted Wake-Sleep (RWS) and the thermodynamic variational objective (TVO) when training generative models.

Hybrid Privacy-Preserving Neural Network (HPPNN) implementing linear layers by Homomorphic Encryption (HE) and nonlinear layers by Garbled Circuit (GC) is one of the most promising secure solutions to emerging Machine Learning as a Service (MLaaS). Unfortunately, a HPPNN suffers from long inference latency, e.g., $\sim100$ seconds per image, which makes MLaaS unsatisfactory. Because HE-based linear layers of a HPPNN cost $93\%$ inference latency, it is critical to select a set of HE parameters to minimize computational overhead of linear layers. Prior HPPNNs over-pessimistically select huge HE parameters to maintain large noise budgets, since they use the same set of HE parameters for an entire network and ignore the error tolerance capability of a network. In this paper, for fast and accurate secure neural network inference, we propose an automated layer-wise parameter selector, AutoPrivacy, that leverages deep reinforcement learning to automatically determine a set of HE parameters for each linear layer in a HPPNN. The learning-based HE parameter selection policy outperforms conventional rule-based HE parameter selection policy. Compared to prior HPPNNs, AutoPrivacy-optimized HPPNNs reduce inference latency by $53\%\sim70\%$ with negligible loss of accuracy.

The theory of discrete-time online learning has been successfully applied in many problems that involve sequential decision-making under uncertainty. However, in many applications including contractual hiring in online freelancing platforms and server allocation in cloud computing systems, the outcome of each action is observed only after a random and action-dependent time. Furthermore, as a consequence of certain ethical and economic concerns, the controller may impose deadlines on the completion of each task, and require fairness across different groups in the allocation of total time budget $B$. In order to address these applications, we consider continuous-time online learning problem with fairness considerations, and present a novel framework based on continuous-time utility maximization. We show that this formulation recovers reward-maximizing, max-min fair and proportionally fair allocation rules across different groups as special cases. We characterize the optimal offline policy, which allocates the total time between different actions in an optimally fair way (as defined by the utility function), and impose deadlines to maximize time-efficiency. In the absence of any statistical knowledge, we propose a novel online learning algorithm based on dual ascent optimization for time averages, and prove that it achieves $\tilde{O}(B^{-1/2})$ regret bound.

As machine learning has become more prevalent, researchers have begun to recognize the necessity of ensuring machine learning systems are fair. Recently, there has been an interest in defining a notion of fairness that mitigates over-representation in traditional clustering.

In this paper we extend this notion to hierarchical clustering, where the goal is to recursively partition the data to optimize a specific objective. For various natural objectives, we obtain simple, efficient algorithms to find a provably good fair hierarchical clustering. Empirically, we show that our algorithms can find a fair hierarchical clustering, with only a negligible loss in the objective.

In machine learning applications such as ranking fairness or fairness over intersectional groups, one often encounters optimization problems with an extremely large number of constraints. In particular, with ranking fairness tasks, there may even be a variable number of constraints, e.g. one for each query in the training set. In these cases, the standard approach of optimizing a Lagrangian while maintaining one Lagrange multiplier per constraint may no longer be practical. Our proposal is to associate a feature vector with each constraint, and to learn a ``multiplier model’’ that maps each such vector to the corresponding Lagrange multiplier. We prove optimality, approximate feasibility and generalization guarantees under assumptions on the flexibility of the multiplier model, and empirically demonstrate that our method is effective on real-world case studies.

We study an online learning problem subject to the constraint of individual fairness, which requires that similar individuals are treated similarly. Unlike prior work on individual fairness, we do not assume the similarity measure among individuals is known, nor do we assume that such measure takes a certain parametric form. Instead, we leverage the existence of an auditor who detects fairness violations without enunciating the quantitative measure. In each round, the auditor examines the learner's decisions and attempts to identify a pair of individuals that are treated unfairly by the learner. We provide a general reduction framework that reduces online classification in our model to standard online classification, which allows us to leverage existing online learning algorithms to achieve sub-linear regret and number of fairness violations. Surprisingly, in the stochastic setting where the data are drawn independently from a distribution, we are also able to establish PAC-style fairness and accuracy generalization guarantees (Rothblum and Yona (2018)), despite only having access to a very restricted form of fairness feedback. Our fairness generalization bound qualitatively matches the uniform convergence bound of Rothblum and Yona (2018), while also providing a meaningful accuracy generalization guarantee. Our results resolve an open question by Gillen et al. (2018) by showing that online learning under an unknown individual fairness constraint is possible even without assuming a strong parametric form of the underlying similarity measure.

We study the problem of learning an optimal regression function subject to a fairness constraint. It requires that, conditionally on the sensitive feature, the distribution of the function output remains the same. This constraint naturally extends the notion of demographic parity, often used in classification, to the regression setting. We tackle this problem by leveraging on a proxy-discretized version, for which we derive an explicit expression of the optimal fair predictor. This result naturally suggests a two stage approach, in which we first estimate the (unconstrained) regression function from a set of labeled data and then we recalibrate it with another set of unlabeled data. The recalibration step can be efficiently performed via a smooth optimization. We derive rates of convergence of the proposed estimator to the optimal fair predictor both in terms of the risk and fairness constraint. Finally, we present numerical experiments illustrating that the proposed method is often superior or competitive with state-of-the-art methods.

Previous research in fair classification mostly focuses on a single decision model. In reality, there usually exist multiple decision models within a system and all of which may contain a certain amount of discrimination. Such realistic scenarios introduce new challenges to fair classification: since discrimination may be transmitted from upstream models to downstream models, building decision models separately without taking upstream models into consideration cannot guarantee to achieve fairness. In this paper, we propose an approach that learns multiple classifiers and achieves fairness for all of them simultaneously, by treating each decision model as a soft intervention and inferring the post-intervention distributions to formulate the loss function as well as the fairness constraints. We adopt surrogate functions to smooth the loss function and constraints, and theoretically show that the excess risk of the proposed loss function can be bounded in a form that is the same as that for traditional surrogated loss functions. Experiments using both synthetic and real-world datasets show the effectiveness of our approach.

As deep learning models become tasked with more and more decisions that impact human lives, such as criminal recidivism, loan repayment, and face recognition for law enforcement, bias is becoming a growing concern. Debiasing algorithms are typically split into three paradigms: pre-processing, in-processing, and post-processing. However, in computer vision or natural language applications, it is common to start with a large generic model and then fine-tune to a specific use-case. Pre- or in-processing methods would require retraining the entire model from scratch, while post-processing methods only have black-box access to the model, so they do not leverage the weights of the trained model. Creating debiasing algorithms specifically for this fine-tuning use-case has largely been neglected.

In this work, we initiate the study of a new paradigm in debiasing research, intra-processing, which sits between in-processing and post-processing methods. Intra-processing methods are designed specifically to debias large models which have been trained on a generic dataset, and fine-tuned on a more specific task. We show how to repurpose existing in-processing methods for this use-case, and we also propose three baseline algorithms: random perturbation, layerwise optimization, and adversarial debiasing. We evaluate these methods across three popular datasets from the AIF360 toolkit, as well as on the CelebA faces dataset. Our code is available at https://github.com/abacusai/intraprocessing_debiasing.

We initiate the study of fair classifiers that are robust to perturbations in the training distribution. Despite recent progress, the literature on fairness has largely ignored the design of fair and robust classifiers. In this work, we develop classifiers that are fair not only with respect to the training distribution but also for a class of distributions that are weighted perturbations of the training samples. We formulate a min-max objective function whose goal is to minimize a distributionally robust training loss, and at the same time, find a classifier that is fair with respect to a class of distributions. We first reduce this problem to finding a fair classifier that is robust with respect to the class of distributions. Based on an online learning algorithm, we develop an iterative algorithm that provably converges to such a fair and robust solution. Experiments on standard machine learning fairness datasets suggest that, compared to the state-of-the-art fair classifiers, our classifier retains fairness guarantees and test accuracy for a large class of perturbations on the test set. Furthermore, our experiments show that there is an inherent trade-off between fairness robustness and accuracy of such classifiers.

What is a fair performance metric? We consider the choice of fairness metrics through the lens of metric elicitation -- a principled framework for selecting performance metrics that best reflect implicit preferences. The use of metric elicitation enables a practitioner to tune the performance and fairness metrics to the task, context, and population at hand. Specifically, we propose a novel strategy to elicit group-fair performance metrics for multiclass classification problems with multiple sensitive groups that also includes selecting the trade-off between predictive performance and fairness violation. The proposed elicitation strategy requires only relative preference feedback and is robust to both finite sample and feedback noise.

Much of the previous machine learning (ML) fairness literature assumes that protected features such as race and sex are present in the dataset, and relies upon them to mitigate fairness concerns. However, in practice factors like privacy and regulation often preclude the collection of protected features, or their use for training or inference, severely limiting the applicability of traditional fairness research. Therefore, we ask: How can we train a ML model to improve fairness when we do not even know the protected group memberships? In this work we address this problem by proposing Adversarially Reweighted Learning (ARL). In particular, we hypothesize that non-protected features and task labels are valuable for identifying fairness issues, and can be used to co-train an adversarial reweighting approach for improving fairness. Our results show that ARL improves Rawlsian Max-Min fairness, with notable AUC improvements for worst-case protected groups in multiple datasets, outperforming state-of-the-art alternatives.

Developing learning methods which do not discriminate subgroups in the population is a central goal of algorithmic fairness. One way to reach this goal is by modifying the data representation in order to meet certain fairness constraints. In this work we measure fairness according to demographic parity. This requires the probability of the possible model decisions to be independent of the sensitive information. We argue that the goal of imposing demographic parity can be substantially facilitated within a multitask learning setting. We present a method for learning a shared fair representation across multiple tasks, by means of different new constraints based on MMD and Sinkhorn Divergences. We derive learning bounds establishing that the learned representation transfers well to novel tasks. We present experiments on three real world datasets, showing that the proposed method outperforms state-of-the-art approaches by a significant margin.

Although many fairness criteria have been proposed for decision making, their long-term impact on the well-being of a population remains unclear. In this work, we study the dynamics of population qualification and algorithmic decisions under a partially observed Markov decision problem setting. By characterizing the equilibrium of such dynamics, we analyze the long-term impact of static fairness constraints on the equality and improvement of group well-being. Our results show that static fairness constraints can either promote equality or exacerbate disparity depending on the driving factor of qualification transitions and the effect of sensitive attributes on feature distributions. We also consider possible interventions that can effectively improve group qualification or promote equality of group qualification. Our theoretical results and experiments on static real-world datasets with simulated dynamics show that our framework can be used to facilitate social science studies.

We study the problem of learning a real-valued function that satisfies the Demographic Parity constraint. It demands the distribution of the predicted output to be independent of the sensitive attribute. We consider the case that the sensitive attribute is available for prediction. We establish a connection between fair regression and optimal transport theory, based on which we derive a close form expression for the optimal fair predictor. Specifically, we show that the distribution of this optimum is the Wasserstein barycenter of the distributions induced by the standard regression function on the sensitive groups. This result offers an intuitive interpretation of the optimal fair prediction and suggests a simple post-processing algorithm to achieve fairness. We establish risk and distribution-free fairness guarantees for this procedure. Numerical experiments indicate that our method is very effective in learning fair models, with a relative increase in error rate that is inferior to the relative gain in fairness.

Fair representation learning provides an effective way of enforcing fairness constraints without compromising utility for downstream users. A desirable family of such fairness constraints, each requiring similar treatment for similar individuals, is known as individual fairness. In this work, we introduce the first method that enables data consumers to obtain certificates of individual fairness for existing and new data points. The key idea is to map similar individuals to close latent representations and leverage this latent proximity to certify individual fairness. That is, our method enables the data producer to learn and certify a representation where for a data point all similar individuals are at l-infinity distance at most epsilon, thus allowing data consumers to certify individual fairness by proving epsilon-robustness of their classifier. Our experimental evaluation on five real-world datasets and several fairness constraints demonstrates the expressivity and scalability of our approach.

In algorithmically fair prediction problems, a standard goal is to ensure the equality of fairness metrics across multiple overlapping groups simultaneously. We reconsider this standard fair classification problem using a probabilistic population analysis, which, in turn, reveals the Bayes-optimal classifier. Our approach unifies a variety of existing group-fair classification methods and enables extensions to a wide range of non-decomposable multiclass performance metrics and fairness measures. The Bayes-optimal classifier further inspires consistent procedures for algorithmically fair classification with overlapping groups. On a variety of real datasets, the proposed approach outperforms baselines in terms of its fairness-performance tradeoff.

We present a statistically consistent algorithm for constrained classification problems where the objective (e.g. F-measure, G-mean) and the constraints (e.g. demographic parity, coverage) are defined by general functions of the confusion matrix. The key idea is to reduce the problem into a sequence of plug-in classifier learning problems, which is done by formulating an optimization problem over the intersection of the set of achievable confusion matrices and the set of feasible matrices. For objective and constraints that are convex functions of the confusion matrix, our algorithm requires $O(1/\epsilon^2)$ calls to the plug-in routine, which improves on the $O(1/\epsilon^3)$ rate achieved by Narasimhan (2018). We demonstrate empirically that our algorithm performs at least as well as the state-of-the-art methods for these problems.

Causal discovery is at the core of human cognition. It enables us to reason about the environment and make counterfactual predictions about unseen scenarios that can vastly differ from our previous experiences. We consider the task of causal discovery from videos in an end-to-end fashion without supervision on the ground-truth graph structure. In particular, our goal is to discover the structural dependencies among environmental and object variables: inferring the type and strength of interactions that have a causal effect on the behavior of the dynamical system. Our model consists of (a) a perception module that extracts a semantically meaningful and temporally consistent keypoint representation from images, (b) an inference module for determining the graph distribution induced by the detected keypoints, and (c) a dynamics module that can predict the future by conditioning on the inferred graph. We assume access to different configurations and environmental conditions, i.e., data from unknown interventions on the underlying system; thus, we can hope to discover the correct underlying causal graph without explicit interventions. We evaluate our method in a planar multi-body interaction environment and scenarios involving fabrics of different shapes like shirts and pants. Experiments demonstrate that our model can correctly identify the interactions from a short sequence of images and make long-term future predictions. The causal structure assumed by the model also allows it to make counterfactual predictions and extrapolate to systems of unseen interaction graphs or graphs of various sizes.

One of the common ways children learn is by mimicking adults. Imitation learning focuses on learning policies with suitable performance from demonstrations generated by an expert, with an unspecified performance measure, and unobserved reward signal. Popular methods for imitation learning start by either directly mimicking the behavior policy of an expert (behavior cloning) or by learning a reward function that prioritizes observed expert trajectories (inverse reinforcement learning). However, these methods rely on the assumption that covariates used by the expert to determine her/his actions are fully observed. In this paper, we relax this assumption and study imitation learning when sensory inputs of the learner and the expert differ. First, we provide a non-parametric, graphical criterion that is complete (both necessary and sufficient) for determining the feasibility of imitation from the combinations of demonstration data and qualitative assumptions about the underlying environment, represented in the form of a causal model. We then show that when such a criterion does not hold, imitation could still be feasible by exploiting quantitative knowledge of the expert trajectories. Finally, we develop an efficient procedure for learning the imitating policy from experts' trajectories.

Causal treatment effect estimation is a key problem that arises in a variety of real-world settings, from personalized medicine to governmental policy making. There has been a flurry of recent work in machine learning on estimating causal effects when one has access to an instrument. However, to achieve identifiability, they in general require one-size-fits-all assumptions such as an additive error model for the outcome. An alternative is partial identification, which provides bounds on the causal effect. Little exists in terms of bounding methods that can deal with the most general case, where the treatment itself can be continuous. Moreover, bounding methods generally do not allow for a continuum of assumptions on the shape of the causal effect that can smoothly trade off stronger background knowledge for more informative bounds. In this work, we provide a method for causal effect bounding in continuous distributions, leveraging recent advances in gradient-based methods for the optimization of computationally intractable objective functions. We demonstrate on a set of synthetic and real-world data that our bounds capture the causal effect when additive methods fail, providing a useful range of answers compatible with observation as opposed to relying on unwarranted structural assumptions.

A fundamental difficulty of causal learning is that causal models can generally not be fully identified based on observational data only. Interventional data, that is, data originating from different experimental environments, improves identifiability. However, the improvement depends critically on the target and nature of the interventions carried out in each experiment. Since in real applications experiments tend to be costly, there is a need to perform the right interventions such that as few as possible are required. In this work we propose a new active learning (i.e. experiment selection) framework (A-ICP) based on Invariant Causal Prediction (ICP) (Peters et al. 2016). For general structural causal models, we characterize the effect of interventions on so-called stable sets, a notion introduced by Pfister et al. 2019. We leverage these results to propose several intervention selection policies for A-ICP which quickly reveal the direct causes of a response variable in the causal graph while maintaining the error control inherent in ICP. Empirically, we analyze the performance of the proposed policies in both population and finite-regime experiments.

One fundamental problem in the empirical sciences is of reconstructing the causal structure that underlies a phenomenon of interest through observation and experimentation. While there exists a plethora of methods capable of learning the equivalence class of causal structures that are compatible with observations, it is less well-understood how to systematically combine observations and experiments to reconstruct the underlying structure. In this paper, we investigate the task of structural learning in non-Markovian systems (i.e., when latent variables affect more than one observable) from a combination of observational and soft experimental data when the interventional targets are unknown. Using causal invariances found across the collection of observational and interventional distributions (not only conditional independences), we define a property called psi-Markov that connects these distributions to a pair consisting of (1) a causal graph D and (2) a set of interventional targets I. Building on this property, our main contributions are two-fold: First, we provide a graphical characterization that allows one to test whether two causal graphs with possibly different sets of interventional targets belong to the same psi-Markov equivalence class. Second, we develop an algorithm capable of harnessing the collection of data to learn the corresponding equivalence class. We then prove that this algorithm is sound and complete, in the sense that it is the most informative in the sample limit, i.e., it discovers as many tails and arrowheads as can be oriented within a psi-Markov equivalence class.

We formulate a general framework for building structural causal models (SCMs) with deep learning components. The proposed approach employs normalising flows and variational inference to enable tractable inference of exogenous noise variables - a crucial step for counterfactual inference that is missing from existing deep causal learning methods. Our framework is validated on a synthetic dataset built on MNIST as well as on a real-world medical dataset of brain MRI scans. Our experimental results indicate that we can successfully train deep SCMs that are capable of all three levels of Pearl's ladder of causation: association, intervention, and counterfactuals, giving rise to a powerful new approach for answering causal questions in imaging applications and beyond.

There has been recent interest in exploring generative goals for counterfactual reasoning, such as individualized treatment effect (ITE) estimation. However, existing solutions often fail to address issues that are unique to causal inference, such as covariate balancing and (infeasible) counterfactual validation. As a step towards more flexible, scalable and accurate ITE estimation, we present a novel generative Bayesian estimation framework that integrates representation learning, adversarial matching and causal estimation. By appealing to the Robinson decomposition, we derive a reformulated variational bound that explicitly targets the causal effect estimation rather than specific predictive goals. Our procedure acknowledges the uncertainties in representation and solves a Fenchel mini-max game to resolve the representation imbalance for better counterfactual generalization, justified by new theory. Further, the latent variable formulation employed enables robustness to unobservable latent confounders, extending the scope of its applicability. The utility of the proposed solution is demonstrated via an extensive set of tests against competing solutions, both under various simulation setups and to real-world datasets, with encouraging results reported.

We present a new method for linear and nonlinear, lagged and contemporaneous constraint-based causal discovery from observational time series in the presence of latent confounders. We show that existing causal discovery methods such as FCI and variants suffer from low recall in the autocorrelated time series case and identify low effect size of conditional independence tests as the main reason. Information-theoretical arguments show that effect size can often be increased if causal parents are included in the conditioning sets. To identify parents early on, we suggest an iterative procedure that utilizes novel orientation rules to determine ancestral relationships already during the edge removal phase. We prove that the method is order-independent, and sound and complete in the oracle case. Extensive simulation studies for different numbers of variables, time lags, sample sizes, and further cases demonstrate that our method indeed achieves much higher recall than existing methods for the case of autocorrelated continuous variables while keeping false positives at the desired level. This performance gain grows with stronger autocorrelation. At github.com/jakobrunge/tigramite we provide Python code for all methods involved in the simulation studies.

We study the problem of discovering the simplest latent variable that can make two observed discrete variables conditionally independent. The minimum entropy required for such a latent is known as common entropy in information theory. We extend this notion to Renyi common entropy by minimizing the Renyi entropy of the latent variable. To efficiently compute common entropy, we propose an iterative algorithm that can be used to discover the trade-off between the entropy of the latent variable and the conditional mutual information of the observed variables. We show two applications of common entropy in causal inference: First, under the assumption that there are no low-entropy mediators, it can be used to distinguish direct causation from spurious correlation among almost all joint distributions on simple causal graphs with two observed variables. Second, common entropy can be used to improve constraint-based methods such as PC or FCI algorithms in the small-sample regime, where these methods are known to struggle. We propose a modification to these constraint-based methods to assess if a separating set found by these algorithms are valid using common entropy. We finally evaluate our algorithms on synthetic and real data to establish their performance.

Entropic causal inference is a framework for inferring the causal direction between two categorical variables from observational data. The central assumption is that the amount of unobserved randomness in the system is not too large. This unobserved randomness is measured by the entropy of the exogenous variable in the underlying structural causal model, which governs the causal relation between the observed variables. Kocaoglu et al. conjectured that the causal direction is identifiable when the entropy of the exogenous variable is not too large. In this paper, we prove a variant of their conjecture. Namely, we show that for almost all causal models where the exogenous variable has entropy that does not scale with the number of states of the observed variables, the causal direction is identifiable from observational data. We also consider the minimum entropy coupling-based algorithmic approach presented by Kocaoglu et al., and for the first time demonstrate algorithmic identifiability guarantees using a finite number of samples. We conduct extensive experiments to evaluate the robustness of the method to relaxing some of the assumptions in our theory and demonstrate that both the constant-entropy exogenous variable and the no latent confounder assumptions can be relaxed in practice. We also empirically characterize the number of observational samples needed for causal identification. Finally, we apply the algorithm on Tuebingen cause-effect pairs dataset.

The challenge of generalizing causal knowledge across different environments is pervasive in scientific explorations, including in AI, ML, and Data Science. Experiments are usually performed in one environment (e.g., in a lab, on Earth) with the intent, almost invariably, of being used elsewhere (e.g., outside the lab, on Mars), where the conditions are likely to be different. In the causal inference literature, this generalization task has been formalized under the rubric of transportability (Pearl and Bareinboim, 2011), where a number of criteria and algorithms have been developed for various settings. Despite the generality of such results, transportability theory has been confined to atomic, do()-interventions. In practice, many real-world applications require more complex, stochastic interventions; for instance, in reinforcement learning, agents need to continuously adapt to the changing conditions of an uncertain and unknown environment. In this paper, we extend transportability theory to encompass these more complex types of interventions, which are known as "soft," both relative to the input as well as the target distribution of the analysis. Specifically, we develop a graphical condition that is both necessary and sufficient for deciding soft-transportability. Second, we develop an algorithm to determine whether a non-atomic intervention is computable from a combination of the distributions available across domains. As a corollary, we show that the $\sigma$-calculus is complete for the task of soft-transportability.

Learning causal effects from data is a fundamental problem across the sciences. Determining the identifiability of a target effect from a combination of the observational distribution and the causal graph underlying a phenomenon is well-understood in theory. However, in practice, it remains a challenge to apply the identification theory to estimate the identified causal functionals from finite samples. Although a plethora of effective estimators have been developed under the setting known as the back-door (also called conditional ignorability), there exists still no systematic way of estimating arbitrary causal functionals that are both computationally and statistically attractive. This paper aims to bridge this gap, from causal identification to causal estimation. We note that estimating functionals from limited samples based on the empirical risk minimization (ERM) principle has been pervasive in the machine learning literature, and these methods have been extended to causal inference under the back-door setting. In this paper, we develop a learning framework that marries two families of methods, benefiting from the generality of the causal identification theory and the effectiveness of the estimators produced based on the principle of ERM. Specifically, we develop a sound and complete algorithm that generates causal functionals in the form of weighted distributions that are amenable to the ERM optimization. We then provide a practical procedure for learning causal effects from finite samples and a causal graph. Finally, experimental results support the effectiveness of our approach.

Learning a causal directed acyclic graph from data is a challenging task that involves solving a combinatorial problem for which the solution is not always identifiable. A new line of work reformulates this problem as a continuous constrained optimization one, which is solved via the augmented Lagrangian method. However, most methods based on this idea do not make use of interventional data, which can significantly alleviate identifiability issues. This work constitutes a new step in this direction by proposing a theoretically-grounded method based on neural networks that can leverage interventional data. We illustrate the flexibility of the continuous-constrained framework by taking advantage of expressive neural architectures such as normalizing flows. We show that our approach compares favorably to the state of the art in a variety of settings, including perfect and imperfect interventions for which the targeted nodes may even be unknown.

Causal discovery aims to recover causal structures or models underlying the observed data. Despite its success in certain domains, most existing methods focus on causal relations between observed variables, while in many scenarios the observed ones may not be the underlying causal variables (e.g., image pixels), but are generated by latent causal variables or confounders that are causally related. To this end, in this paper, we consider Linear, Non-Gaussian Latent variable Models (LiNGLaMs), in which latent confounders are also causally related, and propose a Generalized Independent Noise (GIN) condition to estimate such latent variable graphs. Specifically, for two observed random vectors $\mathbf{Y}$ and $\mathbf{Z}$, GIN holds if and only if $\omega^{\intercal}\mathbf{Y}$ and $\mathbf{Z}$ are statistically independent, where $\omega$ is a parameter vector characterized from the cross-covariance between $\mathbf{Y}$ and $\mathbf{Z}$. From the graphical view, roughly speaking, GIN implies that causally earlier latent common causes of variables in $\mathbf{Y}$ d-separate $\mathbf{Y}$ from $\mathbf{Z}$. Interestingly, we find that the independent noise condition, i.e., if there is no confounder, causes are independent from the error of regressing the effect on the causes, can be seen as a special case of GIN. Moreover, we show that GIN helps locate latent variables and identify their causal structure, including causal directions. We further develop a recursive learning algorithm to achieve these goals. Experimental results on synthetic and real-world data demonstrate the effectiveness of our method.

Multivariate zero-inflated count data arise in a wide range of areas such as economics, social sciences, and biology. To infer causal relationships in zero-inflated count data, we propose a new zero-inflated Poisson Bayesian network (ZIPBN) model. We show that the proposed ZIPBN is identifiable with cross-sectional data. The proof is based on the well-known characterization of Markov equivalence class which is applicable to other distribution families. For causal structural learning, we introduce a fully Bayesian inference approach which exploits the parallel tempering Markov chain Monte Carlo algorithm to efficiently explore the multi-modal network space. We demonstrate the utility of the proposed ZIPBN in causal discoveries for zero-inflated count data by simulation studies with comparison to alternative Bayesian network methods. Additionally, real single-cell RNA-sequencing data with known causal relationships will be used to assess the capability of ZIPBN for discovering causal relationships in real-world problems.

We establish finite-sample guarantees for a polynomial-time algorithm for learning a nonlinear, nonparametric directed acyclic graphical (DAG) model from data. The analysis is model-free and does not assume linearity, additivity, independent noise, or faithfulness. Instead, we impose a condition on the residual variances that is closely related to previous work on linear models with equal variances. Compared to an optimal algorithm with oracle knowledge of the variable ordering, the additional cost of the algorithm is linear in the dimension $d$ and the number of samples $n$. Finally, we compare the proposed algorithm to existing approaches in a simulation study.

Although Sinkhorn divergences are now routinely used in data sciences to compare probability distributions, the computational effort required to compute them remains expensive, growing in general quadratically in the size $n$ of the support of these distributions. Indeed, solving optimal transport (OT) with an entropic regularization requires computing a $n\times n$ kernel matrix (the neg-exponential of a $n\times n$ pairwise ground cost matrix) that is repeatedly applied to a vector. We propose to use instead ground costs of the form $c(x,y)=-\log\dotp{\varphi(x)}{\varphi(y)}$ where $\varphi$ is a map from the ground space onto the positive orthant $\RR^r_+$, with $r\ll n$. This choice yields, equivalently, a kernel $k(x,y)=\dotp{\varphi(x)}{\varphi(y)}$, and ensures that the cost of Sinkhorn iterations scales as $O(nr)$. We show that usual cost functions can be approximated using this form. Additionaly, we take advantage of the fact that our approach yields approximation that remain fully differentiable with respect to input distributions, as opposed to previously proposed adaptive low-rank approximations of the kernel matrix, to train a faster variant of OT-GAN~\cite{salimans2018improving}.

Modern large-scale kernel-based tests such as maximum mean discrepancy (MMD) and kernelized Stein discrepancy (KSD) optimize kernel hyperparameters on a held-out sample via data splitting to obtain the most powerful test statistics. While data splitting results in a tractable null distribution, it suffers from a reduction in test power due to smaller test sample size. Inspired by the selective inference framework, we propose an approach that enables learning the hyperparameters and testing on the full sample without data splitting. Our approach can correctly calibrate the test in the presence of such dependency, and yield a test threshold in closed form. At the same significance level, our approach’s test power is empirically larger than that of the data-splitting approach, regardless of its split proportion.

Operator-valued kernels have shown promise in supervised learning problems with functional inputs and functional outputs. The crucial (and possibly restrictive) assumption of positive definiteness of operator-valued kernels has been instrumental in developing efficient algorithms. In this work, we consider operator-valued kernels which might not be necessarily positive definite. To tackle the indefiniteness of operator-valued kernels, we harness the machinery of Reproducing Kernel Krein Spaces (RKKS) of function-valued functions. A representer theorem is illustrated which yields a suitable loss stabilization problem for supervised learning with function-valued inputs and outputs. Analysis of generalization properties of the proposed framework is given. An iterative Operator based Minimum Residual (OpMINRES) algorithm is proposed for solving the loss stabilization problem. Experiments with indefinite operator-valued kernels on synthetic and real data sets demonstrate the utility of the proposed approach.

We consider settings in which the data of interest correspond to pairs of ordered times, e.g, the birth times of the first and second child, the times at which a new user creates an account and makes the first purchase on a website, and the entry and survival times of patients in a clinical trial. In these settings, the two times are not independent (the second occurs after the first), yet it is still of interest to determine whether there exists significant dependence "beyond" their ordering in time. We refer to this notion as "quasi-(in)dependence." For instance, in a clinical trial, to avoid biased selection, we might wish to verify that recruitment times are quasi-independent of survival times, where dependencies might arise due to seasonal effects. In this paper, we propose a nonparametric statistical test of quasi-independence. Our test considers a potentially infinite space of alternatives, making it suitable for complex data where the nature of the possible quasi-dependence is not known in advance. Standard parametric approaches are recovered as special cases, such as the classical conditional Kendall's tau, and log-rank tests. The tests apply in the right-censored setting: an essential feature in clinical trials, where patients can withdraw from the study. We provide an asymptotic analysis of our test-statistic, and demonstrate in experiments that our test obtains better power than existing approaches, while being more computationally efficient.

Shape constraints (such as non-negativity, monotonicity, convexity) play a central role in a large number of applications, as they usually improve performance for small sample size and help interpretability. However enforcing these shape requirements in a hard fashion is an extremely challenging problem. Classically, this task is tackled (i) in a soft way (without out-of-sample guarantees), (ii) by specialized transformation of the variables on a case-by-case basis, or (iii) by using highly restricted function classes, such as polynomials or polynomial splines. In this paper, we prove that hard affine shape constraints on function derivatives can be encoded in kernel machines which represent one of the most flexible and powerful tools in machine learning and statistics. Particularly, we present a tightened second-order cone constrained reformulation, that can be readily implemented in convex solvers. We prove performance guarantees on the solution, and demonstrate the efficiency of the approach in joint quantile regression with applications to economics and to the analysis of aircraft trajectories, among others.

The objective in statistical Optimal Transport (OT) is to consistently estimate the optimal transport plan/map solely using samples from the given source and target marginal distributions. This work takes the novel approach of posing statistical OT as that of learning the transport plan's kernel mean embedding from sample based estimates of marginal embeddings. The proposed estimator controls overfitting by employing maximum mean discrepancy based regularization, which is complementary to $\phi$-divergence (entropy) based regularization popularly employed in existing estimators. A key result is that, under very mild conditions, $\epsilon$-optimal recovery of the transport plan as well as the Barycentric-projection based transport map is possible with a sample complexity that is completely dimension-free. Moreover, the implicit smoothing in the kernel mean embeddings enables out-of-sample estimation. An appropriate representer theorem is proved leading to a kernelized convex formulation for the estimator, which can then be potentially used to perform OT even in non-standard domains. Empirical results illustrate the efficacy of the proposed approach.

High dimensional black-box optimization has broad applications but remains a challenging problem to solve. Given a set of samples xi, yi, building a global model (like Bayesian Optimization (BO)) suffers from the curse of dimensionality in the high-dimensional search space, while a greedy search may lead to sub-optimality. By recursively splitting the search space into regions with high/low function values, recent works like LaNAS shows good performance in Neural Architecture Search (NAS), reducing the sample complexity empirically. In this paper, we coin LA-MCTS that extends LaNAS to other domains. Unlike previous approaches, LA-MCTS learns the partition of the search space using a few samples and their function values in an online fashion. While LaNAS uses linear partition and performs uniform sampling in each region, our LA-MCTS adopts a nonlinear decision boundary and learns a local model to pick good candidates. If the nonlinear partition function and the local model fits well with ground-truth black-box function, then good partitions and candidates can be reached with much fewer samples. LA-MCTS serves as a meta-algorithm by using existing black-box optimizers (e.g., BO, TuRBO as its local models, achieving strong performance in general black-box optimization and reinforcement learning benchmarks, in particular for high-dimensional problems.

Wasserstein barycenters provide a geometrically meaningful way to aggregate probability distributions, built on the theory of optimal transport. They are difficult to compute in practice, however, leading previous work to restrict their supports to finite sets of points. Leveraging a new dual formulation for the regularized Wasserstein barycenter problem, we introduce a stochastic algorithm that constructs a continuous approximation of the barycenter. We establish strong duality and use the corresponding primal-dual relationship to parametrize the barycenter implicitly using the dual potentials of regularized transport problems. The resulting problem can be solved with stochastic gradient descent, which yields an efficient online algorithm to approximate the barycenter of continuous distributions given sample access. We demonstrate the effectiveness of our approach and compare against previous work on synthetic examples and real-world applications.

Although optimal transport (OT) problems admit closed form solutions in a very few notable cases, e.g. in 1D or between Gaussians, these closed forms have proved extremely fecund for practitioners to define tools inspired from the OT geometry. On the other hand, the numerical resolution of OT problems using entropic regularization has given rise to many applications, but because there are no known closed-form solutions for entropic regularized OT problems, these approaches are mostly algorithmic, not informed by elegant closed forms. In this paper, we propose to fill the void at the intersection between these two schools of thought in OT by proving that the entropy-regularized optimal transport problem between two Gaussian measures admits a closed form. Contrary to the unregularized case, for which the explicit form is given by the Wasserstein-Bures distance, the closed form we obtain is differentiable everywhere, even for Gaussians with degenerate covariance matrices. We obtain this closed form solution by solving the fixed-point equation behind Sinkhorn's algorithm, the default method for computing entropic regularized OT. Remarkably, this approach extends to the generalized unbalanced case --- where Gaussian measures are scaled by positive constants. This extension leads to a closed form expression for unbalanced Gaussians as well, and highlights the mass transportation / destruction trade-off seen in unbalanced optimal transport. Moreover, in both settings, we show that the optimal transportation plans are (scaled) Gaussians and provide analytical formulas of their parameters. These formulas constitute the first non-trivial closed forms for entropy-regularized optimal transport, thus providing a ground truth for the analysis of entropic OT and Sinkhorn's algorithm.

Bayesian optimization (BO) is a popular framework for optimizing black-box functions. In many applications,  the objective function can be evaluated at multiple fidelities to enable a trade-off between the cost and accuracy. To reduce the optimization cost, many multi-fidelity BO methods have been proposed. Despite their success, these methods either ignore or over-simplify the strong, complex correlations across the fidelities. While the acquisition function is therefore easy and convenient to calculate,  these methods can be inefficient in estimating the objective function. To address this issue, we propose Deep Neural Network Multi-Fidelity Bayesian Optimization (DNN-MFBO) that can flexibly capture all kinds of complicated relationships between the fidelities to improve the objective function estimation and hence the optimization performance. We use sequential,  fidelity-wise Gauss-Hermite quadrature and moment-matching to compute a mutual information-based acquisition function in a tractable and highly efficient way. We show the advantages of our method in both synthetic benchmark datasets and real-world applications in engineering design.

Bayesian optimization (BO) is a popular approach to optimize expensive-to-evaluate black-box functions. A significant challenge in BO is to scale to high-dimensional parameter spaces while retaining sample efficiency. A solution considered in existing literature is to embed the high-dimensional space in a lower-dimensional manifold, often via a random linear embedding. In this paper, we identify several crucial issues and misconceptions about the use of linear embeddings for BO. We study the properties of linear embeddings from the literature and show that some of the design choices in current approaches adversely impact their performance. We show empirically that properly addressing these issues significantly improves the efficacy of linear embeddings for BO on a range of problems, including learning a gait policy for robot locomotion.

A recent Graph Neural Network (GNN) approach for learning to branch has been shown to successfully reduce the running time of branch-and-bound algorithms for Mixed Integer Linear Programming (MILP). While the GNN relies on a GPU for inference, MILP solvers are purely CPU-based. This severely limits its application as many practitioners may not have access to high-end GPUs. In this work, we ask two key questions. First, in a more realistic setting where only a CPU is available, is the GNN model still competitive? Second, can we devise an alternate computationally inexpensive model that retains the predictive power of the GNN architecture? We answer the first question in the negative, and address the second question by proposing a new hybrid architecture for efficient branching on CPU machines. The proposed architecture combines the expressive power of GNNs with computationally inexpensive multi-layer perceptrons (MLP) for branching. We evaluate our methods on four classes of MILP problems, and show that they lead to up to 26% reduction in solver running time compared to state-of-the-art methods without a GPU, while extrapolating to harder problems than it was trained on. The code for this project is publicly available at https://github.com/pg2455/Hybrid-learn2branch.

Solving optimization problem is the key to decision making in many real-life analytics applications. However, the coefficients of the optimization problems are often uncertain and dependent on external factors, such as future demand or energy- or stock prices. Machine learning (ML) models, especially neural networks, are increasingly being used to estimate these coefficients in a data-driven way. Hence, end-to-end predict-and-optimize approaches, which consider how effective the predicted values are to solve the optimization problem, have received increasing attention. In case of integer linear programming problems, a popular approach to overcome their non-differentiabilty is to add a quadratic penalty term to the continuous relaxation, such that results from differentiating over quadratic programs can be used. Instead we investigate the use of the more principled logarithmic barrier term, as widely used in interior point solvers for linear programming. Instead of differentiating the KKT conditions, we consider the homogeneous self-dual formulation of the LP and we show the relation between the interior point step direction and corresponding gradients needed for learning. Finally, our empirical experiments demonstrate our approach performs as good as if not better than the state-of-the-art QPTL (Quadratic Programming task loss) formulation of Wilder et al. and SPO approach of Elmachtoub and Grigas.

Learning heuristics for combinatorial optimization problems through graph neural networks have recently shown promising results on some classic NP-hard problems. These are single-level optimization problems with only one player. Multilevel combinatorial optimization problems are their generalization, encompassing situations with multiple players taking decisions sequentially. By framing them in a multi-agent reinforcement learning setting, we devise a value-based method to learn to solve multilevel budgeted combinatorial problems involving two players in a zero-sum game over a graph. Our framework is based on a simple curriculum: if an agent knows how to estimate the value of instances with budgets up to $B$, then solving instances with budget $B+1$ can be done in polynomial time regardless of the direction of the optimization by checking the value of every possible afterstate. Thus, in a bottom-up approach, we generate datasets of heuristically solved instances with increasingly larger budgets to train our agent. We report results close to optimality on graphs up to $100$ nodes and a $185 \times$ speedup on average compared to the quickest exact solver known for the Multilevel Critical Node problem, a max-min-max trilevel problem that has been shown to be at least $\Sigma_2^p$-hard.

This article develops a Bayesian optimization (BO) method which acts directly over raw strings, proposing the first uses of string kernels and genetic algorithms within BO loops. Recent applications of BO over strings have been hindered by the need to map inputs into a smooth and unconstrained latent space. Learning this projection is computationally and data-intensive. Our approach instead builds a powerful Gaussian process surrogate model based on string kernels, naturally supporting variable length inputs, and performs efficient acquisition function maximization for spaces with syntactic constraints. Experiments demonstrate considerably improved optimization over existing approaches across a broad range of constraints, including the popular setting where syntax is governed by a context-free grammar.

For multi-valued functions---such as when the conditional distribution on targets given the inputs is multi-modal---standard regression approaches are not always desirable because they provide the conditional mean. Modal regression algorithms address this issue by instead finding the conditional mode(s). Most, however, are nonparametric approaches and so can be difficult to scale. Further, parametric approximators, like neural networks, facilitate learning complex relationships between inputs and targets. In this work, we propose a parametric modal regression algorithm. We use the implicit function theorem to develop an objective, for learning a joint function over inputs and targets. We empirically demonstrate on several synthetic problems that our method (i) can learn multi-valued functions and produce the conditional modes, (ii) scales well to high-dimensional inputs, and (iii) can even be more effective for certain uni-modal problems, particularly for high-frequency functions. We demonstrate that our method is competitive in a real-world modal regression problem and two regular regression datasets.

The existence of adversarial examples capable of fooling trained neural network classifiers calls for a much better understanding of possible attacks to guide the development of safeguards against them. This includes attack methods in the challenging {\em non-interactive blackbox} setting, where adversarial attacks are generated without any access, including queries, to the target model. Prior attacks in this setting have relied mainly on algorithmic innovations derived from empirical observations (e.g., that momentum helps), lacking principled transferability guarantees. In this work, we provide a theoretical foundation for crafting transferable adversarial examples to entire hypothesis classes. We introduce \textit{Adversarial Example Games} (AEG), a framework that models the crafting of adversarial examples as a min-max game between a generator of attacks and a classifier. AEG provides a new way to design adversarial examples by adversarially training a generator and a classifier from a given hypothesis class (e.g., architecture). We prove that this game has an equilibrium, and that the optimal generator is able to craft adversarial examples that can attack any classifier from the corresponding hypothesis class. We demonstrate the efficacy of AEG on the MNIST and CIFAR-10 datasets, outperforming prior state-of-the-art approaches with an average relative improvement of $29.9\%$ and $47.2\%$ against undefended and robust models (Table \ref{table:q2} \& \ref{table:q3}) respectively.

Recent work has shown that, when integrated with adversarial training, self-supervised pre-training can lead to state-of-the-art robustness In this work, we improve robustness-aware self-supervised pre-training by learning representations that are consistent under both data augmentations and adversarial perturbations. Our approach leverages a recent contrastive learning framework, which learns representations by maximizing feature consistency under differently augmented views. This fits particularly well with the goal of adversarial robustness, as one cause of adversarial fragility is the lack of feature invariance, i.e., small input perturbations can result in undesirable large changes in features or even predicted labels. We explore various options to formulate the contrastive task, and demonstrate that by injecting adversarial perturbations, contrastive pre-training can lead to models that are both label-efficient and robust. We empirically evaluate the proposed Adversarial Contrastive Learning (ACL) and show it can consistently outperform existing methods. For example on the CIFAR-10 dataset, ACL outperforms the previous state-of-the-art unsupervised robust pre-training approach by 2.99% on robust accuracy and 2.14% on standard accuracy. We further demonstrate that ACL pre-training can improve semi-supervised adversarial training, even when only a few labeled examples are available. Our codes and pre-trained models have been released at: https://github.com/VITA-Group/Adversarial-Contrastive-Learning.

Metric learning is an important family of algorithms for classification and similarity search, but the robustness of learned metrics against small adversarial perturbations is less studied. In this paper, we show that existing metric learning algorithms, which focus on boosting the clean accuracy, can result in metrics that are less robust than the Euclidean distance. To overcome this problem, we propose a novel metric learning algorithm to find a Mahalanobis distance that is robust against adversarial perturbations, and the robustness of the resulting model is certifiable. Experimental results show that the proposed metric learning algorithm improves both certified robust errors and empirical robust errors (errors under adversarial attacks). Furthermore, unlike neural network defenses which usually encounter a trade-off between clean and robust errors, our method does not sacrifice clean errors compared with previous metric learning methods.

Research in adversarial learning follows a cat and mouse game between attackers and defenders where attacks are proposed, they are mitigated by new defenses, and subsequently new attacks are proposed that break earlier defenses, and so on. However, it has remained unclear as to whether there are conditions under which no better attacks or defenses can be proposed. In this paper, we propose a game-theoretic framework for studying attacks and defenses which exist in equilibrium. Under a locally linear decision boundary model for the underlying binary classifier, we prove that the Fast Gradient Method attack and a Randomized Smoothing defense form a Nash Equilibrium. We then show how this equilibrium defense can be approximated given finitely many samples from a data-generating distribution, and derive a generalization bound for the performance of our approximation.

We establish a theoretical link between adversarial training and operator norm regularization for deep neural networks. Specifically, we prove that $l_p$-norm constrained projected gradient ascent based adversarial training with an $l_q$-norm loss on the logits of clean and perturbed inputs is equivalent to data-dependent (p, q) operator norm regularization. This fundamental connection confirms the long-standing argument that a network’s sensitivity to adversarial examples is tied to its spectral properties and hints at novel ways to robustify and defend against adversarial attacks. We provide extensive empirical evidence on state-of-the-art network architectures to support our theoretical results.

Several recent results provide theoretical insights into the phenomena of adversarial examples. Existing results, however, are often limited due to a gap between the simplicity of the models studied and the complexity of those deployed in practice. In this work, we strike a better balance by considering a model that involves learning a representation while at the same time giving a precise generalization bound and a robustness certificate. We focus on the hypothesis class obtained by combining a sparsity-promoting encoder coupled with a linear classifier, and show an interesting interplay between the expressivity and stability of the (supervised) representation map and a notion of margin in the feature space. We bound the robust risk (to $\ell_2$-bounded perturbations) of hypotheses parameterized by dictionaries that achieve a mild encoder gap on training data. Furthermore, we provide a robustness certificate for end-to-end classification. We demonstrate the applicability of our analysis by computing certified accuracy on real data, and compare with other alternatives for certified robustness.

Adversarial training (AT) is one of the most effective defenses against adversarial attacks for deep learning models. In this work, we advocate incorporating the hypersphere embedding (HE) mechanism into the AT procedure by regularizing the features onto compact manifolds, which constitutes a lightweight yet effective module to blend in the strength of representation learning. Our extensive analyses reveal that AT and HE are well coupled to benefit the robustness of the adversarially trained models from several aspects. We validate the effectiveness and adaptability of HE by embedding it into the popular AT frameworks including PGD-AT, ALP, and TRADES, as well as the FreeAT and FastAT strategies. In the experiments, we evaluate our methods under a wide range of adversarial attacks on the CIFAR-10 and ImageNet datasets, which verifies that integrating HE can consistently enhance the model robustness for each AT framework with little extra computation.

We analyze the influence of adversarial training on the loss landscape of machine learning models. To this end, we first provide analytical studies of the properties of adversarial loss functions under different adversarial budgets. We then demonstrate that the adversarial loss landscape is less favorable to optimization, due to increased curvature and more scattered gradients. Our conclusions are validated by numerical analyses, which show that training under large adversarial budgets impede the escape from suboptimal random initialization, cause non-vanishing gradients and make the models' minima found sharper. Based on these observations, we show that a periodic adversarial scheduling (PAS) strategy can effectively overcome these challenges, yielding better results than vanilla adversarial training while being much less sensitive to the choice of learning rate.

Recent research finds CNN models for image classification demonstrate overlapped adversarial vulnerabilities: adversarial attacks can mislead CNN models with small perturbations, which can effectively transfer between different models trained on the same dataset. Adversarial training, as a general robustness improvement technique, eliminates the vulnerability in a single model by forcing it to learn robust features. The process is hard, often requires models with large capacity, and suffers from significant loss on clean data accuracy. Alternatively, ensemble methods are proposed to induce sub-models with diverse outputs against a transfer adversarial example, making the ensemble robust against transfer attacks even if each sub-model is individually non-robust. Only small clean accuracy drop is observed in the process. However, previous ensemble training methods are not efficacious in inducing such diversity and thus ineffective on reaching robust ensemble. We propose DVERGE, which isolates the adversarial vulnerability in each sub-model by distilling non-robust features, and diversifies the adversarial vulnerability to induce diverse outputs against a transfer attack. The novel diversity metric and training procedure enables DVERGE to achieve higher robustness against transfer attacks comparing to previous ensemble methods, and enables the improved robustness when more sub-models are added to the ensemble. The code of this work is available at https://github.com/zjysteven/DVERGE.

Due to its decentralized nature, Federated Learning (FL) lends itself to adversarial attacks in the form of backdoors during training. The goal of a backdoor is to corrupt the performance of the trained model on specific sub-tasks (e.g., by classifying green cars as frogs). A range of FL backdoor attacks have been introduced in the literature, but also methods to defend against them, and it is currently an open question whether FL systems can be tailored to be robust against backdoors. In this work, we provide evidence to the contrary. We first establish that, in the general case, robustness to backdoors implies model robustness to adversarial examples, a major open problem in itself. Furthermore, detecting the presence of a backdoor in a FL model is unlikely assuming first-order oracles or polynomial time. We couple our theoretical results with a new family of backdoor attacks, which we refer to as edge-case backdoors. An edge-case backdoor forces a model to misclassify on seemingly easy inputs that are however unlikely to be part of the training, or test data, i.e., they live on the tail of the input distribution. We explain how these edge-case backdoors can lead to unsavory failures and may have serious repercussions on fairness. We further exhibit that, with careful tuning at the side of the adversary, one can insert them across a range of machine learning tasks (e.g., image classification, OCR, text prediction, sentiment analysis), and bypass state-of-the-art defense mechanisms.

Previous work on adversarially robust neural networks for image classification requires large training sets and computationally expensive training procedures. On the other hand, few-shot learning methods are highly vulnerable to adversarial examples. The goal of our work is to produce networks which both perform well at few-shot classification tasks and are simultaneously robust to adversarial examples. We develop an algorithm, called Adversarial Querying (AQ), for producing adversarially robust meta-learners, and we thoroughly investigate the causes for adversarial vulnerability. Moreover, our method achieves far superior robust performance on few-shot image classification tasks, such as Mini-ImageNet and CIFAR-FS, than robust transfer learning.

Advances in the development of adversarial attacks have been fundamental to the progress of adversarial defense research. Efficient and effective attacks are crucial for reliable evaluation of defenses, and also for developing robust models. Adversarial attacks are often generated by maximizing standard losses such as the cross-entropy loss or maximum-margin loss within a constraint set using Projected Gradient Descent (PGD). In this work, we introduce a relaxation term to the standard loss, that finds more suitable gradient-directions, increases attack efficacy and leads to more efficient adversarial training. We propose Guided Adversarial Margin Attack (GAMA), which utilizes function mapping of the clean image to guide the generation of adversaries, thereby resulting in stronger attacks. We evaluate our attack against multiple defenses and show improved performance when compared to existing attacks. Further, we propose Guided Adversarial Training (GAT), which achieves state-of-the-art performance amongst single-step defenses by utilizing the proposed relaxation term for both attack generation and training.

We consider the blackbox transfer-based targeted adversarial attack threat model in the realm of deep neural network (DNN) image classifiers. Rather than focusing on crossing decision boundaries at the output layer of the source model, our method perturbs representations throughout the extracted feature hierarchy to resemble other classes. We design a flexible attack framework that allows for multi-layer perturbations and demonstrates state-of-the-art targeted transfer performance between ImageNet DNNs. We also show the superiority of our feature space methods under a relaxation of the common assumption that the source and target models are trained on the same dataset and label space, in some instances achieving a $10\times$ increase in targeted success rate relative to other blackbox transfer methods. Finally, we analyze why the proposed methods outperform existing attack strategies and show an extension of the method in the case when limited queries to the blackbox model are allowed.

Vulnerability to adversarial attacks is one of the principal hurdles to the adoption of deep learning in safety-critical applications. Despite significant efforts, both practical and theoretical, the problem remains open. In this paper, we analyse the geometry of adversarial attacks in the large-data, overparametrized limit for Bayesian Neural Networks (BNNs). We show that, in the limit, vulnerability to gradient-based attacks arises as a result of degeneracy in the data distribution, i.e., when the data lies on a lower-dimensional submanifold of the ambient space. As a direct consequence, we demonstrate that in the limit BNN posteriors are robust to gradient-based adversarial attacks. Experimental results on the MNIST and Fashion MNIST datasets with BNNs trained with Hamiltonian Monte Carlo and Variational Inference support this line of argument, showing that BNNs can display both high accuracy and robustness to gradient based adversarial attacks.

A deep reinforcement learning (DRL) agent observes its states through observations, which may contain natural measurement errors or adversarial noises. Since the observations deviate from the true states, they can mislead the agent into making suboptimal actions. Several works have shown this vulnerability via adversarial attacks, but how to improve the robustness of DRL under this setting has not been well studied. We show that naively applying existing techniques on improving robustness for classification tasks, like adversarial training, are ineffective for many RL tasks. We propose the state-adversarial Markov decision process (SA-MDP) to study the fundamental properties of this problem, and develop a theoretically principled policy regularization which can be applied to a large family of DRL algorithms, including deep deterministic policy gradient (DDPG), proximal policy optimization (PPO) and deep Q networks (DQN), for both discrete and continuous action control problems. We significantly improve the robustness of DDPG, PPO and DQN agents under a suite of strong white box adversarial attacks, including two new attacks of our own. Additionally, we find that a robust policy noticeably improves DRL performance in a number of environments.

Adaptive attacks have (rightfully) become the de facto standard for evaluating defenses to adversarial examples. We find, however, that typical adaptive evaluations are incomplete. We demonstrate that 13 defenses recently published at ICLR, ICML and NeurIPS---and which illustrate a diverse set of defense strategies---can be circumvented despite attempting to perform evaluations using adaptive attacks.

While prior evaluation papers focused mainly on the end result---showing that a defense was ineffective---this paper focuses on laying out the methodology and the approach necessary to perform an adaptive attack. Some of our attack strategies are generalizable, but no single strategy would have been sufficient for all defenses. This underlines our key message that adaptive attacks cannot be automated and always require careful and appropriate tuning to a given defense. We hope that these analyses will serve as guidance on how to properly perform adaptive attacks against defenses to adversarial examples, and thus will allow the community to make further progress in building more robust models.

We extensively study how to combine Generative Adversarial Networks and learned compression to obtain a state-of-the-art generative lossy compression system. In particular, we investigate normalization layers, generator and discriminator architectures, training strategies, as well as perceptual losses. In contrast to previous work, i) we obtain visually pleasing reconstructions that are perceptually similar to the input, ii) we operate in a broad range of bitrates, and iii) our approach can be applied to high-resolution images. We bridge the gap between rate-distortion-perception theory and practice by evaluating our approach both quantitatively with various perceptual metrics, and with a user study. The study shows that our method is preferred to previous approaches even if they use more than 2x the bitrate.

From the beginning of zero-shot learning research, visual attributes have been shown to play an important role. In order to better transfer attribute-based knowledge from known to unknown classes, we argue that an image representation with integrated attribute localization ability would be beneficial for zero-shot learning. To this end, we propose a novel zero-shot representation learning framework that jointly learns discriminative global and local features using only class-level attributes. While a visual-semantic embedding layer learns global features, local features are learned through an attribute prototype network that simultaneously regresses and decorrelates attributes from intermediate features. We show that our locality augmented image representations achieve a new state-of-the-art on three zero-shot learning benchmarks. As an additional benefit, our model points to the visual evidence of the attributes in an image, e.g. for the CUB dataset, confirming the improved attribute localization ability of our image representation.

Many recent datasets contain a variety of different data modalities, for instance, image, question, and answer data in visual question answering (VQA). When training deep net classifiers on those multi-modal datasets, the modalities get exploited at different scales, i.e., some modalities can more easily contribute to the classification results than others. This is suboptimal because the classifier is inherently biased towards a subset of the modalities. To alleviate this shortcoming, we propose a novel regularization term based on the functional entropy. Intuitively, this term encourages to balance the contribution of each modality to the classification result. However, regularization with the functional entropy is challenging. To address this, we develop a method based on the log-Sobolev inequality, which bounds the functional entropy with the functional-Fisher-information. Intuitively, this maximizes the amount of information that the modalities contribute. On the two challenging multi-modal datasets VQA-CPv2, and SocialIQ, we obtain state-of-the-art results while more uniformly exploiting the modalities. In addition, we demonstrate the efficacy of our method on Colored MNIST.

Cross-domain disentanglement is the problem of learning representations partitioned into domain-invariant and domain-specific representations, which is a key to successful domain transfer or measuring semantic distance between two domains. Grounded in information theory, we cast the simultaneous learning of domain-invariant and domain-specific representations as a joint objective of multiple information constraints, which does not require adversarial training or gradient reversal layers. We derive a tractable bound of the objective and propose a generative model named Interaction Information Auto-Encoder (IIAE). Our approach reveals insights on the desirable representation for cross-domain disentanglement and its connection to Variational Auto-Encoder (VAE). We demonstrate the validity of our model in the image-to-image translation and the cross-domain retrieval tasks. We further show that our model achieves the state-of-the-art performance in the zero-shot sketch based image retrieval task, even without external knowledge.

Image-based 3D shape retrieval (IBSR) aims to find the corresponding 3D shape of a given 2D image from a large 3D shape database. The common routine is to map 2D images and 3D shapes into an embedding space and define (or learn) a shape similarity measure. While metric learning with some adaptation techniques seems to be a natural solution to shape similarity learning, the performance is often unsatisfactory for fine-grained shape retrieval. In the paper, we identify the source of the poor performance and propose a practical solution to this problem. We find that the shape difference between a negative pair is entangled with the texture gap, making metric learning ineffective in pushing away negative pairs. To tackle this issue, we develop a geometry-focused multi-view metric learning framework empowered by texture synthesis. The synthesis of textures for 3D shape models creates hard triplets, which suppress the adverse effects of rich texture in 2D images, thereby push the network to focus more on discovering geometric characteristics. Our approach shows state-of-the-art performance on a recently released large-scale 3D-FUTURE [1] repository, as well as three widely studied benchmarks, including Pix3D [2], Stanford Cars [3], and Comp Cars [4]. Codes will be made publicly available at: https://github.com/3D-FRONT-FUTURE/IBSR-texture.

Few-shot image generation seeks to generate more data of a given domain, with only few available training examples. As it is unreasonable to expect to fully infer the distribution from just a few observations (e.g., emojis), we seek to leverage a large, related source domain as pretraining (e.g., human faces). Thus, we wish to preserve the diversity of the source domain, while adapting to the appearance of the target. We adapt a pretrained model, without introducing any additional parameters, to the few examples of the target domain. Crucially, we regularize the changes of the weights during this adaptation, in order to best preserve the information of the source dataset, while fitting the target. We demonstrate the effectiveness of our algorithm by generating high-quality results of different target domains, including those with extremely few examples (e.g., 10). We also analyze the performance of our method with respect to some important factors, such as the number of examples and the similarity between the source and target domain.

Image-to-image translation has recently achieved remarkable results. But despite current success, it suffers from inferior performance when translations between classes require large shape changes. We attribute this to the high-resolution bottlenecks which are used by current state-of-the-art image-to-image methods. Therefore, in this work, we propose a novel deep hierarchical Image-to-Image Translation method, called DeepI2I. We learn a model by leveraging hierarchical features: (a) structural information contained in the bottom layers and (b) semantic information extracted from the top layers. To enable the training of deep I2I models on small datasets, we propose a novel transfer learning method, that transfers knowledge from pre-trained GANs. Specifically, we leverage the discriminator of a pre-trained GANs (i.e. BigGAN or StyleGAN) to initialize both the encoder and the discriminator and the pre-trained generator to initialize the generator of our model. Applying knowledge transfer leads to an alignment problem between the encoder and generator. We introduce an adaptor network to address this. On many-class image-to-image translation on three datasets (Animal faces, Birds, and Foods) we decrease mFID by at least 35% when compared to the state-of-the-art. Furthermore, we qualitatively and quantitatively demonstrate that transfer learning significantly improves the performance of I2I systems, especially for small datasets.
Finally, we are the first to perform I2I translations for domains with over 100 classes.

Raven’s Progressive Matrices are multiple-choice intelligence tests, where one tries to complete the missing location in a 3x3 grid of abstract images. Previous attempts to address this test have focused solely on selecting the right answer out of the multiple choices. In this work, we focus, instead, on generating a correct answer given the grid, which is a harder task, by definition. The proposed neural model combines multiple advances in generative models, including employing multiple pathways through the same network, using the reparameterization trick along two pathways to make their encoding compatible, a selective application of variational losses, and a complex perceptual loss that is coupled with a selective backpropagation procedure. Our algorithm is able not only to generate a set of plausible answers but also to be competitive to the state of the art methods in multiple-choice tests.

We present a novel texture synthesis framework, enabling the generation of infinite, high-quality 3D textures given a 2D exemplar image. Inspired by recent advances in natural texture synthesis, we train deep neural models to generate textures by non-linearly combining learned noise frequencies. To achieve a highly realistic output conditioned on an exemplar patch, we propose a novel loss function that combines ideas from both style transfer and generative adversarial networks. In particular, we train the synthesis network to match the Gram matrices of deep features from a discriminator network. In addition, we propose two architectural concepts and an extrapolation strategy that significantly improve generalization performance. In particular, we inject both model input and condition into hidden network layers by learning to scale and bias hidden activations. Quantitative and qualitative evaluations on a diverse set of exemplars motivate our design decisions and show that our system performs superior to previous state of the art. Finally, we conduct a user study that confirms the benefits of our framework.

Given the ever-increasing computational costs of modern machine learning models, we need to find new ways to reuse such expert models and thus tap into the resources that have been invested in their creation. Recent work suggests that the power of these massive models is captured by the representations they learn. Therefore, we seek a model that can relate between different existing representations and propose to solve this task with a conditionally invertible network. This network demonstrates its capability by (i) providing generic transfer between diverse domains, (ii) enabling controlled content synthesis by allowing modification in other domains, and (iii) facilitating diagnosis of existing representations by translating them into interpretable domains such as images. Our domain transfer network can translate between fixed representations without having to learn or finetune them. This allows users to utilize various existing domain-specific expert models from the literature that had been trained with extensive computational resources. Experiments on diverse conditional image synthesis tasks, competitive image modification results and experiments on image-to-image and text-to-image generation demonstrate the generic applicability of our approach. For example, we translate between BERT and BigGAN, state-of-the-art text and image models to provide text-to-image generation, which neither of both experts can perform on their own.

We propose a novel lightweight generative adversarial network for efficient image manipulation using natural language descriptions. To achieve this, a new word-level discriminator is proposed, which provides the generator with fine-grained training feedback at word-level, to facilitate training a lightweight generator that has a small number of parameters, but can still correctly focus on specific visual attributes of an image, and then edit them without affecting other contents that are not described in the text. Furthermore, thanks to the explicit training signal related to each word, the discriminator can also be simplified to have a lightweight structure. Compared with the state of the art, our method has a much smaller number of parameters, but still achieves a competitive manipulation performance. Extensive experimental results demonstrate that our method can better disentangle different visual attributes, then correctly map them to corresponding semantic words, and thus achieve a more accurate image modification using natural language descriptions.

Recent advances in Generative Adversarial Networks (GANs) have led to their widespread adoption for the purposes of generating high quality synthetic imagery. While capable of generating photo-realistic images, these models often produce unrealistic samples which fall outside of the data manifold. Several recently proposed techniques attempt to avoid spurious samples, either by rejecting them after generation, or by truncating the model's latent space. While effective, these methods are inefficient, as a large fraction of training time and model capacity are dedicated towards samples that will ultimately go unused. In this work we propose a novel approach to improve sample quality: altering the training dataset via instance selection before model training has taken place. By refining the empirical data distribution before training, we redirect model capacity towards high-density regions, which ultimately improves sample fidelity, lowers model capacity requirements, and significantly reduces training time. Code is available at https://github.com/uoguelph-mlrg/instanceselectionfor_gans.

The increasing impact of black box models, and particularly of unsupervised ones, comes with an increasing interest in tools to understand and interpret them. In this paper, we consider in particular how to characterise visual groupings discovered automatically by deep neural networks, starting with state-of-the-art clustering methods. In some cases, clusters readily correspond to an existing labelled dataset. However, often they do not, yet they still maintain an "intuitive interpretability''. We introduce two concepts, visual learnability and describability, that can be used to quantify the interpretability of arbitrary image groupings, including unsupervised ones. The idea is to measure (1) how well humans can learn to reproduce a grouping by measuring their ability to generalise from a small set of visual examples (learnability) and (2) whether the set of visual examples can be replaced by a succinct, textual description (describability). By assessing human annotators as classifiers, we remove the subjective quality of existing evaluation metrics. For better scalability, we finally propose a class-level captioning system to generate descriptions for visual groupings automatically and compare it to human annotators using the describability metric.

Feature attribution (FA), or the assignment of class-relevance to different locations in an image, is important for many classification problems but is particularly crucial within the neuroscience domain, where accurate mechanistic models of behaviours, or disease, require knowledge of all features discriminative of a trait. At the same time, predicting class relevance from brain images is challenging as phenotypes are typically heterogeneous, and changes occur against a background of significant natural variation. Here, we present a novel framework for creating class specific FA maps through image-to-image translation. We propose the use of a VAE-GAN to explicitly disentangle class relevance from background features for improved interpretability properties, which results in meaningful FA maps. We validate our method on 2D and 3D brain image datasets of dementia (ADNI dataset), ageing (UK Biobank), and (simulated) lesion detection. We show that FA maps generated by our method outperform baseline FA methods when validated against ground truth. More significantly, our approach is the first to use latent space sampling to support exploration of phenotype variation.

Feature attributions are a popular tool for explaining the behavior of Deep Neural Networks (DNNs), but have recently been shown to be vulnerable to attacks that produce divergent explanations for nearby inputs. This lack of robustness is especially problematic in high-stakes applications where adversarially-manipulated explanations could impair safety and trustworthiness. Building on a geometric understanding of these attacks presented in recent work, we identify Lipschitz continuity conditions on models' gradient that lead to robust gradient-based attributions, and observe that smoothness may also be related to the ability of an attack to transfer across multiple attribution methods. To mitigate these attacks in practice, we propose an inexpensive regularization method that promotes these conditions in DNNs, as well as a stochastic smoothing technique that does not require re-training. Our experiments on a range of image models demonstrate that both of these mitigations consistently improve attribution robustness, and confirm the role that smooth geometry plays in these attacks on real, large-scale models.

Neural networks are vulnerable to input perturbations such as additive noise and adversarial attacks. In contrast, human perception is much more robust to such perturbations. The Bayesian brain hypothesis states that human brains use an internal generative model to update the posterior beliefs of the sensory input. This mechanism can be interpreted as a form of self-consistency between the maximum a posteriori (MAP) estimation of an internal generative model and the external environment. Inspired by such hypothesis, we enforce self-consistency in neural networks by incorporating generative recurrent feedback. We instantiate this design on convolutional neural networks (CNNs). The proposed framework, termed Convolutional Neural Networks with Feedback (CNN-F), introduces a generative feedback with latent variables to existing CNN architectures, where consistent predictions are made through alternating MAP inference under a Bayesian framework. In the experiments, CNN-F shows considerably improved adversarial robustness over conventional feedforward CNNs on standard benchmarks.

We introduce COT-GAN, an adversarial algorithm to train implicit generative models optimized for producing sequential data. The loss function of this algorithm is formulated using ideas from Causal Optimal Transport (COT), which combines classic optimal transport methods with an additional temporal causality constraint. Remarkably, we find that this causality condition provides a natural framework to parameterize the cost function that is learned by the discriminator as a robust (worst-case) distance, and an ideal mechanism for learning time dependent data distributions. Following Genevay et al. (2018), we also include an entropic penalization term which allows for the use of the Sinkhorn algorithm when computing the optimal transport cost. Our experiments show effectiveness and stability of COT-GAN when generating both low- and high-dimensional time-series data. The success of the algorithm also relies on a new, improved version of the Sinkhorn divergence which demonstrates less bias in learning.

We consider the identifiability theory of probabilistic models and establish sufficient conditions under which the representations learnt by a very broad family of conditional energy-based models are unique in function space, up to a simple transformation. In our model family, the energy function is the dot-product between two feature extractors, one for the dependent variable, and one for the conditioning variable. We show that under mild conditions, the features are unique up to scaling and permutation. Our results extend recent developments in nonlinear ICA, and in fact, they lead to an important generalization of ICA models. In particular, we show that our model can be used for the estimation of the components in the framework of Independently Modulated Component Analysis (IMCA), a new generalization of nonlinear ICA that relaxes the independence assumption. A thorough empirical study show that representations learnt by our model from real-world image datasets are identifiable, and improve performance in transfer learning and semi-supervised learning tasks.

Recent approaches for modelling dynamics of physical systems with neural networks enforce Lagrangian or Hamiltonian structure to improve prediction and generalization. However, when coordinates are embedded in high-dimensional data such as images, these approaches either lose interpretability or can only be applied to one particular example. We introduce a new unsupervised neural network model that learns Lagrangian dynamics from images, with interpretability that benefits prediction and control. The model infers Lagrangian dynamics on generalized coordinates that are simultaneously learned with a coordinate-aware variational autoencoder (VAE). The VAE is designed to account for the geometry of physical systems composed of multiple rigid bodies in the plane. By inferring interpretable Lagrangian dynamics, the model learns physical system properties, such as kinetic and potential energy, which enables long-term prediction of dynamics in the image space and synthesis of energy-based controllers.

An important component of autoencoder methods is the method by which the information capacity of the latent representation is minimized or limited. In this work, the rank of the covariance matrix of the codes is implicitly minimized by relying on the fact that gradient descent learning in multi-layer linear networks leads to minimum-rank solutions. By inserting a number of extra linear layers between the encoder and the decoder, the system spontaneously learns representations with a low effective dimension. The model, dubbed Implicit Rank-Minimizing Autoencoder (IRMAE), is simple, deterministic, and learns continuous latent space. We demonstrate the validity of the method on several image generation and representation learning tasks.

We propose a novel unsupervised generative model that learns to disentangle object identity from other low-level aspects in class-imbalanced data. We first investigate the issues surrounding the assumptions about uniformity made by InfoGAN, and demonstrate its ineffectiveness to properly disentangle object identity in imbalanced data. Our key idea is to make the discovery of the discrete latent factor of variation invariant to identity-preserving transformations in real images, and use that as a signal to learn the appropriate latent distribution representing object identity. Experiments on both artificial (MNIST, 3D cars, 3D chairs, ShapeNet) and real-world (YouTube-Faces) imbalanced datasets demonstrate the effectiveness of our method in disentangling object identity as a latent factor of variation.

Many problems in machine learning (ML) can be cast as learning functions from sets to graphs, or more generally to hypergraphs; in short, Set2Graph functions. Examples include clustering, learning vertex and edge features on graphs, and learning features on triplets in a collection.

A natural approach for building Set2Graph models is to characterize all linear equivariant set-to-hypergraph layers and stack them with non-linear activations. This posses two challenges: (i) the expressive power of these networks is not well understood; and (ii) these models would suffer from high, often intractable computational and memory complexity, as their dimension grows exponentially.

This paper advocates a family of neural network models for learning Set2Graph functions that is both practical and of maximal expressive power (universal), that is, can approximate arbitrary continuous Set2Graph functions over compact sets. Testing these models on different machine learning tasks, mainly an application to particle physics, we find them favorable to existing baselines.

Generative Adversarial Networks (GANs) struggle to generate structured objects like molecules and game maps. The issue is that structured objects must satisfy hard requirements (e.g., molecules must be chemically valid) that are difficult to acquire from examples alone. As a remedy, we propose Constrained Adversarial Networks (CANs), an extension of GANs in which the constraints are embedded into the model during training. This is achieved by penalizing the generator proportionally to the mass it allocates to invalid structures. In contrast to other generative models, CANs support efficient inference of valid structures (with high probability) and allows to turn on and off the learned constraints at inference time. CANs handle arbitrary logical constraints and leverage knowledge compilation techniques to efficiently evaluate the disagreement between the model and the constraints. Our setup is further extended to hybrid logical-neural constraints for capturing very complex constraints, like graph reachability. An extensive empirical analysis shows that CANs efficiently generate valid structures that are both high-quality and novel.

Despite success on a wide range of problems related to vision, generative adversarial networks (GANs) often suffer from inferior performance due to unstable training, especially for text generation. To solve this issue, we propose a new variational GAN training framework which enjoys superior training stability. Our approach is inspired by a connection of GANs and reinforcement learning under a variational perspective. The connection leads to (1) probability ratio clipping that regularizes generator training to prevent excessively large updates, and (2) a sample re-weighting mechanism that improves discriminator training by downplaying bad-quality fake samples. Moreover, our variational GAN framework can provably overcome the training issue in many GANs that an optimal discriminator cannot provide any informative gradient to training generator. By plugging the training approach in diverse state-of-the-art GAN architectures, we obtain significantly improved performance over a range of tasks, including text generation, text style transfer, and image generation.

Our understanding of learning input-output relationships with neural nets has improved rapidly in recent years, but little is known about the convergence of the underlying representations, even in the simple case of linear autoencoders (LAEs). We show that when trained with proper regularization, LAEs can directly learn the optimal representation -- ordered, axis-aligned principal components. We analyze two such regularization schemes: non-uniform L2 regularization and a deterministic variant of nested dropout [Rippel et al, ICML' 2014]. Though both regularization schemes converge to the optimal representation, we show that this convergence is slow due to ill-conditioning that worsens with increasing latent dimension. We show that the inefficiency of learning the optimal representation is not inevitable -- we present a simple modification to the gradient descent update that greatly speeds up convergence empirically.

Knowledge base completion (KBC) aims to automatically infer missing facts by exploiting information already present in a knowledge base (KB). A promising approach for KBC is to embed knowledge into latent spaces and make predictions from learned embeddings. However, existing embedding models are subject to at least one of the following limitations: (1) theoretical inexpressivity, (2) lack of support for prominent inference patterns (e.g., hierarchies), (3) lack of support for KBC over higher-arity relations, and (4) lack of support for incorporating logical rules. Here, we propose a spatio-translational embedding model, called BoxE, that simultaneously addresses all these limitations. BoxE embeds entities as points, and relations as a set of hyper-rectangles (or boxes), which spatially characterize basic logical properties. This seemingly simple abstraction yields a fully expressive model offering a natural encoding for many desired logical properties. BoxE can both capture and inject rules from rich classes of rule languages, going well beyond individual inference patterns. By design, BoxE naturally applies to higher-arity KBs. We conduct a detailed experimental analysis, and show that BoxE achieves state-of-the-art performance, both on benchmark knowledge graphs and on more general KBs, and we empirically show the power of integrating logical rules.

We present BlockGAN, an image generative model that learns object-aware 3D scene representations directly from unlabelled 2D images. Current work on scene representation learning either ignores scene background or treats the whole scene as one object. Meanwhile, work that considers scene compositionality treats scene objects only as image patches or 2D layers with alpha maps. Inspired by the computer graphics pipeline, we design BlockGAN to learn to first generate 3D features of background and foreground objects, then combine them into 3D features for the whole scene, and finally render them into realistic images. This allows BlockGAN to reason over occlusion and interaction between objects’ appearance, such as shadow and lighting, and provides control over each object’s 3D pose and identity, while maintaining image realism. BlockGAN is trained end-to-end, using only unlabelled single images, without the need for 3D geometry, pose labels, object masks, or multiple views of the same scene. Our experiments show that using explicit 3D features to represent objects allows BlockGAN to learn disentangled representations both in terms of objects (foreground and background) and their properties (pose and identity).

Learning object-centric representations of multi-object scenes is a promising approach towards machine intelligence, facilitating high-level reasoning and control from visual sensory data. However, current approaches for \textit{unsupervised object-centric scene representation} are incapable of aggregating information from multiple observations of a scene. As a result, these ``single-view'' methods form their representations of a 3D scene based only on a single 2D observation (view). Naturally, this leads to several inaccuracies, with these methods falling victim to single-view spatial ambiguities. To address this, we propose \textit{The Multi-View and Multi-Object Network (MulMON)}---a method for learning accurate, object-centric representations of multi-object scenes by leveraging multiple views. In order to sidestep the main technical difficulty of the \textit{multi-object-multi-view} scenario---maintaining object correspondences across views---MulMON iteratively updates the latent object representations for a scene over multiple views. To ensure that these iterative updates do indeed aggregate spatial information to form a complete 3D scene understanding, MulMON is asked to predict the appearance of the scene from novel viewpoints during training. Through experiments we show that MulMON better-resolves spatial ambiguities than single-view methods---learning more accurate and disentangled object representations---and also achieves new functionality in predicting object segmentations for novel viewpoints.

This paper introduces Deep Statistical Solvers (DSS), a new class of trainable solvers for optimization problems, arising e.g., from system simulations. The key idea is to learn a solver that generalizes to a given distribution of problem instances. This is achieved by directly using as loss the objective function of the problem, as opposed to most previous Machine Learning based approaches, which mimic the solutions attained by an existing solver. Though both types of approaches outperform classical solvers with respect to speed for a given accuracy, a distinctive advantage of DSS is that they can be trained without a training set of sample solutions. Focusing on use cases of systems of interacting and interchangeable entities (e.g. molecular dynamics, power systems, discretized PDEs), the proposed approach is instantiated within a class of Graph Neural Networks. Under sufficient conditions, we prove that the corresponding set of functions contains approximations to any arbitrary precision of the actual solution of the optimization problem. The proposed approach is experimentally validated on large linear problems, demonstrating super-generalisation properties; And on AC power grid simulations, on which the predictions of the trained model have a correlation higher than 99.99% with the outputs of the classical Newton-Raphson method (known for its accuracy), while being 2 to 3 orders of magnitude faster.

Graphical models are widely used in science to represent joint probability distributions with an underlying conditional dependence structure. The inverse problem of learning a discrete graphical model given i.i.d samples from its joint distribution can be solved with near-optimal sample complexity using a convex optimization method known as Generalized Regularized Interaction Screening Estimator (GRISE). But the computational cost of GRISE becomes prohibitive when the energy function of the true graphical model has higher order terms. We introduce NeurISE, a neural net based algorithm for graphical model learning, to tackle this limitation of GRISE. We use neural nets as function approximators in an Interaction Screening objective function. The optimization of this objective then produces a neural-net representation for the conditionals of the graphical model. NeurISE algorithm is seen to be a better alternative to GRISE when the energy function of the true model has a high order with a high degree of symmetry. In these cases NeurISE is able to find the correct parsimonious representation for the conditionals without being fed any prior information about the true model. NeurISE can also be used to learn the underlying structure of the true model with some simple modifications to its training procedure. In addition, we also show a variant of NeurISE that can be used to learn a neural net representation for the full energy function of the true model.

Training neural network models with discrete (categorical or structured) latent variables can be computationally challenging, due to the need for marginalization over large or combinatorial sets. To circumvent this issue, one typically resorts to sampling-based approximations of the true marginal, requiring noisy gradient estimators (e.g., score function estimator) or continuous relaxations with lower-variance reparameterized gradients (e.g., Gumbel-Softmax). In this paper, we propose a new training strategy which replaces these estimators by an exact yet efficient marginalization. To achieve this, we parameterize discrete distributions over latent assignments using differentiable sparse mappings: sparsemax and its structured counterparts. In effect, the support of these distributions is greatly reduced, which enables efficient marginalization. We report successful results in three tasks covering a range of latent variable modeling applications: a semisupervised deep generative model, a latent communication game, and a generative model with a bit-vector latent representation. In all cases, we obtain good performance while still achieving the practicality of sampling-based approximations.

Homomorphic Encryption (HE) based secure Neural Networks(NNs) inference is one of the most promising security solutions to emerging Machine Learning as a Service (MLaaS). In the HE-based MLaaS setting, a client encrypts the sensitive data, and uploads the encrypted data to the server that directly processes the encrypted data without decryption, and returns the encrypted result to the client. The clients' data privacy is preserved since only the client has the private key. Existing HE-enabled Neural Networks (HENNs), however, suffer from heavy computational overheads. The state-of-the-art HENNs adopt ciphertext packing techniques to reduce homomorphic multiplications by packing multiple messages into one single ciphertext. Nevertheless, rotations are required in these HENNs to implement the sum of the elements within the same ciphertext. We observed that HENNs have to pay significant computing overhead on rotations, and each of rotations is $\sim 10\times$ more expensive than homomorphic multiplications between ciphertext and plaintext. So the massive rotations have become a primary obstacle of efficient HENNs. In this paper, we propose a fast, frequency-domain deep neural network called Falcon, for fast inferences on encrypted data. Falcon includes a fast Homomorphic Discrete Fourier Transform (HDFT) using block-circulant matrices to homomorphically support spectral operations. We also propose several efficient methods to reduce inference latency, including Homomorphic Spectral Convolution and Homomorphic Spectral Fully Connected operations by combing the batched HE and block-circulant matrices. Our experimental results show Falcon achieves the state-of-the-art inference accuracy and reduces the inference latency by $45.45\%\sim 85.34\%$ over prior HENNs on MNIST and CIFAR-10.

Finding accurate solutions to partial differential equations (PDEs) is a crucial task in all scientific and engineering disciplines. It has recently been shown that machine learning methods can improve the solution accuracy by correcting for effects not captured by the discretized PDE. We target the problem of reducing numerical errors of iterative PDE solvers and compare different learning approaches for finding complex correction functions. We find that previously used learning approaches are significantly outperformed by methods that integrate the solver into the training loop and thereby allow the model to interact with the PDE during training. This provides the model with realistic input distributions that take previous corrections into account, yielding improvements in accuracy with stable rollouts of several hundred recurrent evaluation steps and surpassing even tailored supervised variants. We highlight the performance of the differentiable physics networks for a wide variety of PDEs, from non-linear advection-diffusion systems to three-dimensional Navier-Stokes flows.

Meta-materials are an important emerging class of engineered materials in which complex macroscopic behaviour--whether electromagnetic, thermal, or mechanical--arises from modular substructure. Simulation and optimization of these materials are computationally challenging, as rich substructures necessitate high-fidelity finite element meshes to solve the governing PDEs. To address this, we leverage parametric modular structure to learn component-level surrogates, enabling cheaper high-fidelity simulation. We use a neural network to model the stored potential energy in a component given boundary conditions. This yields a structured prediction task: macroscopic behavior is determined by the minimizer of the system's total potential energy, which can be approximated by composing these surrogate models. Composable energy surrogates thus permit simulation in the reduced basis of component boundaries. Costly ground-truth simulation of the full structure is avoided, as training data are generated by performing finite element analysis of individual components. Using dataset aggregation to choose training data allows us to learn energy surrogates which produce accurate macroscopic behavior when composed, accelerating simulation of parametric meta-materials.

One difficulty in using artificial agents for human-assistive applications lies in the challenge of accurately assisting with a person's goal(s). Existing methods tend to rely on inferring the human's goal, which is challenging when there are many potential goals or when the set of candidate goals is difficult to identify. We propose a new paradigm for assistance by instead increasing the human's ability to control their environment, and formalize this approach by augmenting reinforcement learning with human empowerment. This task-agnostic objective increases the person's autonomy and ability to achieve any eventual state. We test our approach against assistance based on goal inference, highlighting scenarios where our method overcomes failure modes stemming from goal ambiguity or misspecification. As existing methods for estimating empowerment in continuous domains are computationally hard, precluding its use in real time learned assistance, we also propose an efficient empowerment-inspired proxy metric. Using this, we are able to successfully demonstrate our method in a shared autonomy user study for a challenging simulated teleoperation task with human-in-the-loop training.

Effective intersection control can play an important role in reducing traffic congestion and associated vehicular emissions. This is vitally needed in developing countries, where air pollution is reaching life threatening levels. This paper presents EcoLight intersection control for developing regions, where budget is constrained and network connectivity is very poor. EcoLight learns effective control offline using state-of-the-art Deep Reinforcement Learning methods, but deploys highly efficient runtime control algorithms on low cost embedded devices that work stand-alone on road without server connectivity. EcoLight optimizes both average case and worst case values of throughput, travel time and other metrics, as evaluated on open-source datasets from New York and on a custom developing region dataset.

Retrosynthesis is the process of recursively decomposing target molecules into available building blocks. It plays an important role in solving problems in organic synthesis planning. To automate or assist in the retrosynthesis analysis, various retrosynthesis prediction algorithms have been proposed. However, most of them are cumbersome and lack interpretability about their predictions. In this paper, we devise a novel template-free algorithm for automatic retrosynthetic expansion inspired by how chemists approach retrosynthesis prediction. Our method disassembles retrosynthesis into two steps: i) identify the potential reaction center of the target molecule through a novel graph neural network and generate intermediate synthons, and ii) generate the reactants associated with synthons via a robust reactant generation model. While outperforming the state-of-the-art baselines by a significant margin, our model also provides chemically reasonable interpretation.

When designing new molecules with particular properties, it is not only important what to make but crucially how to make it. These instructions form a synthesis directed acyclic graph (DAG), describing how a large vocabulary of simple building blocks can be recursively combined through chemical reactions to create more complicated molecules of interest. In contrast, many current deep generative models for molecules ignore synthesizability. We therefore propose a deep generative model that better represents the real world process, by directly outputting molecule synthesis DAGs. We argue that this provides sensible inductive biases, ensuring that our model searches over the same chemical space that chemists would also have access to, as well as interpretability. We show that our approach is able to model chemical space well, producing a wide range of diverse molecules, and allows for unconstrained optimization of an inherently constrained problem: maximize certain chemical properties such that discovered molecules are synthesizable.

Block-based visual programming environments play a critical role in introducing computing concepts to K-12 students. One of the key pedagogical challenges in these environments is in designing new practice tasks for a student that match a desired level of difficulty and exercise specific programming concepts. In this paper, we formalize the problem of synthesizing visual programming tasks. In particular, given a reference visual task $\task^{in}$ and its solution code $\code^{in}$, we propose a novel methodology to automatically generate a set $\{(\task^{out}, \code^{out})\}$ of new tasks along with solution codes such that tasks $\task^{in}$ and $\task^{out}$ are conceptually similar but visually dissimilar. Our methodology is based on the realization that the mapping from the space of visual tasks to their solution codes is highly discontinuous; hence, directly mutating reference task $\task^{in}$ to generate new tasks is futile. Our task synthesis algorithm operates by first mutating code $\code^{in}$ to obtain a set of codes $\{\code^{out}\}$. Then, the algorithm performs symbolic execution over a code $\code^{out}$ to obtain a visual task $\task^{out}$; this step uses the Monte Carlo Tree Search (MCTS) procedure to guide the search in the symbolic tree. We demonstrate the effectiveness of our algorithm through an extensive empirical evaluation and user study on reference tasks taken from the Hour of Code: Classic Maze challenge by Code.org and the Intro to Programming with Karel course by CodeHS.com.

We present a deep imitation learning framework for robotic bimanual manipulation in a continuous state-action space. A core challenge is to generalize the manipulation skills to objects in different locations. We hypothesize that modeling the relational information in the environment can significantly improve generalization. To achieve this, we propose to (i) decompose the multi-modal dynamics into elemental movement primitives, (ii) parameterize each primitive using a recurrent graph neural network to capture interactions, and (iii) integrate a high-level planner that composes primitives sequentially and a low-level controller to combine primitive dynamics and inverse kinematics control. Our model is a deep, hierarchical, modular architecture. Compared to baselines, our model generalizes better and achieves higher success rates on several simulated bimanual robotic manipulation tasks. We open source the code for simulation, data, and models at: https://github.com/Rose-STL-Lab/HDR-IL.

Predicting the motion of agents such as pedestrians or human-driven vehicles is one of the most critical problems in the autonomous driving domain. The overall safety of driving and the comfort of a passenger directly depend on its successful solution. The motion prediction problem also remains one of the most challenging problems in autonomous driving engineering, mainly due to high variance of the possible agent’s future behavior given a situation. The two phenomena responsible for the said variance are the multimodality caused by the uncertainty of the agent’s intent (e.g., turn right or move forward) and uncertainty in the realization of a given intent (e.g., which lane to turn into). To be useful within a real-time autonomous driving pipeline, a motion prediction system must provide efficient ways to describe and quantify this uncertainty, such as computing posterior modes and their probabilities or estimating density at the point corresponding to a given trajectory. It also should not put substantial density on physically impossible trajectories, as they can confuse the system processing the predictions. In this paper, we introduce the PRANK method, which satisfies these requirements. PRANK takes rasterized bird-eye images of agent’s surroundings as an input and extracts features of the scene with a convolutional neural network. It then produces the conditional distribution of agent’s trajectories plausible in the given scene. The key contribution of PRANK is a way to represent that distribution using nearest-neighbor methods in latent trajectory space, which allows for efficient inference in real time. We evaluate PRANK on the in-house and Argoverse datasets, where it shows competitive results.

Memory-based meta-learning is a powerful technique to build agents that adapt fast to any task within a target distribution. A previous theoretical study has argued that this remarkable performance is because the meta-training protocol incentivises agents to behave Bayes-optimally. We empirically investigate this claim on a number of prediction and bandit tasks. Inspired by ideas from theoretical computer science, we show that meta-learned and Bayes-optimal agents not only behave alike, but they even share a similar computational structure, in the sense that one agent system can approximately simulate the other. Furthermore, we show that Bayes-optimal agents are fixed points of the meta-learning dynamics. Our results suggest that memory-based meta-learning is a general technique for numerically approximating Bayes-optimal agents; that is, even for task distributions for which we currently don't possess tractable models.

In this study, we demonstrate that the linear combination of atomic orbitals (LCAO), an approximation introduced by Pauling and Lennard-Jones in the 1920s, corresponds to graph convolutional networks (GCNs) for molecules. However, GCNs involve unnecessary nonlinearity and deep architecture. We also verify that molecular GCNs are based on a poor basis function set compared with the standard one used in theoretical calculations or quantum chemical simulations. From these observations, we describe the quantum deep field (QDF), a machine learning (ML) model based on an underlying quantum physics, in particular the density functional theory (DFT). We believe that the QDF model can be easily understood because it can be regarded as a single linear layer GCN. Moreover, it uses two vanilla feedforward neural networks to learn an energy functional and a Hohenberg--Kohn map that have nonlinearities inherent in quantum physics and the DFT. For molecular energy prediction tasks, we demonstrated the viability of an ``extrapolation,'' in which we trained a QDF model with small molecules, tested it with large molecules, and achieved high extrapolation performance. We believe that we should move away from the competition of interpolation accuracy within benchmark datasets and evaluate ML models based on physics using an extrapolation setting; this will lead to reliable and practical applications, such as fast, large-scale molecular screening for discovering effective materials.

Biological brains are inherently limited in their capacity to process and store information, but are nevertheless capable of solving complex tasks with apparent ease. Intelligent behavior is related to these limitations, since resource constraints drive the need to generalize and assign importance differentially to features in the environment or memories of past experiences. Recently, there have been parallel efforts in reinforcement learning and neuroscience to understand strategies adopted by artificial and biological agents to circumvent limitations in information storage. However, the two threads have been largely separate. In this article, we propose a dynamical framework to maximize expected reward under constraints of limited resources, which we implement with a cost function that penalizes precise representations of action-values in memory, each of which may vary in its precision. We derive from first principles an algorithm, Dynamic Resource Allocator (DRA), which we apply to two standard tasks in reinforcement learning and a model-based planning task, and find that it allocates more resources to items in memory that have a higher impact on cumulative rewards. Moreover, DRA learns faster when starting with a higher resource budget than what it eventually allocates for performing well on tasks, which may explain why frontal cortical areas in biological brains appear more engaged in early stages of learning before settling to lower asymptotic levels of activity. Our work provides a normative solution to the problem of learning how to allocate costly resources to a collection of uncertain memories in a manner that is capable of adapting to changes in the environment.

Ensembles of geophysical models improve projection accuracy and express uncertainties. We develop a novel data-driven ensembling strategy for combining geophysical models using Bayesian Neural Networks, which infers spatiotemporally varying model weights and bias while accounting for heteroscedastic uncertainties in the observations. This produces more accurate and uncertainty-aware projections without sacrificing interpretability. Applied to the prediction of total column ozone from an ensemble of 15 chemistry-climate models, we find that the Bayesian neural network ensemble (BayNNE) outperforms existing ensembling methods, achieving a 49.4% reduction in RMSE for temporal extrapolation, and a 67.4% reduction in RMSE for polar data voids, compared to a weighted mean. Uncertainty is also well-characterized, with 90.6% of the data points in our extrapolation validation dataset lying within 2 standard deviations and 98.5% within 3 standard deviations.

We study the problem of inferring communication structures that can solve cooperative multi-agent planning problems while minimizing the amount of communication. We quantify the amount of communication as the maximum degree of the communication graph; this metric captures settings where agents have limited bandwidth. Minimizing communication is challenging due to the combinatorial nature of both the decision space and the objective; for instance, we cannot solve this problem by training neural networks using gradient descent. We propose a novel algorithm that synthesizes a control policy that combines a programmatic communication policy used to generate the communication graph with a transformer policy network used to choose actions. Our algorithm first trains the transformer policy, which implicitly generates a "soft" communication graph; then, it synthesizes a programmatic communication policy that "hardens" this graph, forming a neurosymbolic transformer. Our experiments demonstrate how our approach can synthesize policies that generate low-degree communication graphs while maintaining near-optimal performance.

Designing reward functions is difficult: the designer has to specify what to do (what it means to complete the task) as well as what not to do (side effects that should be avoided while completing the task). To alleviate the burden on the reward designer, we propose an algorithm to automatically generate an auxiliary reward function that penalizes side effects. This auxiliary objective rewards the ability to complete possible future tasks, which decreases if the agent causes side effects during the current task. The future task reward can also give the agent an incentive to interfere with events in the environment that make future tasks less achievable, such as irreversible actions by other agents. To avoid this interference incentive, we introduce a baseline policy that represents a default course of action (such as doing nothing), and use it to filter out future tasks that are not achievable by default. We formally define interference incentives and show that the future task approach with a baseline policy avoids these incentives in the deterministic case. Using gridworld environments that test for side effects and interference, we show that our method avoids interference and is more effective for avoiding side effects than the common approach of penalizing irreversible actions.

We present a novel form of explanation for Reinforcement Learning, based around the notion of intended outcome. These explanations describe the outcome an agent is trying to achieve by its actions. We provide a simple proof that general methods for post-hoc explanations of this nature are impossible in traditional reinforcement learning. Rather, the information needed for the explanations must be collected in conjunction with training the agent. We derive approaches designed to extract local explanations based on intention for several variants of Q-function approximation and prove consistency between the explanations and the Q-values learned. We demonstrate our method on multiple reinforcement learning problems, and provide code to help researchers introspecting their RL environments and algorithms.

Neural sequence-to-sequence models are well established for applications which can be cast as mapping a single input sequence into a single output sequence. In this work, we focus on one-to-many sequence transduction problems, such as extracting multiple sequential sources from a mixture sequence. We extend the standard sequence-to-sequence model to a conditional multi-sequence model, which explicitly models the relevance between multiple output sequences with the probabilistic chain rule. Based on this extension, our model can conditionally infer output sequences one-by-one by making use of both input and previously-estimated contextual output sequences. This model additionally has a simple and efficient stop criterion for the end of the transduction, making it able to infer the variable number of output sequences. We take speech data as a primary test field to evaluate our methods since the observed speech data is often composed of multiple sources due to the nature of the superposition principle of sound waves. Experiments on several different tasks including speech separation and multi-speaker speech recognition show that our conditional multi-sequence models lead to consistent improvements over the conventional non-conditional models.

In many natural domains, changing a small part of an entity can transform its semantics; for example, a single word change can alter the meaning of a sentence, or a single amino acid change can mutate a viral protein to escape antiviral treatment or immunity. Although identifying such mutations can be desirable (for example, therapeutic design that anticipates avenues of viral escape), the rules governing semantic change are often hard to quantify. Here, we introduce the problem of identifying mutations with a large effect on semantics, but where valid mutations are under complex constraints (for example, English grammar or biological viability), which we refer to as constrained semantic change search (CSCS). We propose an unsupervised solution based on language models that simultaneously learn continuous latent representations. We report good empirical performance on CSCS of single-word mutations to news headlines, map a continuous semantic space of viral variation, and, notably, show unprecedented zero-shot prediction of single-residue escape mutations to key influenza and HIV proteins, suggesting a productive link between modeling natural language and pathogenic evolution.

While neural conversation models have shown great potentials towards generating informative and engaging responses via introducing external knowledge, learning such a model often requires knowledge-grounded dialogues that are difficult to obtain. To overcome the data challenge and reduce the cost of building a knowledge-grounded dialogue system, we explore the problem under a zero-resource setting by assuming no context-knowledge-response triples are needed for training. To this end, we propose representing the knowledge that bridges a context and a response and the way that the knowledge is expressed as latent variables, and devise a variational approach that can effectively estimate a generation model from independent dialogue corpora and knowledge corpora. Evaluation results on three benchmarks of knowledge-grounded dialogue generation indicate that our model can achieve comparable performance with state-of-the-art methods that rely on knowledge-grounded dialogues for training, and exhibits a good generalization ability over different datasets.

For mental disorders, patients' underlying mental states are non-observed latent constructs which have to be inferred from observed multi-domain measurements such as diagnostic symptoms and patient functioning scores. Additionally, substantial heterogeneity in the disease diagnosis between patients needs to be addressed for optimizing individualized treatment policy in order to achieve precision medicine. To address these challenges, we propose an integrated learning framework that can simultaneously learn patients' underlying mental states and recommend optimal treatments for each individual. This learning framework is based on the measurement theory in psychiatry for modeling multiple disease diagnostic measures as arising from the underlying causes (true mental states). It allows incorporation of the multivariate pre- and post-treatment outcomes as well as biological measures while preserving the invariant structure for representing patients' latent mental states. A multi-layer neural network is used to allow complex treatment effect heterogeneity. Optimal treatment policy can be inferred for future patients by comparing their potential mental states under different treatments given the observed multi-domain pre-treatment measurements. Experiments on simulated data and a real-world clinical trial data show that the learned treatment polices compare favorably to alternative methods on heterogeneous treatment effects, and have broad utilities which lead to better patient outcomes on multiple domains.

In this work, we study the causal relations among German regions in terms of the spread of Covid-19 since the beginning of the pandemic, taking into account the restriction policies that were applied by the different federal states. We loose a strictly formulated assumption for a causal feature selection method for time series data, robust to latent confounders, which we subsequently apply on Covid-19 case numbers. We present findings about the spread of the virus in Germany and the causal impact of restriction measures, discussing the role of various policies in containing the spread. Since our results are based on rather limited target time series (only the numbers of reported cases), care should be exercised in interpreting them. However, it is encouraging that already such limited data seems to contain causal signals. This suggests that as more data becomes available, our causal approach may contribute towards meaningful causal analysis of political interventions on the development of Covid-19, and thus also towards the development of rational and data-driven methodologies for choosing interventions.

We propose to jointly analyze experts' eye movements and verbal narrations to discover important and interpretable knowledge patterns to better understand their decision-making processes. The discovered patterns can further enhance data-driven statistical models by fusing experts' domain knowledge to support complex human-machine collaborative decision-making. Our key contribution is a novel dynamic Bayesian nonparametric model that assigns latent knowledge patterns into key phases involved in complex decision-making. Each phase is characterized by a unique distribution of word topics discovered from verbal narrations and their dynamic interactions with eye movement patterns, indicating experts' special perceptual behavior within a given decision-making stage. A new split-merge-switch sampler is developed to efficiently explore the posterior state space with an improved mixing rate. Case studies on diagnostic error prediction and disease morphology categorization help demonstrate the effectiveness of the proposed model and discovered knowledge patterns.

Survival analysis models the distribution of time until an event of interest, such as discharge from the hospital or admission to the ICU. When a model’s predicted number of events within any time interval is similar to the observed number, it is called well-calibrated. A survival model’s calibration can be measured using, for instance, distributional calibration (D-CALIBRATION) [Haider et al., 2020] which computes the squared difference between the observed and predicted number of events within different time intervals. Classically, calibration is addressed in post-training analysis. We develop explicit calibration (X-CAL), which turns D-CALIBRATION into a differentiable objective that can be used in survival modeling alongside maximum likelihood estimation and other objectives. X-CAL allows us to directly optimize calibration and strike a desired trade-off between predictive power and calibration. In our experiments, we fit a variety of shallow and deep models on simulated data, a survival dataset based on MNIST, on length-of-stay prediction using MIMIC-III data, and on brain cancer data from The Cancer Genome Atlas. We show that the models we study can be miscalibrated. We give experimental evidence on these datasets that X-CAL improves D-CALIBRATION without a large decrease in concordance or likelihood.

In today’s clinical practice, magnetic resonance imaging (MRI) is routinely accelerated through subsampling of the associated Fourier domain. Currently, the construction of these subsampling strategies - known as experimental design - relies primarily on heuristics. We propose to learn experimental design strategies for accelerated MRI with policy gradient methods. Unexpectedly, our experiments show that a simple greedy approximation of the objective leads to solutions nearly on-par with the more general non-greedy approach. We offer a partial explanation for this phenomenon rooted in greater variance in the non-greedy objective's gradient estimates, and experimentally verify that this variance hampers non-greedy models in adapting their policies to individual MR images. We empirically show that this adaptivity is key to improving subsampling designs.

To what extent are effectiveness estimates of nonpharmaceutical interventions (NPIs) against COVID-19 influenced by the assumptions our models make? To answer this question, we investigate 2 state-of-the-art NPI effectiveness models and propose 6 variants that make different structural assumptions. In particular, we investigate how well NPI effectiveness estimates generalise to unseen countries, and their sensitivity to unobserved factors. Models that account for noise in disease transmission compare favourably. We further evaluate how robust estimates are to different choices of epidemiological parameters and data. Focusing on models that assume transmission noise, we find that previously published results are remarkably robust across these variables. Finally, we mathematically ground the interpretation of NPI effectiveness estimates when certain common assumptions do not hold.

Transplant-organs are a scarce medical resource. The uniqueness of each organ and the patients' heterogeneous responses to the organs present a unique and challenging machine learning problem. In this problem there are two key challenges: (i) assigning each organ "optimally" to a patient in the queue; (ii) accurately estimating the potential outcomes associated with each patient and each possible organ. In this paper, we introduce OrganITE, an organ-to-patient assignment methodology that assigns organs based not only on its own estimates of the potential outcomes but also on organ scarcity. By modelling and accounting for organ scarcity we significantly increase total life years across the population, compared to the existing greedy approaches that simply optimise life years for the current organ available. Moreover, we propose an individualised treatment effect model capable of addressing the high dimensionality of the organ space. We test our method on real and simulated data, resulting in as much as an additional year of life expectancy as compared to existing organ-to-patient policies.

Counterpoint is an important concept in Western music theory. In the past century, there have been significant interests in incorporating counterpoint into Chinese folk music composition. In this paper, we propose a reinforcement learning-based system, named FolkDuet, towards the online countermelody generation for Chinese folk melodies. With no existing data of Chinese folk duets, FolkDuet employs two reward models based on out-of-domain data, i.e. Bach chorales, and monophonic Chinese folk melodies. An interaction reward model is trained on the duets formed from outer parts of Bach chorales to model counterpoint interaction, while a style reward model is trained on monophonic melodies of Chinese folk songs to model melodic patterns. With both rewards, the generator of FolkDuet is trained to generate countermelodies while maintaining the Chinese folk style. The entire generation process is performed in an online fashion, allowing real-time interactive human-machine duet improvisation. Experiments show that the proposed algorithm achieves better subjective and objective results than the baselines.

In this paper, we propose Patience-based Early Exit, a straightforward yet effective inference method that can be used as a plug-and-play technique to simultaneously improve the efficiency and robustness of a pretrained language model (PLM). To achieve this, our approach couples an internal-classifier with each layer of a PLM and dynamically stops inference when the intermediate predictions of the internal classifiers do not change for a pre-defined number of steps. Our approach improves inference efficiency as it allows the model to make a prediction with fewer layers. Meanwhile, experimental results with an ALBERT model show that our method can improve the accuracy and robustness of the model by preventing it from overthinking and exploiting multiple classifiers for prediction, yielding a better accuracy-speed trade-off compared to existing early exit methods.

In this work, we propose TGLS, a novel framework for unsupervised Text Generation by Learning from Search. We start by applying a strong search algorithm (in particular, simulated annealing) towards a heuristically defined objective that (roughly) estimates the quality of sentences. Then, a conditional generative model learns from the search results, and meanwhile smooth out the noise of search. The alternation between search and learning can be repeated for performance bootstrapping. We demonstrate the effectiveness of TGLS on two real-world natural language generation tasks, unsupervised paraphrasing and text formalization. Our model significantly outperforms unsupervised baseline methods in both tasks. Especially, it achieves comparable performance to strong supervised methods for paraphrase generation.

To what extent can a neural network systematically reason over symbolic facts? Evidence suggests that large pre-trained language models (LMs) acquire some reasoning capacity, but this ability is difficult to control. Recently, it has been shown that Transformer-based models succeed in consistent reasoning over explicit symbolic facts, under a "closed-world" assumption. However, in an open-domain setup, it is desirable to tap into the vast reservoir of implicit knowledge already encoded in the parameters of pre-trained LMs. In this work, we provide a first demonstration that LMs can be trained to reliably perform systematic reasoning combining both implicit, pre-trained knowledge and explicit natural language statements.
To do this, we describe a procedure for automatically generating datasets that teach a model new reasoning skills, and demonstrate that models learn to effectively perform inference which involves implicit taxonomic and world knowledge, chaining and counting. Finally, we show that "teaching" models to reason generalizes beyond the training distribution: they successfully compose the usage of multiple reasoning skills in single examples. Our work paves a path towards open-domain systems that constantly improve by interacting with users who can instantly correct a model by adding simple natural language statements.

Speech synthesis is an important practical generative modeling problem that has seen great progress over the last few years, with likelihood-based autoregressive neural models now outperforming traditional concatenative systems. A downside of such autoregressive models is that they require executing tens of thousands of sequential operations per second of generated audio, making them ill-suited for deployment on specialized deep learning hardware. Here, we propose a new learning method that allows us to train highly parallel models of speech, without requiring access to an analytical likelihood function. Our approach is based on a generalized energy distance between the distributions of the generated and real audio. This spectral energy distance is a proper scoring rule with respect to the distribution over magnitude-spectrograms of the generated waveform audio and offers statistical consistency guarantees. The distance can be calculated from minibatches without bias, and does not involve adversarial learning, yielding a stable and consistent method for training implicit generative models. Empirically, we achieve state-of-the-art generation quality among implicit generative models, as judged by the recently-proposed cFDSD metric. When combining our method with adversarial techniques, we also improve upon the recently-proposed GAN-TTS model in terms of Mean Opinion Score as judged by trained human evaluators.

Compositional generalization is a basic and essential intellective capability of human beings, which allows us to recombine known parts readily. However, existing neural network based models have been proven to be extremely deficient in such a capability. Inspired by work in cognition which argues compositionality can be captured by variable slots with symbolic functions, we present a refreshing view that connects a memory-augmented neural model with analytical expressions, to achieve compositional generalization. Our model consists of two cooperative neural modules, Composer and Solver, fitting well with the cognitive argument while being able to be trained in an end-to-end manner via a hierarchical reinforcement learning algorithm. Experiments on the well-known benchmark SCAN demonstrate that our model seizes a great ability of compositional generalization, solving all challenges addressed by previous works with 100% accuracies.

We present a new operator-free, measure-theoretic approach to the conditional mean embedding as a random variable taking values in a reproducing kernel Hilbert space. While the kernel mean embedding of marginal distributions has been defined rigorously, the existing operator-based approach of the conditional version lacks a rigorous treatment, and depends on strong assumptions that hinder its analysis. Our approach does not impose any of the assumptions that the operator-based counterpart requires. We derive a natural regression interpretation to obtain empirical estimates, and provide a thorough analysis of its properties, including universal consistency with improved convergence rates. As natural by-products, we obtain the conditional analogues of the Maximum Mean Discrepancy and Hilbert-Schmidt Independence Criterion, and demonstrate their behaviour via simulations.

We study the risk (i.e. generalization error) of Kernel Ridge Regression (KRR) for a kernel $K$ with ridge $\lambda>0$ and i.i.d. observations. For this, we introduce two objects: the Signal Capture Threshold (SCT) and the Kernel Alignment Risk Estimator (KARE). The SCT $\vartheta_{K,\lambda}$ is a function of the data distribution: it can be used to identify the components of the data that the KRR predictor captures, and to approximate the (expected) KRR risk. This then leads to a KRR risk approximation by the KARE $\rho_{K, \lambda}$, an explicit function of the training data, agnostic of the true data distribution. We phrase the regression problem in a functional setting. The key results then follow from a finite-size adaptation of the resolvent method for general Wishart random matrices. Under a natural universality assumption (that the KRR moments depend asymptotically on the first two moments of the observations) we capture the mean and variance of the KRR predictor. We numerically investigate our findings on the Higgs and MNIST datasets for various classical kernels: the KARE gives an excellent approximation of the risk. This supports our universality hypothesis. Using the KARE, one can compare choices of Kernels and hyperparameters directly from the training set. The KARE thus provides a promising data-dependent procedure to select Kernels that generalize well.

We prove new explicit upper bounds on the leverage scores of Fourier sparse functions under both the Gaussian and Laplace measures. In particular, we study s-sparse functions of the form $f(x) = \sum_{j=1}^s a_j e^{i \lambda_j x}$ for coefficients $a_j \in C$ and frequencies $\lambda_j \in R$. Bounding Fourier sparse leverage scores under various measures is of pure mathematical interest in approximation theory, and our work extends existing results for the uniform measure [Erd17,CP19a]. Practically, our bounds are motivated by two important applications in machine learning: 1. Kernel Approximation. They yield a new random Fourier features algorithm for approximating Gaussian and Cauchy (rational quadratic) kernel matrices. For low-dimensional data, our method uses a near optimal number of features, and its runtime is polynomial in the *statistical dimension* of the approximated kernel matrix. It is the first ``oblivious sketching method'' with this property for any kernel besides the polynomial kernel, resolving an open question of [AKM+17,AKK+20b]. 2. Active Learning. They can be used as non-uniform sampling distributions for robust active learning when data follows a Gaussian or Laplace distribution. Using the framework of [AKM+19], we provide essentially optimal results for bandlimited and multiband interpolation, and Gaussian process regression. These results generalize existing work that only applies to uniformly distributed data.

Orthogonal Monte Carlo (OMC) is a very effective sampling algorithm imposing structural geometric conditions (orthogonality) on samples for variance reduction. Due to its simplicity and superior performance as compared to its Quasi Monte Carlo counterparts, OMC is used in a wide spectrum of challenging machine learning applications ranging from scalable kernel methods to predictive recurrent neural networks, generative models and reinforcement learning. However theoretical understanding of the method remains very limited. In this paper we shed new light on the theoretical principles behind OMC, applying theory of negatively dependent random variables to obtain several new concentration results. As a corollary, we manage to obtain first uniform convergence results for OMCs and consequently, substantially strengthen best known downstream guarantees for kernel ridge regression via OMCs. We also propose novel extensions of the method leveraging theory of algebraic varieties over finite fields and particle algorithms, called Near-Orthogonal Monte Carlo (NOMC). We show that NOMC is the first algorithm consistently outperforming OMC in applications ranging from kernel methods to approximating distances in probabilistic metric spaces.

Cortical networks are strongly recurrent, and neurons have intrinsic temporal dynamics. This sets them apart from deep feed-forward networks. Despite the tremendous progress in the application of deep feed-forward networks and their theoretical understanding, it remains unclear how the interplay of recurrence and non-linearities in recurrent cortical networks contributes to their function. The purpose of this work is to present a solvable recurrent network model that links to feed forward networks. By perturbative methods we transform the time-continuous, recurrent dynamics into an effective feed-forward structure of linear and non-linear temporal kernels. The resulting analytical expressions allow us to build optimal time-series classifiers from random reservoir networks. Firstly, this allows us to optimize not only the readout vectors, but also the input projection, demonstrating a strong potential performance gain. Secondly, the analysis exposes how the second order stimulus statistics is a crucial element that interacts with the non-linearity of the dynamics and boosts performance.

Data augmentation has become an important part of modern deep learning pipelines and is typically needed to achieve state of the art performance for many learning tasks. It utilizes invariant transformations of the data, such as rotation, scale, and color shift, and the transformed images are added to the training set. However, these transformations are often chosen heuristically and a clear theoretical framework to explain the performance benefits of data augmentation is not available. In this paper, we develop such a framework to explain data augmentation as averaging over the orbits of the group that keeps the data distribution approximately invariant, and show that it leads to variance reduction. We study finite-sample and asymptotic empirical risk minimization and work out as examples the variance reduction in certain two-layer neural networks. We further propose a strategy to exploit the benefits of data augmentation for general learning tasks.

Classical learning theory suggests that the optimal generalization performance of a machine learning model should occur at an intermediate model complexity, with simpler models exhibiting high bias and more complex models exhibiting high variance of the predictive function. However, such a simple trade-off does not adequately describe deep learning models that simultaneously attain low bias and variance in the heavily overparameterized regime. A primary obstacle in explaining this behavior is that deep learning algorithms typically involve multiple sources of randomness whose individual contributions are not visible in the total variance. To enable fine-grained analysis, we describe an interpretable, symmetric decomposition of the variance into terms associated with the randomness from sampling, initialization, and the labels. Moreover, we compute the high-dimensional asymptotic behavior of this decomposition for random feature kernel regression, and analyze the strikingly rich phenomenology that arises. We find that the bias decreases monotonically with the network width, but the variance terms exhibit non-monotonic behavior and can diverge at the interpolation boundary, even in the absence of label noise. The divergence is caused by the interaction between sampling and initialization and can therefore be eliminated by marginalizing over samples (i.e. bagging) or over the initial parameters (i.e. ensemble learning).

A recent line of research has highlighted the existence of a ``double descent'' phenomenon in deep learning, whereby increasing the number of training examples N causes the generalization error of neural networks to peak when N is of the same order as the number of parameters P. In earlier works, a similar phenomenon was shown to exist in simpler models such as linear regression, where the peak instead occurs when N is equal to the input dimension D. Since both peaks coincide with the interpolation threshold, they are often conflated in the litterature. In this paper, we show that despite their apparent similarity, these two scenarios are inherently different. In fact, both peaks can co-exist when neural networks are applied to noisy regression tasks. The relative size of the peaks is then governed by the degree of nonlinearity of the activation function. Building on recent developments in the analysis of random feature models, we provide a theoretical ground for this sample-wise triple descent. As shown previously, the nonlinear peak at N=P is a true divergence caused by the extreme sensitivity of the output function to both the noise corrupting the labels and the initialization of the random features (or the weights in neural networks). This peak survives in the absence of noise, but can be suppressed by regularization. In contrast, the linear peak at N=D is solely due to overfitting the noise in the labels, and forms earlier during training. We show that this peak is implicitly regularized by the nonlinearity, which is why it only becomes salient at high noise and is weakly affected by explicit regularization. Throughout the paper, we compare the analytical results obtained in the random feature model with the outcomes of numerical experiments involving realistic neural networks.

Training recurrent neural networks (RNNs) on low-dimensional tasks has been widely used to model functional biological networks. However, the solutions found by learning and the effect of initial connectivity are not well understood. Here, we examine RNNs trained using gradient descent on different tasks inspired by the neuroscience literature. We find that the changes in recurrent connectivity can be described by low-rank matrices. This observation holds even in the presence of random initial connectivity, although this initial connectivity has full rank and significantly accelerates training. To understand the origin of these observations, we turn to an analytically tractable setting: training a linear RNN on a simpler task. We show how the low-dimensional task structure leads to low-rank changes to connectivity, and how random initial connectivity facilitates learning. Altogether, our study opens a new perspective to understand learning in RNNs in light of low-rank connectivity changes and the synergistic role of random initialization.

This article characterizes the exact asymptotics of random Fourier feature (RFF) regression, in the realistic setting where the number of data samples $n$, their dimension $p$, and the dimension of feature space $N$ are all large and comparable. In this regime, the random RFF Gram matrix no longer converges to the well-known limiting Gaussian kernel matrix (as it does when $N \to \infty$ alone), but it still has a tractable behavior that is captured by our analysis. This analysis also provides accurate estimates of training and test regression errors for large $n,p,N$. Based on these estimates, a precise characterization of two qualitatively different phases of learning, including the phase transition between them, is provided; and the corresponding double descent test error curve is derived from this phase transition behavior. These results do not depend on strong assumptions on the data distribution, and they perfectly match empirical results on real-world data sets.

For a certain scaling of the initialization of stochastic gradient descent (SGD), wide neural networks (NN) have been shown to be well approximated by reproducing kernel Hilbert space (RKHS) methods. Recent empirical work showed that, for some classification tasks, RKHS methods can replace NNs without a large loss in performance. On the other hand, two-layers NNs are known to encode richer smoothness classes than RKHS and we know of special examples for which SGD-trained NN provably outperform RKHS. This is true even in the wide network limit, for a different scaling of the initialization.

How can we reconcile the above claims? For which tasks do NNs outperform RKHS? If covariates are nearly isotropic, RKHS methods suffer from the curse of dimensionality, while NNs can overcome it by learning the best low-dimensional representation. Here we show that this curse of dimensionality becomes milder if the covariates display the same low-dimensional structure as the target function, and we precisely characterize this tradeoff. Building on these results, we present the spiked covariates model that can capture in a unified framework both behaviors observed in earlier works.

We hypothesize that such a latent low-dimensional structure is present in image classification. We numerically test this hypothesis by showing that specific perturbations of the training distribution degrade the performances of RKHS methods much more significantly than NNs.

This paper studies the statistical complexity of kernel hyperparameter tuning in the setting of active regression under adversarial noise. We consider the problem of finding the best interpolant from a class of kernels with unknown hyperparameters, assuming only that the noise is square-integrable. We provide finite-sample guarantees for the problem, characterizing how increasing the complexity of the kernel class increases the complexity of learning kernel hyperparameters. For common kernel classes (e.g. squared-exponential kernels with unknown lengthscale), our results show that hyperparameter optimization increases sample complexity by just a logarithmic factor, in comparison to the setting where optimal parameters are known in advance. Our result is based on a subsampling guarantee for linear regression under multiple design matrices which may be of independent interest.

This paper studies two-layers Neural Networks (NN), where the first layer contains random weights, and the second layer is trained using Ridge regularization. This model has been the focus of numerous recent works, showing that despite its simplicity, it captures some of the empirically observed behaviors of NN in the overparametrized regime, such as the double-descent curve where the generalization error decreases as the number of weights increases to $+\infty$. This paper establishes asymptotic distribution results for this 2-layers NN model in the regime where the ratios $\frac p n$ and $\frac d n$ have finite limits, where $n$ is the sample size, $p$ the ambient dimension and $d$ is the width of the first layer. We show that a weighted average of the derivatives of the trained NN at the observed data is asymptotically normal, in a setting with Lipschitz activation functions in a linear regression response with Gaussian features under possibly non-linear perturbations. We then leverage this asymptotic normality result to construct confidence intervals (CIs) for single components of the unknown regression vector. The novelty of our results are threefold: (1) Despite the nonlinearity induced by the activation function, we characterize the asymptotic distribution of a weighted average of the gradients of the network after training; (2) It provides the first frequentist uncertainty quantification guarantees, in the form of valid ($1\text{-}\alpha$)-CIs, based on NN estimates; (3) It shows that the double-descent phenomenon occurs in terms of the length of the CIs, with the length increasing and then decreasing as $\frac d n\nearrow +\infty$ for certain fixed values of $\frac p n$. We also provide a toolbox to predict the length of CIs numerically, which lets us compare activation functions and other parameters in terms of CI length.

We investigate the problem of testing the global null in the high-dimensional regression models when the feature dimension $p$ grows proportionally to the number of observations $n$. Despite a number of prior work studying this problem, whether there exists a test that is model-agnostic, efficient to compute and enjoys a high power, still remains unsettled. In this paper, we answer this question in the affirmative by leveraging the random projection techniques, and propose a testing procedure that blends the classical $F$-test with a random projection step. When combined with a systematic choice of the projection dimension, the proposed procedure is proved to be minimax optimal and, meanwhile, reduces the computation and data storage requirements. We illustrate our results in various scenarios when the underlying feature matrix exhibits an intrinsic lower dimensional structure (such as approximate low-rank or has exponential/polynomial eigen-decay), and it turns out that the proposed test achieves sharp adaptive rates. Our theoretical findings are further validated by comparisons to other state-of-the-art tests on synthetic data.

We consider the theory of regression on a manifold using reproducing kernel Hilbert space methods. Manifold models arise in a wide variety of modern machine learning problems, and our goal is to help understand the effectiveness of various implicit and explicit dimensionality-reduction methods that exploit manifold structure. Our first key contribution is to establish a novel nonasymptotic version of the Weyl law from differential geometry. From this we are able to show that certain spaces of smooth functions on a manifold are effectively finite-dimensional, with a complexity that scales according to the manifold dimension rather than any ambient data dimension. Finally, we show that given (potentially noisy) function values taken uniformly at random over a manifold, a kernel regression estimator (derived from the spectral decomposition of the manifold) yields minimax-optimal error bounds that are controlled by the effective dimension.

Neural networks have been shown to perform incredibly well in classification tasks over structured high-dimensional datasets. However, the learning dynamics of such networks is still poorly understood. In this paper we study in detail the training dynamics of a simple type of neural network: a single hidden layer trained to perform a classification task. We show that in a suitable mean-field limit this case maps to a single-node learning problem with a time-dependent dataset determined self-consistently from the average nodes population. We specialize our theory to the prototypical case of a linearly separable dataset and a linear hinge loss, for which the dynamics can be explicitly solved in the infinite dataset limit. This allow us to address in a simple setting several phenomena appearing in modern networks such as slowing down of training dynamics, crossover between feature and lazy learning, and overfitting. Finally, we asses the limitations of mean-field theory by studying the case of large but finite number of nodes and of training samples.

We consider a covariate shift problem where one has access to several different training datasets for the same learning problem and a small validation set which possibly differs from all the individual training distributions. The distribution shift is due, in part, to \emph{unobserved} features in the datasets. The objective, then, is to find the best mixture distribution over the training datasets (with only observed features) such that training a learning algorithm using this mixture has the best validation performance. Our proposed algorithm, \textsf{Mix\&Match}, combines stochastic gradient descent (SGD) with optimistic tree search and model re-use (evolving partially trained models with samples from different mixture distributions) over the space of mixtures, for this task. We prove a novel high probability bound on the final SGD iterate without relying on a global gradient norm bound, and use it to show the advantages of model re-use. Additionally, we provide simple regret guarantees for our algorithm with respect to recovering the optimal mixture, given a total budget of SGD evaluations. Finally, we validate our algorithm on two real-world datasets.

This paper presents one-bit supervision, a novel setting of learning from incomplete annotations, in the scenario of image classification. Instead of training a model upon the accurate label of each sample, our setting requires the model to query with a predicted label of each sample and learn from the answer whether the guess is correct. This provides one bit (yes or no) of information, and more importantly, annotating each sample becomes much easier than finding the accurate label from many candidate classes. There are two keys to training a model upon one-bit supervision: improving the guess accuracy and making use of incorrect guesses. For these purposes, we propose a multi-stage training paradigm which incorporates negative label suppression into an off-the-shelf semi-supervised learning algorithm. In three popular image classification benchmarks, our approach claims higher efficiency in utilizing the limited amount of annotations.

Multi-Source Domain Adaptation (MSDA) deals with the transfer of task knowledge from multiple labeled source domains to an unlabeled target domain, under a domain-shift. Existing methods aim to minimize this domain-shift using auxiliary distribution alignment objectives. In this work, we present a different perspective to MSDA wherein deep models are observed to implicitly align the domains under label supervision. Thus, we aim to utilize implicit alignment without additional training objectives to perform adaptation. To this end, we use pseudo-labeled target samples and enforce a classifier agreement on the pseudo-labels, a process called Self-supervised Implicit Alignment (SImpAl). We find that SImpAl readily works even under category-shift among the source domains. Further, we propose classifier agreement as a cue to determine the training convergence, resulting in a simple training algorithm. We provide a thorough evaluation of our approach on five benchmarks, along with detailed insights into each component of our approach.

We propose a novel framework to perform classification via deep learning in the presence of noisy annotations. When trained on noisy labels, deep neural networks have been observed to first fit the training data with clean labels during an "early learning" phase, before eventually memorizing the examples with false labels. We prove that early learning and memorization are fundamental phenomena in high-dimensional classification tasks, even in simple linear models, and give a theoretical explanation in this setting. Motivated by these findings, we develop a new technique for noisy classification tasks, which exploits the progress of the early learning phase. In contrast with existing approaches, which use the model output during early learning to detect the examples with clean labels, and either ignore or attempt to correct the false labels, we take a different route and instead capitalize on early learning via regularization. There are two key elements to our approach. First, we leverage semi-supervised learning techniques to produce target probabilities based on the model outputs. Second, we design a regularization term that steers the model towards these targets, implicitly preventing memorization of the false labels. The resulting framework is shown to provide robustness to noisy annotations on several standard benchmarks and real-world datasets, where it achieves results comparable to the state of the art.

We develop a novel generative model for zero-shot learning to recognize fine-grained unseen classes without training samples. Our observation is that generating holistic features of unseen classes fails to capture every attribute needed to distinguish small differences among classes. We propose a feature composition framework that learns to extract attribute-based features from training samples and combines them to construct fine-grained features for unseen classes. Feature composition allows us to not only selectively compose features of unseen classes from only relevant training samples, but also obtain diversity among composed features via changing samples used for composition. In addition, instead of building a global feature of an unseen class, we use all attribute-based features to form a dense representation consisting of fine-grained attribute details. To recognize unseen classes, we propose a novel training scheme that uses a discriminative model to construct features that are subsequently used to train itself. Therefore, we directly train the discriminative model on composed features without learning separate generative models. We conduct experiments on four popular datasets of DeepFashion, AWA2, CUB, and SUN, showing that our method significantly improves the state of the art.

Unsupervised domain adaptation methods traditionally assume that all source categories are present in the target domain. In practice, little may be known about the category overlap between the two domains. While some methods address target settings with either partial or open-set categories, they assume that the particular setting is known a priori. We propose a more universally applicable domain adaptation approach that can handle arbitrary category shift, called Domain Adaptative Neighborhood Clustering via Entropy optimization (DANCE). Our approach combines two novel ideas: First, as we cannot fully rely on source categories to learn features discriminative for the target, we propose a novel neighborhood clustering technique to learn the structure of the target domain in a self-supervised way. Second, we use entropy-based feature alignment and rejection to align target features with the source, or reject them as unknown categories based on their entropy. We show through extensive experiments that DANCE outperforms baselines across open-set, open-partial and partial domain adaptation settings.

Adversarial learning has demonstrated good performance in the unsupervised domain adaptation setting, by learning domain-invariant representations. However, recent work has shown limitations of this approach when label distributions differ between the source and target domains. In this paper, we propose a new assumption, \textit{generalized label shift} ($\glsa$), to improve robustness against mismatched label distributions. $\glsa$ states that, conditioned on the label, there exists a representation of the input that is invariant between the source and target domains. Under $\glsa$, we provide theoretical guarantees on the transfer performance of any classifier. We also devise necessary and sufficient conditions for $\glsa$ to hold, by using an estimation of the relative class weights between domains and an appropriate reweighting of samples. Our weight estimation method could be straightforwardly and generically applied in existing domain adaptation (DA) algorithms that learn domain-invariant representations, with small computational overhead. In particular, we modify three DA algorithms, JAN, DANN and CDAN, and evaluate their performance on standard and artificial DA tasks. Our algorithms outperform the base versions, with vast improvements for large label distribution mismatches. Our code is available at \url{https://tinyurl.com/y585xt6j}.

People easily recognize new visual categories that are new combinations of known components. This compositional generalization capacity is critical for learning in real-world domains like vision and language because the long tail of new combinations dominates the distribution. Unfortunately, learning systems struggle with compositional generalization because they often build on features that are correlated with class labels even if they are not "essential" for the class. This leads to consistent misclassification of samples from a new distribution, like new combinations of known components.

Here we describe an approach for compositional generalization that builds on causal ideas. First, we describe compositional zero-shot learning from a causal perspective, and propose to view zero-shot inference as finding "which intervention caused the image?". Second, we present a causal-inspired embedding model that learns disentangled representations of elementary components of visual objects from correlated (confounded) training data. We evaluate this approach on two datasets for predicting new combinations of attribute-object pairs: A well-controlled synthesized images dataset and a real world dataset which consists of fine-grained types of shoes. We show improvements compared to strong baselines.

Self-supervised learning aims to learn good representations with unlabeled data. Recent works have shown that larger models benefit more from self-supervised learning than smaller models. As a result, the gap between supervised and self-supervised learning has been greatly reduced for larger models. In this work, instead of designing a new pseudo task for self-supervised learning, we develop a model compression method to compress an already learned, deep self-supervised model (teacher) to a smaller one (student). We train the student model so that it mimics the relative similarity between the datapoints in the teacher's embedding space. For AlexNet, our method outperforms all previous methods including the fully supervised model on ImageNet linear evaluation (59.0% compared to 56.5%) and on nearest neighbor evaluation (50.7% compared to 41.4%). To the best of our knowledge, this is the first time a self-supervised AlexNet has outperformed supervised one on ImageNet classification. Our code is available here: https://github.com/UMBCvision/CompRess

One paradigm for learning from few labeled examples while making best use of a large amount of unlabeled data is unsupervised pretraining followed by supervised fine-tuning. Although this paradigm uses unlabeled data in a task-agnostic way, in contrast to common approaches to semi-supervised learning for computer vision, we show that it is surprisingly effective for semi-supervised learning on ImageNet. A key ingredient of our approach is the use of big (deep and wide) networks during pretraining and fine-tuning. We find that, the fewer the labels, the more this approach (task-agnostic use of unlabeled data) benefits from a bigger network. After fine-tuning, the big network can be further improved and distilled into a much smaller one with little loss in classification accuracy by using the unlabeled examples for a second time, but in a task-specific way. The proposed semi-supervised learning algorithm can be summarized in three steps: unsupervised pretraining of a big ResNet model using SimCLRv2, supervised fine-tuning on a few labeled examples, and distillation with unlabeled examples for refining and transferring the task-specific knowledge. This procedure achieves 73.9% ImageNet top-1 accuracy with just 1% of the labels ($\le$13 labeled images per class) using ResNet-50, a 10X improvement in label efficiency over the previous state-of-the-art. With 10% of labels, ResNet-50 trained with our method achieves 77.5% top-1 accuracy, outperforming standard supervised training with all of the labels.

Partial-label learning (PLL) is a multi-class classification problem, where each training example is associated with a set of candidate labels. Even though many practical PLL methods have been proposed in the last two decades, there lacks a theoretical understanding of the consistency of those methods - none of the PLL methods hitherto possesses a generation process of candidate label sets, and then it is still unclear why such a method works on a specific dataset and when it may fail given a different dataset. In this paper, we propose the first generation model of candidate label sets, and develop two PLL methods that are guaranteed to be provably consistent, i.e., one is risk-consistent and the other is classifier-consistent. Our methods are advantageous, since they are compatible with any deep network or stochastic optimizer. Furthermore, thanks to the generation model, we would be able to answer the two questions above by testing if the generation model matches given candidate label sets. Experiments on benchmark and real-world datasets validate the effectiveness of the proposed generation model and two PLL methods.

We present a novel multi-source uncertainty prediction approach that enables deep learning (DL) models to be actively trained with much less labeled data. By leveraging the second-order uncertainty representation provided by subjective logic (SL), we conduct evidence-based theoretical analysis and formally decompose the predicted entropy over multiple classes into two distinct sources of uncertainty: vacuity and dissonance, caused by lack of evidence and conflict of strong evidence, respectively. The evidence based entropy decomposition provides deeper insights on the nature of uncertainty, which can help effectively explore a large and high-dimensional unlabeled data space. We develop a novel loss function that augments DL based evidence prediction with uncertainty anchor sample identification. The accurately estimated multiple sources of uncertainty are systematically integrated and dynamically balanced using a data sampling function for label-efficient active deep learning (ADL). Experiments conducted over both synthetic and real data and comparison with competitive AL methods demonstrate the effectiveness of the proposed ADL model.

A transcompiler, also known as source-to-source translator, is a system that converts source code from a high-level programming language (such as C++ or Python) to another. Transcompilers are primarily used for interoperability, and to port codebases written in an obsolete or deprecated language (e.g. COBOL, Python 2) to a modern one. They typically rely on handcrafted rewrite rules, applied to the source code abstract syntax tree. Unfortunately, the resulting translations often lack readability, fail to respect the target language conventions, and require manual modifications in order to work properly. The overall translation process is time-consuming and requires expertise in both the source and target languages, making code-translation projects expensive. Although neural models significantly outperform their rule-based counterparts in the context of natural language translation, their applications to transcompilation have been limited due to the scarcity of parallel data in this domain. In this paper, we propose to leverage recent approaches in unsupervised machine translation to train a fully unsupervised neural transcompiler. We train our model on source code from open source GitHub projects, and show that it can translate functions between C++, Java, and Python with high accuracy. Our method relies exclusively on monolingual source code, requires no expertise in the source or target languages, and can easily be generalized to other programming languages. We also build and release a test set composed of 852 parallel functions, along with unit tests to check the correctness of translations. We show that our model outperforms rule-based commercial baselines by a significant margin.

Recent success of pre-trained language models crucially hinges on fine-tuning them on large amounts of labeled data for the downstream task, that are typically expensive to acquire or difficult to access for many applications. We study self-training as one of the earliest semi-supervised learning approaches to reduce the annotation bottleneck by making use of large-scale unlabeled data for the target task. Standard self-training mechanism randomly samples instances from the unlabeled pool to generate pseudo-labels and augment labeled data. We propose an approach to improve self-training by incorporating uncertainty estimates of the underlying neural network leveraging recent advances in Bayesian deep learning. Specifically, we propose (i) acquisition functions to select instances from the unlabeled pool leveraging Monte Carlo (MC) Dropout, and (ii) learning mechanism leveraging model confidence for self-training. As an application, we focus on text classification with five benchmark datasets. We show our methods leveraging only 20-30 labeled samples per class for each task for training and for validation perform within 3% of fully supervised pre-trained language models fine-tuned on thousands of labels with an aggregate accuracy of 91% and improvement of up to 12% over baselines.

Discriminatively localizing sounding objects in cocktail-party, i.e., mixed sound scenes, is commonplace for humans, but still challenging for machines. In this paper, we propose a two-stage learning framework to perform self-supervised class-aware sounding object localization. First, we propose to learn robust object representations by aggregating the candidate sound localization results in the single source scenes. Then, class-aware object localization maps are generated in the cocktail-party scenarios by referring the pre-learned object knowledge, and the sounding objects are accordingly selected by matching audio and visual object category distributions, where the audiovisual consistency is viewed as the self-supervised signal. Experimental results in both realistic and synthesized cocktail-party videos demonstrate that our model is superior in filtering out silent objects and pointing out the location of sounding objects of different classes. Code is available at https://github.com/DTaoo/Discriminative-Sounding-Objects-Localization.

Generative adversarial networks (GANs) were originally envisioned as unsupervised generative models that learn to follow a target distribution. Variants such as conditional GANs, auxiliary-classifier GANs (ACGANs) project GANs on to supervised and semi-supervised learning frameworks by providing labelled data and using multi-class discriminators. In this paper, we approach the supervised GAN problem from a different perspective, one that is motivated by the philosophy of the famous Persian poet Rumi who said, "The art of knowing is knowing what to ignore." In the GAN framework, we not only provide the GAN positive data that it must learn to model, but also present it with so-called negative samples that it must learn to avoid — we call this "The Rumi Framework." This formulation allows the discriminator to represent the underlying target distribution better by learning to penalize generated samples that are undesirable — we show that this capability accelerates the learning process of the generator. We present a reformulation of the standard GAN (SGAN) and least-squares GAN (LSGAN) within the Rumi setting. The advantage of the reformulation is demonstrated by means of experiments conducted on MNIST, Fashion MNIST, CelebA, and CIFAR-10 datasets. Finally, we consider an application of the proposed formulation to address the important problem of learning an under-represented class in an unbalanced dataset. The Rumi approach results in substantially lower FID scores than the standard GAN frameworks while possessing better generalization capability.

Given a discrete probability measure supported on $N$ atoms and a set of $n$ real-valued functions, there exists a probability measure that is supported on a subset of $n+1$ of the original $N$ atoms and has the same mean when integrated against each of the $n$ functions. If $ N \gg n$ this results in a huge reduction of complexity. We give a simple geometric characterization of barycenters via negative cones and derive a randomized algorithm that computes this new measure by ``greedy geometric sampling''. We then study its properties, and benchmark it on synthetic and real-world data to show that it can be very beneficial in the $N\gg n$ regime. A Python implementation is available at \url{https://github.com/FraCose/Recombination_Random_Algos}.

We investigate stochastic combinatorial multi-armed bandit with semi-bandit feedback (CMAB). In CMAB, the question of the existence of an efficient policy with an optimal asymptotic regret (up to a factor poly-logarithmic with the action size) is still open for many families of distributions, including mutually independent outcomes, and more generally the multivariate \emph{sub-Gaussian} family. We propose to answer the above question for these two families by analyzing variants of the Combinatorial Thompson Sampling policy (CTS). For mutually independent outcomes in $[0,1]$, we propose a tight analysis of CTS using Beta priors. We then look at the more general setting of multivariate sub-Gaussian outcomes and propose a tight analysis of CTS using Gaussian priors. This last result gives us an alternative to the Efficient Sampling for Combinatorial Bandit policy (ESCB), which, although optimal, is not computationally efficient.

We consider the problem of online learning and its application to solving minimax games. For the online learning problem, Follow the Perturbed Leader (FTPL) is a widely studied algorithm which enjoys the optimal $O(T^{1/2})$ \emph{worst case} regret guarantee for both convex and nonconvex losses. In this work, we show that when the sequence of loss functions is \emph{predictable}, a simple modification of FTPL which incorporates optimism can achieve better regret guarantees, while retaining the optimal worst-case regret guarantee for unpredictable sequences. A key challenge in obtaining these tighter regret bounds is the stochasticity and optimism in the algorithm, which requires different analysis techniques than those commonly used in the analysis of FTPL. The key ingredient we utilize in our analysis is the dual view of perturbation as regularization. While our algorithm has several applications, we consider the specific application of minimax games. For solving smooth convex-concave games, our algorithm only requires access to a linear optimization oracle. For Lipschitz and smooth nonconvex-nonconcave games, our algorithm requires access to an optimization oracle which computes the perturbed best response. In both these settings, our algorithm solves the game up to an accuracy of $O(T^{-1/2})$ using $T$ calls to the optimization oracle. An important feature of our algorithm is that it is highly parallelizable and requires only $O(T^{1/2})$ iterations, with each iteration making $O(T^{1/2})$ parallel calls to the optimization oracle.

We provide online convex optimization algorithms that guarantee improved full-matrix regret bounds. These algorithms extend prior work in several ways. First, we seamlessly allow for the incorporation of constraints without requiring unknown oracle-tuning for any learning rate parameters. Second, we improve the regret of the full-matrix AdaGrad algorithm by suggesting a better learning rate value and showing how to tune the learning rate to this value on-the-fly. Third, all our bounds are obtained via a general framework for constructing regret bounds that depend on an arbitrary sequence of norms.

One of the main strengths of online algorithms is their ability to adapt to arbitrary data sequences. This is especially important in nonparametric settings, where performance is measured against rich classes of comparator functions that are able to fit complex environments. Although such hard comparators and complex environments may exhibit local regularities, efficient algorithms, which can provably take advantage of these local patterns, are hardly known. We fill this gap by introducing efficient online algorithms (based on a single versatile master algorithm) each adapting to one of the following regularities: (i) local Lipschitzness of the competitor function, (ii) local metric dimension of the instance sequence, (iii) local performance of the predictor across different regions of the instance space. Extending previous approaches, we design algorithms that dynamically grow hierarchical ε-nets on the instance space whose prunings correspond to different “locality profiles” for the problem at hand. Using a technique based on tree experts, we simultaneously and efficiently compete against all such prunings, and prove regret bounds each scaling with a quantity associated with a different type of local regularity. When competing against “simple” locality profiles, our technique delivers regret bounds that are significantly better than those proven using the previous approach. On the other hand, the time dependence of our bounds is not worse than that obtained by ignoring any local regularities.

We study the problem of online learning with primary and secondary losses. For example, a recruiter making decisions of which job applicants to hire might weigh false positives and false negatives equally (the primary loss) but the applicants might weigh false negatives much higher (the secondary loss). We consider the following question: Can we combine ``expert advice'' to achieve low regret with respect to the primary loss, while at the same time performing {\em not much worse than the worst expert} with respect to the secondary loss? Unfortunately, we show that this goal is unachievable without any bounded variance assumption on the secondary loss. More generally, we consider the goal of minimizing the regret with respect to the primary loss and bounding the secondary loss by a linear threshold. On the positive side, we show that running any switching-limited algorithm can achieve this goal if all experts satisfy the assumption that the secondary loss does not exceed the linear threshold by $o(T)$ for any time interval. If not all experts satisfy this assumption, our algorithms can achieve this goal given access to some external oracles which determine when to deactivate and reactivate experts.

We study an online linear optimization (OLO) problem in which the learner is provided access to $K$ ``hint'' vectors in each round prior to making a decision. In this setting, we devise an algorithm that obtains logarithmic regret whenever there exists a convex combination of the $K$ hints that has positive correlation with the cost vectors. This significantly extends prior work that considered only the case $K=1$. To accomplish this, we develop a way to combine many arbitrary OLO algorithms to obtain regret only a logarithmically worse factor than the minimum regret of the original algorithms in hindsight; this result is of independent interest.

We present \textproc{Gaptron}, a randomized first-order algorithm for online multiclass classification. In the full information setting we provide expected mistake bounds for \textproc{Gaptron} with respect to the logistic loss, hinge loss, and the smooth hinge loss with $O(K)$ regret, where the expectation is with respect to the learner's randomness and $K$ is the number of classes. In the bandit classification setting we show that \textproc{Gaptron} is the first linear time algorithm with $O(K\sqrt{T})$ expected regret. Additionally, the expected mistake bound of \textproc{Gaptron} does not depend on the dimension of the feature vector, contrary to previous algorithms with $O(K\sqrt{T})$ regret in the bandit classification setting. We present a new proof technique that exploits the gap between the zero-one loss and surrogate losses rather than exploiting properties such as exp-concavity or mixability, which are traditionally used to prove logarithmic or constant regret bounds.

In the setting of online learning, Implicit algorithms turn out to be highly successful from a practical standpoint. However, the tightest regret analyses only show marginal improvements over Online Mirror Descent. In this work, we shed light on this behavior carrying out a careful regret analysis. We prove a novel static regret bound that depends on the temporal variability of the sequence of loss functions, a quantity which is often encountered when considering dynamic competitors. We show, for example, that the regret can be constant if the temporal variability is constant and the learning rate is tuned appropriately, without the need of smooth losses. Moreover, we present an adaptive algorithm that achieves this regret bound without prior knowledge of the temporal variability and prove a matching lower bound. Finally, we validate our theoretical findings on classification and regression datasets.

We revisit the fundamental problem of prediction with expert advice, in a setting where the environment is benign and generates losses stochastically, but the feedback observed by the learner is subject to a moderate adversarial corruption. We prove that a variant of the classical Multiplicative Weights algorithm with decreasing step sizes achieves constant regret in this setting and performs optimally in a wide range of environments, regardless of the magnitude of the injected corruption. Our results reveal a surprising disparity between the often comparable Follow the Regularized Leader (FTRL) and Online Mirror Descent (OMD) frameworks: we show that for experts in the corrupted stochastic regime, the regret performance of OMD is in fact strictly inferior to that of FTRL.

Automatic differentiation, as implemented today, does not have a simple mathematical model adapted to the needs of modern machine learning. In this work we articulate the relationships between differentiation of programs as implemented in practice, and differentiation of nonsmooth functions. To this end we provide a simple class of functions, a nonsmooth calculus, and show how they apply to stochastic approximation methods. We also evidence the issue of artificial critical points created by algorithmic differentiation and show how usual methods avoid these points with probability one.

We consider the problem of online learning with non-convex losses. In terms of feedback, we assume that the learner observes – or otherwise constructs – an inexact model for the loss function encountered at each stage, and we propose a mixed-strategy learning policy based on dual averaging. In this general context, we derive a series of tight regret minimization guarantees, both for the learner’s static (external) regret, as well as the regret incurred against the best dynamic policy in hindsight. Subsequently, we apply this general template to the case where the learner only has access to the actual loss incurred at each stage of the process. This is achieved by means of a kernel-based estimator which generates an inexact model for each round’s loss function using only the learner’s realized losses as input.

Reducing the variance of the gradient estimator is known to improve the convergence rate of stochastic gradient-based optimization and sampling algorithms. One way of achieving variance reduction is to design importance sampling strategies. Recently, the problem of designing such schemes was formulated as an online learning problem with bandit feedback, and algorithms with sub-linear static regret were designed. In this work, we build on this framework and propose a simple and efficient algorithm for adaptive importance sampling for finite-sum optimization and sampling with decreasing step-sizes. Under standard technical conditions, we show that our proposed algorithm achieves O(T^{2/3}) and O(T^{5/6}) dynamic regret for SGD and SGLD respectively when run with O(1/t) step sizes. We achieve this dynamic regret bound by leveraging our knowledge of the dynamics defined by the algorithm, and combining ideas from online learning and variance-reduced stochastic optimization. We validate empirically the performance of our algorithm and identify settings in which it leads to significant improvements.

The rapid proliferation of decentralized learning systems mandates the need for differentially-private cooperative learning. In this paper, we study this in context of the contextual linear bandit: we consider a collection of agents cooperating to solve a common contextual bandit, while ensuring that their communication remains private. For this problem, we devise FedUCB, a multiagent private algorithm for both centralized and decentralized (peer-to-peer) federated learning. We provide a rigorous technical analysis of its utility in terms of regret, improving several results in cooperative bandit learning, and provide rigorous privacy guarantees as well. Our algorithms provide competitive performance both in terms of pseudoregret bounds and empirical benchmark performance in various multi-agent settings.

We address the question of repeatedly learning linear classifiers against agents who are \emph{strategically} trying to \emph{game} the deployed classifiers, and we use the \emph{Stackelberg regret} to measure the performance of our algorithms. First, we show that Stackelberg and external regret for the problem of strategic classification are \emph{strongly incompatible}: i.e., there exist worst-case scenarios, where \emph{any} sequence of actions providing \emph{sublinear} external regret might result in \emph{linear} Stackelberg regret and vice versa. Second, we present a strategy-aware algorithm for minimizing the Stackelberg regret for which we prove nearly matching upper and lower regret bounds. Finally, we provide simulations to complement our theoretical analysis. Our results advance the growing literature of learning from revealed preferences, which has so far focused on ``smoother'' assumptions from the perspective of the learner and the agents respectively.

Neural architecture search (NAS) enables researchers to automatically explore broad design spaces in order to improve efficiency of neural networks. This efficiency is especially important in the case of on-device deployment, where improvements in accuracy should be balanced out with computational demands of a model. In practice, performance metrics of model are computationally expensive to obtain. Previous work uses a proxy (e.g., number of operations) or a layer-wise measurement of neural network layers to estimate end-to-end hardware performance but the imprecise prediction diminishes the quality of NAS. To address this problem, we propose BRP-NAS, an efficient hardware-aware NAS enabled by an accurate performance predictor-based on graph convolutional network (GCN). What is more, we investigate prediction quality on different metrics and show that sample efficiency of the predictor-based NAS can be improved by considering binary relations of models and an iterative data selection strategy. We show that our proposed method outperforms all prior methods on NAS-Bench-101 and NAS-Bench-201, and that our predictor can consistently learn to extract useful features from the DARTS search space, improving upon the second-order baseline. Finally, to raise awareness of the fact that accurate latency estimation is not a trivial task, we release LatBench -- a latency dataset of NAS-Bench-201 models running on a broad range of devices.

Neural Architecture Search (NAS) was first proposed to achieve state-of-the-art performance through the discovery of new architecture patterns, without human intervention. An over-reliance on expert knowledge in the search space design has however led to increased performance (local optima) without significant architectural breakthroughs, thus preventing truly novel solutions from being reached. In this work we 1) are the first to investigate casting NAS as a problem of finding the optimal network generator and 2) we propose a new, hierarchical and graph-based search space capable of representing an extremely large variety of network types, yet only requiring few continuous hyper-parameters. This greatly reduces the dimensionality of the problem, enabling the effective use of Bayesian Optimisation as a search strategy. At the same time, we expand the range of valid architectures, motivating a multi-objective learning approach. We demonstrate the effectiveness of this strategy on six benchmark datasets and show that our search space generates extremely lightweight yet highly competitive models.

Neural Architecture Search (NAS) has shown great potentials in finding better neural network designs. Sample-based NAS is the most reliable approach which aims at exploring the search space and evaluating the most promising architectures. However, it is computationally very costly. As a remedy, the one-shot approach has emerged as a popular technique for accelerating NAS using weight-sharing. However, due to the weight-sharing of vastly different networks, the one-shot approach is less reliable than the sample-based approach. In this work, we propose BONAS (Bayesian Optimized Neural Architecture Search), a sample-based NAS framework which is accelerated using weight-sharing to evaluate multiple related architectures simultaneously. Specifically, we apply Graph Convolutional Network predictor as a surrogate model for Bayesian Optimization to select multiple related candidate models in each iteration. We then apply weight-sharing to train multiple candidate models simultaneously. This approach not only accelerates the traditional sample-based approach significantly, but also keeps its reliability. This is because weight-sharing among related architectures are more reliable than those in the one-shot approach. Extensive experiments are conducted to verify the effectiveness of our method over many competing algorithms.

Synchronization is a key step in data-parallel distributed machine learning (ML). Different synchronization systems and strategies perform differently, and to achieve optimal parallel training throughput requires synchronization strategies that adapt to model structures and cluster configurations. Existing synchronization systems often only consider a single or a few synchronization aspects, and the burden of deciding the right synchronization strategy is then placed on the ML practitioners, who may lack the required expertise. In this paper, we develop a model- and resource-dependent representation for synchronization, which unifies multiple synchronization aspects ranging from architecture, message partitioning, placement scheme, to communication topology. Based on this representation, we build an end-to-end pipeline, AutoSync, to automatically optimize synchronization strategies given model structures and resource specifications, lowering the bar for data-parallel distributed ML. By learning from low-shot data collected in only 200 trial runs, AutoSync can discover synchronization strategies up to 1.6x better than manually optimized ones. We develop transfer-learning mechanisms to further reduce the auto-optimization cost -- the simulators can transfer among similar model architectures, among similar cluster configurations, or both. We also present a dataset that contains over 10000 synchronization strategies and run-time pairs on a diverse set of models and cluster specifications.

Most machine learning tasks are inherently multi-objective. This means that the learner has to come up with a model that performs well across a number of base objectives $\cL_{1}, \ldots, \cL_{p}$, as opposed to a single one. Since optimizing with respect to multiple objectives at the same time is often computationally expensive, the base objectives are often combined in an ensemble $\sum_{k=1}^{p}\lambda_{k}\cL_{k}$, thereby reducing the problem to scalar optimization. The mixture weights $\lambda_{k}$ are set to uniform or some other fixed distribution, based on the learner's preferences. We argue that learning with a fixed distribution on the mixture weights runs the risk of overfitting to some individual objectives and significantly harming others, despite performing well on an entire ensemble. Moreover, in reality, the true preferences of a learner across multiple objectives are often unknown or hard to express as a specific distribution. Instead, we propose a new framework of \emph{Agnostic Learning with Multiple Objectives} ($\almo$), where a model is optimized for \emph{any} weights in the mixture of base objectives. We present data-dependent Rademacher complexity guarantees for learning in the $\almo$ framework, which are used to guide a scalable optimization algorithm and the corresponding regularization. We present convergence guarantees for this algorithm, assuming convexity of the loss functions and the underlying hypothesis space. We further implement the algorithm in a popular symbolic gradient computation framework and empirically demonstrate on a number of datasets the benefits of $\almo$ framework versus learning with a fixed mixture weights distribution.

Learning to optimize (L2O) is gaining increased attention because classical optimizers require laborious, problem-specific design and hyperparameter tuning. However, there are significant performance and practicality gaps between manually designed optimizers and existing L2O models. Specifically, learned optimizers are applicable to only a limited class of problems, often exhibit instability, and generalize poorly. As research efforts focus on increasingly sophisticated L2O models, we argue for an orthogonal, under-explored theme: improved training techniques for L2O models. We first present a progressive, curriculum-based training scheme, which gradually increases the optimizer unroll length to mitigate the well-known L2O dilemma of truncation bias (shorter unrolling) versus gradient explosion (longer unrolling). Secondly, we present an off-policy imitation learning based approach to guide the L2O learning, by learning from the behavior of analytical optimizers. We evaluate our improved training techniques with a variety of state-of-the-art L2O models and immediately boost their performance, without making any change to their model structures. We demonstrate that, using our improved training techniques, one of the earliest and simplest L2O models can be trained to outperform even the latest and most complex L2O models on a number of tasks. Our results demonstrate a greater potential of L2O yet to be unleashed, and prompt a reconsideration of recent L2O model progress. Our codes are publicly available at: https://github.com/VITA-Group/L2O-Training-Techniques.

One of the most efficient methods to solve L2 -regularized primal problems, such as logistic regression and linear support vector machine (SVM) classification, is the widely used trust region Newton algorithm, TRON. While TRON has recently been shown to enjoy substantial speedups on shared-memory multi-core systems, exploiting graphical processing units (GPUs) to speed up the method is significantly more difficult, owing to the highly complex and heavily sequential nature of the algorithm. In this work, we show that using judicious GPU-optimization principles, TRON training time for different losses and feature representations may be drastically reduced. For sparse feature sets, we show that using GPUs to train logistic regression classifiers in LIBLINEAR is up to an order-of-magnitude faster than solely using multithreading. For dense feature sets–which impose far more stringent memory constraints–we show that GPUs substantially reduce the lengthy SVM learning times required for state-of-the-art proteomics analysis, leading to dramatic improvements over recently proposed speedups. Furthermore, we show how GPU speedups may be mixed with multithreading to enable such speedups when the dataset is too large for GPU memory requirements; on a massive dense proteomics dataset of nearly a quarter-billion data instances, these mixed-architecture speedups reduce SVM analysis time from over half a week to less than a single day while using limited GPU memory.

Scaling up the convolutional neural network (CNN) size (e.g., width, depth, etc.) is known to effectively improve model accuracy. However, the large model size impedes training on resource-constrained edge devices. For instance, federated learning (FL) may place undue burden on the compute capability of edge nodes, even though there is a strong practical need for FL due to its privacy and confidentiality properties. To address the resource-constrained reality of edge devices, we reformulate FL as a group knowledge transfer training algorithm, called FedGKT. FedGKT designs a variant of the alternating minimization approach to train small CNNs on edge nodes and periodically transfer their knowledge by knowledge distillation to a large server-side CNN. FedGKT consolidates several advantages into a single framework: reduced demand for edge computation, lower communication bandwidth for large CNNs, and asynchronous training, all while maintaining model accuracy comparable to FedAvg. We train CNNs designed based on ResNet-56 and ResNet-110 using three distinct datasets (CIFAR-10, CIFAR-100, and CINIC-10) and their non-IID variants. Our results show that FedGKT can obtain comparable or even slightly higher accuracy than FedAvg. More importantly, FedGKT makes edge training affordable. Compared to the edge training using FedAvg, FedGKT demands 9 to 17 times less computational power (FLOPs) on edge devices and requires 54 to 105 times fewer parameters in the edge CNN. Our source code is released at FedML (https://fedml.ai).

The notion of task similarity is at the core of various machine learning paradigms, such as domain adaptation and meta-learning. Current methods to quantify it are often heuristic, make strong assumptions on the label sets across the tasks, and many are architecture-dependent, relying on task-specific optimal parameters (e.g., require training a model on each dataset). In this work we propose an alternative notion of distance between datasets that (i) is model-agnostic, (ii) does not involve training, (iii) can compare datasets even if their label sets are completely disjoint and (iv) has solid theoretical footing. This distance relies on optimal transport, which provides it with rich geometry awareness, interpretable correspondences and well-understood properties. Our results show that this novel distance provides meaningful comparison of datasets, and correlates well with transfer learning hardness across various experimental settings and datasets.

Modern machine learning workloads use large models, with complex structures, that are very expensive to execute. The devices that execute complex models are becoming increasingly heterogeneous as we see a flourishing of Domain Specific Architectures (DSAs) being offered as hardware accelerators in addition to CPUs. These trends necessitate distributing the workload across multiple devices. Recent work has shown that significant gains can be obtained with model parallelism, i.e, partitioning a neural network's computational graph onto multiple devices. In particular, this form of parallelism assumes a pipeline of devices, which is fed a stream of samples and yields high throughput for training and inference of DNNs. However, for such settings (large models and multiple heterogeneous devices), we require automated algorithms and toolchains that can partition the ML workload across devices.

In this paper, we identify and isolate the structured optimization problem at the core of device placement of DNN operators, for both inference and training, especially in modern pipelined settings. We then provide algorithms that solve this problem to optimality. We demonstrate the applicability and efficiency of our approaches using several contemporary DNN computation graphs.

Solving optimization problems with unknown parameters often requires learning a predictive model to predict the values of the unknown parameters and then solving the problem using these values. Recent work has shown that including the optimization problem as a layer in the model training pipeline results in predictions of the unobserved parameters that lead to higher decision quality. Unfortunately, this process comes at a large computational cost because the optimization problem must be solved and differentiated through in each training iteration; furthermore, it may also sometimes fail to improve solution quality due to non-smoothness issues that arise when training through a complex optimization layer. To address these shortcomings, we learn a low-dimensional surrogate model of a large optimization problem by representing the feasible space in terms of meta-variables, each of which is a linear combination of the original variables. By training a low-dimensional surrogate model end-to-end, and jointly with the predictive model, we achieve: i) a large reduction in training and inference time; and ii) improved performance by focusing attention on the more important variables in the optimization and learning in a smoother space. Empirically, we demonstrate these improvements on a non-convex adversary modeling task, a submodular recommendation task and a convex portfolio optimization task.

The performance of deep (reinforcement) learning systems crucially depends on the choice of hyperparameters. Their tuning is notoriously expensive, typically requiring an iterative training process to run for numerous steps to convergence. Traditional tuning algorithms only consider the final performance of hyperparameters acquired after many expensive iterations and ignore intermediate information from earlier training steps. In this paper, we present a Bayesian optimization(BO) approach which exploits the iterative structure of learning algorithms for efficient hyperparameter tuning. We propose to learn an evaluation function compressing learning progress at any stage of the training process into a single numeric score according to both training success and stability. Our BO framework is then trade-off the benefit of assessing a hyperparameter setting over additional training steps against their computation cost. We further increase model efficiency by selectively including scores from different training steps for any evaluated hyperparameter set. We demonstrate the efficiency of our algorithm by tuning hyperparameters for the training of deep reinforcement learning agents and convolutional neural networks. Our algorithm outperforms all existing baselines in identifying optimal hyperparameters in minimal time.

A challenge that machine learning practitioners in the industry face is the task of selecting the best model to deploy in production. As a model is often an intermediate component of a production system, online controlled experiments such as A/B tests yield the most reliable estimation of the effectiveness of the whole system, but can only compare two or a few models due to budget constraints. We propose an automated online experimentation mechanism that can efficiently perform model selection from a large pool of models with a small number of online experiments. We derive the probability distribution of the metric of interest that contains the model uncertainty from our Bayesian surrogate model trained using historical logs. Our method efficiently identifies the best model by sequentially selecting and deploying a list of models from the candidate set that balance exploration-exploitation. Using simulations based on real data, we demonstrate the effectiveness of our method on two different tasks.

Resource scheduling and coordination is an NP-hard optimization requiring an efficient allocation of agents to a set of tasks with upper- and lower bound temporal and resource constraints. Due to the large-scale and dynamic nature of resource coordination in hospitals and factories, human domain experts manually plan and adjust schedules on the fly. To perform this job, domain experts leverage heterogeneous strategies and rules-of-thumb honed over years of apprenticeship. What is critically needed is the ability to extract this domain knowledge in a heterogeneous and interpretable apprenticeship learning framework to scale beyond the power of a single human expert, a necessity in safety-critical domains. We propose a personalized and interpretable apprenticeship scheduling algorithm that infers an interpretable representation of all human task demonstrators by extracting decision-making criteria via an inferred, personalized embedding non-parametric in the number of demonstrator types. We achieve near-perfect LfD accuracy in synthetic domains and 88.22\% accuracy on a planning domain with real-world data, outperforming baselines. Finally, our user study showed our methodology produces more interpretable and easier-to-use models than neural networks ($p < 0.05$).

Machine learning as a service has given raise to privacy concerns surrounding clients' data and providers' models and has catalyzed research in private inference (PI): methods to process inferences without disclosing inputs. Recently, researchers have adapted cryptographic techniques to show PI is possible, however all solutions increase inference latency beyond practical limits. This paper makes the observation that existing models are ill-suited for PI and proposes a novel NAS method, named CryptoNAS, for finding and tailoring models to the needs of PI. The key insight is that in PI operator latency cost are inverted: non-linear operations (e.g., ReLU) dominate latency, while linear layers become effectively free. We develop the idea of a ReLU budget as a proxy for inference latency and use CryptoNAS to build models that maximize accuracy within a given budget. CryptoNAS improves accuracy by 3.4% and latency by 2.4x over the state-of-the-art.

Conventional Neural Networks can approximate simple arithmetic operations, but fail to generalize beyond the range of numbers that were seen during training. Neural Arithmetic Units aim to overcome this difficulty, but current arithmetic units are either limited to operate on positive numbers or can only represent a subset of arithmetic operations. We introduce the Neural Power Unit (NPU) that operates on the full domain of real numbers and is capable of learning arbitrary power functions in a single layer. The NPU thus fixes the shortcomings of existing arithmetic units and extends their expressivity. We achieve this by using complex arithmetic without requiring a conversion of the network to complex numbers. A simplification of the unit to the RealNPU yields a highly transparent model. We show that the NPUs outperform their competitors in terms of accuracy and sparsity on artificial arithmetic datasets, and that the RealNPU can discover the governing equations of a dynamical system only from data.

Many science, engineering, and design optimization problems require balancing the trade-offs between several conflicting objectives. The objectives are often black-box functions whose evaluations are time-consuming and costly. Multi-objective Bayesian optimization can be used to automate the process of discovering the set of optimal solutions, called Pareto-optimal, while minimizing the number of performed evaluations. To further reduce the evaluation time in the optimization process, testing of several samples in parallel can be deployed. We propose a novel multi-objective Bayesian optimization algorithm that iteratively selects the best batch of samples to be evaluated in parallel. Our algorithm approximates and analyzes a piecewise-continuous Pareto set representation. This representation allows us to introduce a batch selection strategy that optimizes for both hypervolume improvement and diversity of selected samples in order to efficiently advance promising regions of the Pareto front. Experiments on both synthetic test functions and real-world benchmark problems show that our algorithm predominantly outperforms relevant state-of-the-art methods. Code is available at https://github.com/yunshengtian/DGEMO.

Despite the recent success of Bayesian optimization (BO) in a variety of applications where sample efficiency is imperative, its performance may be seriously compromised in settings characterized by high-dimensional parameter spaces. A solution to preserve the sample efficiency of BO in such problems is to introduce domain knowledge into its formulation. In this paper, we propose to exploit the geometry of non-Euclidean search spaces, which often arise in a variety of domains, to learn structure-preserving mappings and optimize the acquisition function of BO in low-dimensional latent spaces. Our approach, built on Riemannian manifolds theory, features geometry-aware Gaussian processes that jointly learn a nested-manifolds embedding and a representation of the objective function in the latent space. We test our approach in several benchmark artificial landscapes and report that it not only outperforms other high-dimensional BO approaches in several settings, but consistently optimizes the objective functions, as opposed to geometry-unaware BO methods.

This paper presents new algorithms to solve the feature-sparsity constrained PCA problem (FSPCA), which performs feature selection and PCA simultaneously. Existing optimization methods for FSPCA require data distribution assumptions and are lack of global convergence guarantee. Though the general FSPCA problem is NP-hard, we show that, for a low-rank covariance, FSPCA can be solved globally (Algorithm 1). Then, we propose another strategy (Algorithm 2) to solve FSPCA for the general covariance by iteratively building a carefully designed proxy. We prove (data-dependent) approximation bound and convergence guarantees for the new algorithms. For the spectrum of covariance with exponential/Zipf's distribution, we provide exponential/posynomial approximation bound. Experimental results show the promising performance and efficiency of the new algorithms compared with the state-of-the-arts on both synthetic and real-world datasets.

Wasserstein \textbf{D}istributionally \textbf{R}obust \textbf{O}ptimization (DRO) is concerned with finding decisions that perform well on data that are drawn from the worst probability distribution within a Wasserstein ball centered at a certain nominal distribution. In recent years, it has been shown that various DRO formulations of learning models admit tractable convex reformulations. However, most existing works propose to solve these convex reformulations by general-purpose solvers, which are not well-suited for tackling large-scale problems. In this paper, we focus on a family of Wasserstein distributionally robust support vector machine (DRSVM) problems and propose two novel epigraphical projection-based incremental algorithms to solve them. The updates in each iteration of these algorithms can be computed in a highly efficient manner. Moreover, we show that the DRSVM problems considered in this paper satisfy a Hölderian growth condition with explicitly determined growth exponents. Consequently, we are able to establish the convergence rates of the proposed incremental algorithms. Our numerical results indicate that the proposed methods are orders of magnitude faster than the state-of-the-art, and the performance gap grows considerably as the problem size increases.

State-of-the-art optimization is steadily shifting towards massively parallel pipelines with extremely large batch sizes. As a consequence, CPU-bound preprocessing and disk/memory/network operations have emerged as new performance bottlenecks, as opposed to hardware-accelerated gradient computations. In this regime, a recently proposed approach is data echoing (Choi et al., 2019), which takes repeated gradient steps on the same batch while waiting for fresh data to arrive from upstream. We provide the first convergence analyses of "data-echoed" extensions of common optimization methods, showing that they exhibit provable improvements over their synchronous counterparts. Specifically, we show that in convex optimization with stochastic minibatches, data echoing affords speedups on the curvature-dominated part of the convergence rate, while maintaining the optimal statistical rate.

We propose a novel method for gradient-based optimization of black-box simulators using differentiable local surrogate models. In fields such as physics and engineering, many processes are modeled with non-differentiable simulators with intractable likelihoods. Optimization of these forward models is particularly challenging, especially when the simulator is stochastic. To address such cases, we introduce the use of deep generative models to iteratively approximate the simulator in local neighborhoods of the parameter space. We demonstrate that these local surrogates can be used to approximate the gradient of the simulator, and thus enable gradient-based optimization of simulator parameters. In cases where the dependence of the simulator on the parameter space is constrained to a low dimensional submanifold, we observe that our method attains minima faster than baseline methods, including Bayesian optimization, numerical optimization and approaches using score function gradient estimators.

We propose a flexible gradient-based framework for learning linear programs from optimal decisions. Linear programs are often specified by hand, using prior knowledge of relevant costs and constraints. In some applications, linear programs must instead be learned from observations of optimal decisions. Learning from optimal decisions is a particularly challenging bilevel problem, and much of the related inverse optimization literature is dedicated to special cases. We tackle the general problem, learning all parameters jointly while allowing flexible parameterizations of costs, constraints, and loss functions. We also address challenges specific to learning linear programs, such as empty feasible regions and non-unique optimal decisions. Experiments show that our method successfully learns synthetic linear programs and minimum-cost multi-commodity flow instances for which previous methods are not directly applicable. We also provide a fast batch-mode PyTorch implementation of the homogeneous interior point algorithm, which supports gradients by implicit differentiation or backpropagation.

Consider an oracle which takes a point x and returns the minimizer of a convex function f in an l2 ball of radius r around x. It is straightforward to show that roughly r^{-1}\log(1/epsilon) calls to the oracle suffice to find an \epsilon-approximate minimizer of f in an l2 unit ball. Perhaps surprisingly, this is not optimal: we design an accelerated algorithm which attains an epsilon-approximate minimizer with roughly r^{-2/3} \log(1/epsilon) oracle queries, and give a matching lower bound. Further, we implement ball optimization oracles for functions with a locally stable Hessian using a variant of Newton's method and, in certain cases, stochastic first-order methods. The resulting algorithms apply to a number of problems of practical and theoretical import, improving upon previous results for logistic and linfinity regression and achieving guarantees comparable to the
state-of-the-art for lp regression.

In this work, we present new second-order algorithms for composite convex optimization, called Contracting-domain Newton methods. These algorithms are affine-invariant and based on global second-order lower approximation for the smooth component of the objective. Our approach has an interpretation both as a second-order generalization of the conditional gradient method, or as a variant of trust-region scheme. Under the assumption, that the problem domain is bounded, we prove $O(1/k^2)$ global rate of convergence in functional residual, where $k$ is the iteration counter, minimizing convex functions with Lipschitz continuous Hessian. This significantly improves the previously known bound $O(1/k)$ for this type of algorithms. Additionally, we propose a stochastic extension of our method, and present computational results for solving empirical risk minimization problem.

Descent directions such as movement towards Frank-Wolfe vertices, away steps, in-face away steps and pairwise directions have been an important design consideration in conditional gradient descent (CGD) variants. In this work, we attempt to demystify the impact of movement in these directions towards attaining constrained minimizers. The best local direction of descent is the directional derivative of the projection of the gradient, which we refer to as the "shadow" of the gradient. We show that the continuous-time dynamics of moving in the shadow are equivalent to those of PGD however non-trivial to discretize. By projecting gradients in PGD, one not only ensures feasibility but also is able to "wrap" around the convex region. We show that Frank-Wolfe (FW) vertices in fact recover the maximal wrap one can obtain by projecting gradients, thus providing a new perspective to these steps. We also claim that the shadow steps give the best direction of descent emanating from the convex hull of all possible away-vertices. Opening up the PGD movements in terms of shadow steps gives linear convergence, dependent on the number of faces. We combine these insights into a novel Shadow-CG method that uses FW steps (i.e., wrap around the polytope) and shadow steps (i.e., optimal local descent direction), while enjoying linear convergence. Our analysis develops properties of directional derivatives of projections (which may be of independent interest), while providing a unifying view of various descent directions in the CGD literature.

In recent years it was proved that simple modifications of the classical Frank-Wolfe algorithm (aka conditional gradient algorithm) for smooth convex minimization over convex and compact polytopes, converge with linear rate, assuming the objective function has the quadratic growth property. However, the rate of these methods depends explicitly on the dimension of the problem which cannot explain their empirical success for large scale problems. In this paper we first demonstrate that already for very simple problems and even when the optimal solution lies on a low-dimensional face of the polytope, such dependence on the dimension cannot be avoided in worst case. We then revisit the addition of a strict complementarity assumption already considered in Wolfe's classical book \cite{Wolfe1970}, and prove that under this condition, the Frank-Wolfe method with away-steps and line-search converges linearly with rate that depends explicitly only on the dimension of the optimal face, hence providing a significant improvement in case the optimal solution is sparse. We motivate this strict complementarity condition by proving that it implies sparsity-robustness of optimal solutions to noise.

Bayesian optimisation is a popular method for efficient optimisation of expensive black-box functions. Traditionally, BO assumes that the search space is known. However, in many problems, this assumption does not hold. To this end, we propose a novel BO algorithm which expands (and shifts) the search space over iterations based on controlling the expansion rate thought a \emph{hyperharmonic series}. Further, we propose another variant of our algorithm that scales to high dimensions. We show theoretically that for both our algorithms, the cumulative regret grows at sub-linear rates. Our experiments with synthetic and real-world optimisation tasks demonstrate the superiority of our algorithms over the current state-of-the-art methods for Bayesian optimisation in unknown search space.

Convex optimization problems with staged structure appear in several contexts, including optimal control, verification of deep neural networks, and isotonic regression. Off-the-shelf solvers can solve these problems but may scale poorly. We develop a nonconvex reformulation designed to exploit this staged structure. Our reformulation has only simple bound constraints, enabling solution via projected gradient methods and their accelerated variants. The method automatically generates a sequence of primal and dual feasible solutions to the original convex problem, making optimality certification easy. We establish theoretical properties of the nonconvex formulation, showing that it is (almost) free of spurious local minima and has the same global optimum as the convex problem. We modify projected gradient descent to avoid spurious local minimizers so it always converges to the global minimizer. For neural network verification, our approach obtains small duality gaps in only a few gradient steps. Consequently, it can provide tight duality gaps for many large-scale verification problems where both off-the-shelf and specialized solvers struggle.

This paper proposes two efficient algorithms for computing approximate second-order stationary points (SOSPs) of problems with generic smooth non-convex objective functions and generic linear constraints. While finding (approximate) SOSPs for the class of smooth non-convex linearly constrained problems is computationally intractable, we show that generic problem instances in this class can be solved efficiently. Specifically, for a generic problem instance, we show that certain strict complementarity (SC) condition holds for all Karush-Kuhn-Tucker (KKT) solutions. Based on this condition, we design an algorithm named Successive Negative-curvature grAdient Projection (SNAP), which performs either conventional gradient projection or some negative curvature-based projection steps to find SOSPs. SNAP is a second-order algorithm that requires $\widetilde{\mathcal{O}}(\max\{1/\epsilon^2_G,1/\epsilon^3_H\})$ iterations to compute an $(\epsilon_G,\epsilon_H)$-SOSP, where $\widetilde{\mathcal{O}}$ hides the iteration complexity for eigenvalue-decomposition. Building on SNAP, we propose a first-order algorithm, named SNAP$^+$, that requires $\mathcal{O}(1/\epsilon^{2.5})$ iterations to compute $(\epsilon, \sqrt{\epsilon})$-SOSP. The per-iteration computational complexities of our algorithms are polynomial in the number of constraints and problem dimension. To the best of our knowledge, this is the first time that first-order algorithms with polynomial per-iteration complexity and global sublinear rate are designed to find SOSPs of the important class of non-convex problems with linear constraints (almost surely).

Bayesian optimization provides sample-efficient global optimization for a broad range of applications, including automatic machine learning, engineering, physics, and experimental design. We introduce BoTorch, a modern programming framework for Bayesian optimization that combines Monte-Carlo (MC) acquisition functions, a novel sample average approximation optimization approach, auto-differentiation, and variance reduction techniques. BoTorch's modular design facilitates flexible specification and optimization of probabilistic models written in PyTorch, simplifying implementation of new acquisition functions. Our approach is backed by novel theoretical convergence results and made practical by a distinctive algorithmic foundation that leverages fast predictive distributions, hardware acceleration, and deterministic optimization. We also propose a novel "one-shot" formulation of the Knowledge Gradient, enabled by a combination of our theoretical and software contributions. In experiments, we demonstrate the improved sample efficiency of BoTorch relative to other popular libraries.

Market equilibrium is a solution concept with many applications such as digital ad markets, fair division, and resource sharing. For many classes of utility functions, equilibria can be captured by convex programs. We develop simple first-order methods suitable for solving these convex programs for large-scale markets. We focus on three practically-relevant utility classes: linear, quasilinear, and Leontief utilities. Using structural properties of market equilibria under each utility class, we show that the corresponding convex programs can be reformulated as optimization of a structured smooth convex function over a polyhedral set, for which projected gradient achieves linear convergence. To do so, we utilize recent linear convergence results under weakened strong-convexity conditions, and further refine the relevant constants in existing convergence results. Then, we show that proximal gradient (a generalization of projected gradient) with a practical linesearch scheme achieves linear convergence under the Proximal-PL condition, a recently developed error bound condition for convex composite problems. For quasilinear utilities, we show that Mirror Descent applied to a new convex program achieves sublinear last-iterate convergence and yields a form of Proportional Response dynamics, an elegant, interpretable algorithm for computing market equilibria originally developed for linear utilities. Numerical experiments show that Proportional Response is highly efficient for computing approximate market equilibria, while projected gradient with linesearch can be much faster when higher-accuracy solutions are needed.

Crowdsourced data used in machine learning services might carry sensitive information about attributes that users do not want to share. Various methods have been proposed to minimize the potential information leakage of sensitive attributes while maximizing the task accuracy. However, little is known about the theory behind these methods. In light of this gap, we develop a novel theoretical framework for attribute obfuscation. Under our framework, we propose a minimax optimization formulation to protect the given attribute and analyze its inference guarantees against worst-case adversaries. Meanwhile, there is a tension between minimizing information leakage and maximizing task accuracy. To understand this, we prove an information-theoretic lower bound to precisely characterize the fundamental trade-off between accuracy and information leakage. We conduct experiments on two real-world datasets to corroborate the inference guarantees and validate the inherent trade-offs therein. Our results indicate that, among several alternatives, the adversarial learning approach achieves the best trade-off in terms of attribute obfuscation and accuracy maximization.

Recent work proposed the computation of so-called PI-explanations of Naive Bayes Classifiers (NBCs). PI-explanations are subset-minimal sets of feature-value pairs that are sufficient for the prediction, and have been computed with state-of-the-art exact algorithms that are worst-case exponential in time and space. In contrast, we show that the computation of one PI-explanation for an NBC can be achieved in log-linear time, and that the same result also applies to the more general class of linear classifiers. Furthermore, we show that the enumeration of PI-explanations can be obtained with polynomial delay. Experimental results demonstrate the performance gains of the new algorithms when compared with earlier work. The experimental results also investigate ways to measure the quality of heuristic explanations.

We present a neural network (NN) approach to fit and predict implied volatility surfaces (IVSs). Atypically to standard NN applications, financial industry practitioners use such models equally to replicate market prices and to value other financial instruments. In other words, low training losses are as important as generalization capabilities. Importantly, IVS models need to generate realistic arbitrage-free option prices, meaning that no portfolio can lead to risk-free profits. We propose an approach guaranteeing the absence of arbitrage opportunities by penalizing the loss using soft constraints. Furthermore, our method can be combined with standard IVS models in quantitative finance, thus providing a NN-based correction when such models fail at replicating observed market prices. This lets practitioners use our approach as a plug-in on top of classical methods. Empirical results show that this approach is particularly useful when only sparse or erroneous data are available. We also quantify the uncertainty of the model predictions in regions with few or no observations. We further explore how deeper NNs improve over shallower ones, as well as other properties of the network architecture. We benchmark our method against standard IVS models. By evaluating our method on both training sets, and testing sets, namely, we highlight both their capacity to reproduce observed prices and predict new ones.

Explanations of time series models are useful for high stakes applications like healthcare but have received little attention in machine learning literature. We propose FIT, a framework that evaluates the importance of observations for a multivariate time-series black-box model by quantifying the shift in the predictive distribution over time. FIT defines the importance of an observation based on its contribution to the distributional shift under a KL-divergence that contrasts the predictive distribution against a counterfactual where the rest of the features are unobserved. We also demonstrate the need to control for time-dependent distribution shifts. We compare with state-of-the-art baselines on simulated and real-world clinical data and demonstrate that our approach is superior in identifying important time points and observations throughout the time series.

Neural networks often learn to make predictions that overly rely on spurious corre- lation existing in the dataset, which causes the model to be biased. While previous work tackles this issue by using explicit labeling on the spuriously correlated attributes or presuming a particular bias type, we instead utilize a cheaper, yet generic form of human knowledge, which can be widely applicable to various types of bias. We first observe that neural networks learn to rely on the spurious correlation only when it is “easier” to learn than the desired knowledge, and such reliance is most prominent during the early phase of training. Based on the obser- vations, we propose a failure-based debiasing scheme by training a pair of neural networks simultaneously. Our main idea is twofold; (a) we intentionally train the first network to be biased by repeatedly amplifying its “prejudice”, and (b) we debias the training of the second network by focusing on samples that go against the prejudice of the biased network in (a). Extensive experiments demonstrate that our method significantly improves the training of network against various types of biases in both synthetic and real-world datasets. Surprisingly, our framework even occasionally outperforms the debiasing methods requiring explicit supervision of the spuriously correlated attributes.

Explaining AI systems is fundamental both to the development of high performing models and to the trust placed in them by their users. The Shapley framework for explainability has strength in its general applicability combined with its precise, rigorous foundation: it provides a common, model-agnostic language for AI explainability and uniquely satisfies a set of intuitive mathematical axioms. However, Shapley values are too restrictive in one significant regard: they ignore all causal structure in the data. We introduce a less restrictive framework, Asymmetric Shapley values (ASVs), which are rigorously founded on a set of axioms, applicable to any AI system, and can flexibly incorporate any causal structure known to be respected by the data. We demonstrate that ASVs can (i) improve model explanations by incorporating causal information, (ii) provide an unambiguous test for unfair discrimination in model predictions, (iii) enable sequentially incremental explanations in time-series models, and (iv) support feature-selection studies without the need for model retraining.

There is a rich and growing literature on producing local contrastive/counterfactual explanations for black-box models (e.g. neural networks). In these methods, for an input, an explanation is in the form of a contrast point differing in very few features from the original input and lying in a different class. Other works try to build globally interpretable models like decision trees and rule lists based on the data using actual labels or based on the black-box models predictions. Although these interpretable global models can be useful, they may not be consistent with local explanations from a specific black-box of choice. In this work, we explore the question: Can we produce a transparent global model that is simultaneously accurate and consistent with the local (contrastive) explanations of the black-box model? We introduce a local consistency metric that quantifies if the local explanations for the black-box model are also applicable to the proxy/surrogate globally transparent model. Based on a key insight we propose a novel method where we create custom boolean features from local contrastive explanations of the black-box model and then train a globally transparent model that has higher local consistency compared with other known strategies in addition to being accurate.

Many real-world sequential decision-making problems involve critical systems with financial risks and human-life risks. While several works in the past have proposed methods that are safe for deployment, they assume that the underlying problem is stationary. However, many real-world problems of interest exhibit non-stationarity, and when stakes are high, the cost associated with a false stationarity assumption may be unacceptable. We take the first steps towards ensuring safety, with high confidence, for smoothly-varying non-stationary decision problems. Our proposed method extends a type of safe algorithm, called a Seldonian algorithm, through a synthesis of model-free reinforcement learning with time-series analysis. Safety is ensured using sequential hypothesis testing of a policy’s forecasted performance, and confidence intervals are obtained using wild bootstrap.

As data-driven predictive models are increasingly used to inform decisions, it has been argued that decision makers should provide explanations that help individuals understand what would have to change for these decisions to be beneficial ones. However, there has been little discussion on the possibility that individuals may use the above counterfactual explanations to invest effort strategically and maximize their chances of receiving a beneficial decision. In this paper, our goal is to find policies and counterfactual explanations that are optimal in terms of utility in such a strategic setting. We first show that, given a pre-defined policy, the problem of finding the optimal set of counterfactual explanations is NP-hard. Then, we show that the corresponding objective is nondecreasing and satisfies submodularity and this allows a standard greedy algorithm to enjoy approximation guarantees. In addition, we further show that the problem of jointly finding both the optimal policy and set of counterfactual explanations reduces to maximizing a non-monotone submodular function. As a result, we can use a recent randomized algorithm to solve the problem, which also offers approximation guarantees. Finally, we demonstrate that, by incorporating a matroid constraint into the problem formulation, we can increase the diversity of the optimal set of counterfactual explanations and incentivize individuals across the whole spectrum of the population to self improve. Experiments on synthetic and real lending and credit card data illustrate our theoretical findings and show that the counterfactual explanations and decision policies found by our algorithms achieve higher utility than several competitive baselines.

Machine learning is a powerful tool for predicting human-related outcomes, from creditworthiness to heart attack risks. But when deployed transparently, learned models also affect how users act in order to improve outcomes. The standard approach to learning predictive models is agnostic to induced user actions and provides no guarantees as to the effect of actions. We provide a framework for learning predictors that are accurate, while also considering interactions between the learned model and user decisions. For this, we introduce look-ahead regularization which, by anticipating user actions, encourages predictive models to also induce actions that improve outcomes. This regularization carefully tailors the uncertainty estimates that govern confidence in this improvement to the distribution of model-induced actions. We report the results of experiments on real and synthetic data that show the effectiveness of this approach.

In recent years, post-hoc local instance-level and global dataset-level explainability of black-box models has received a lot of attention. Lesser attention has been given to obtaining insights at intermediate or group levels, which is a need outlined in recent works that study the challenges in realizing the guidelines in the General Data Protection Regulation (GDPR). In this paper, we propose a meta-method that, given a typical local explainability method, can build a multilevel explanation tree. The leaves of this tree correspond to local explanations, the root corresponds to global explanation, and intermediate levels correspond to explanations for groups of data points that it automatically clusters. The method can also leverage side information, where users can specify points for which they may want the explanations to be similar. We argue that such a multilevel structure can also be an effective form of communication, where one could obtain few explanations that characterize the entire dataset by considering an appropriate level in our explanation tree. Explanations for novel test points can be cost-efficiently obtained by associating them with the closest training points. When the local explainability technique is generalized additive (viz. LIME, GAMs), we develop fast approximate algorithm for building the multilevel tree and study its convergence behavior. We show that we produce high fidelity sparse explanations on several public datasets and also validate the effectiveness of the proposed technique based on two human studies -- one with experts and the other with non-expert users -- on real world datasets.

We present a flexible framework for learning predictive models that approximately satisfy the equalized odds notion of fairness. This is achieved by introducing a general discrepancy functional that rigorously quantifies violations of this criterion. This differentiable functional is used as a penalty driving the model parameters towards equalized odds. To rigorously evaluate fitted models, we develop a formal hypothesis test to detect whether a prediction rule violates this property, the first such test in the literature. Both the model fitting and hypothesis testing leverage a resampled version of the sensitive attribute obeying equalized odds, by construction. We demonstrate the applicability and validity of the proposed framework both in regression and multi-class classification problems, reporting improved performance over state-of-the-art methods. Lastly, we show how to incorporate techniques for equitable uncertainty quantification---unbiased for each group under study---to communicate the results of the data analysis in exact terms.

Most of the work on interpretable machine learning has focused on designing either inherently interpretable models, which typically trade-off accuracy for interpretability, or post-hoc explanation systems, whose explanation quality can be unpredictable. Our method, ExpO, is a hybridization of these approaches that regularizes a model for explanation quality at training time. Importantly, these regularizers are differentiable, model agnostic, and require no domain knowledge to define. We demonstrate that post-hoc explanations for ExpO-regularized models have better explanation quality, as measured by the common fidelity and stability metrics. We verify that improving these metrics leads to significantly more useful explanations with a user study on a realistic task.

Because of the lack of expertise, to gain benefits from their data, average users have to upload their private data to cloud servers they may not trust. Due to legal or privacy constraints, most users are willing to contribute only their encrypted data, and lack interests or resources to join deep neural network (DNN) training in cloud. To train a DNN on encrypted data in a completely non-interactive way, a recent work proposes a fully homomorphic encryption (FHE)-based technique implementing all activations by \textit{Brakerski-Gentry-Vaikuntanathan} (BGV)-based lookup tables. However, such inefficient lookup-table-based activations significantly prolong private training latency of DNNs.

In this paper, we propose, Glyph, an FHE-based technique to fast and accurately train DNNs on encrypted data by switching between TFHE (Fast Fully Homomorphic Encryption over the Torus) and BGV cryptosystems. Glyph uses logic-operation-friendly TFHE to implement nonlinear activations, while adopts vectorial-arithmetic-friendly BGV to perform multiply-accumulations (MACs). Glyph further applies transfer learning on DNN training to improve test accuracy and reduce the number of MACs between ciphertext and ciphertext in convolutional layers. Our experimental results show Glyph obtains state-of-the-art accuracy, and reduces training latency by 69%~99% over prior FHE-based privacy-preserving techniques on encrypted datasets.

Data poisoning---the process by which an attacker takes control of a model by making imperceptible changes to a subset of the training data---is an emerging threat in the context of neural networks. Existing attacks for data poisoning neural networks have relied on hand-crafted heuristics, because solving the poisoning problem directly via bilevel optimization is generally thought of as intractable for deep models. We propose MetaPoison, a first-order method that approximates the bilevel problem via meta-learning and crafts poisons that fool neural networks. MetaPoison is effective: it outperforms previous clean-label poisoning methods by a large margin. MetaPoison is robust: poisoned data made for one model transfer to a variety of victim models with unknown training settings and architectures. MetaPoison is general-purpose, it works not only in fine-tuning scenarios, but also for end-to-end training from scratch, which till now hasn't been feasible for clean-label attacks with deep nets. MetaPoison can achieve arbitrary adversary goals---like using poisons of one class to make a target image don the label of another arbitrarily chosen class. Finally, MetaPoison works in the real-world. We demonstrate for the first time successful data poisoning of models trained on the black-box Google Cloud AutoML API.

Deep learning models are increasingly popular in many machine learning applications where the training data may contain sensitive information. To provide formal and rigorous privacy guarantee, many learning systems now incorporate differential privacy by training their models with (differentially) private SGD. A key step in each private SGD update is gradient clipping that shrinks the gradient of an individual example whenever its l2 norm exceeds a certain threshold. We first demonstrate how gradient clipping can prevent SGD from converging to a stationary point. We then provide a theoretical analysis on private SGD with gradient clipping. Our analysis fully characterizes the clipping bias on the gradient norm, which can be upper bounded by the Wasserstein distance between the gradient distribution and a geometrically symmetric distribution. Our empirical evaluation further suggests that the gradient distributions along the trajectory of private SGD indeed exhibit such symmetric structure. Together, our results provide an explanation why private SGD with gradient clipping remains effective in practice despite its potential clipping bias. Finally, we develop a new perturbation-based technique that can provably correct the clipping bias even for instances with highly asymmetric gradient distributions.

Coresets are small data summaries that are sufficient for model training. They can be maintained online, enabling efficient handling of large data streams under resource constraints. However, existing constructions are limited to simple models such as k-means and logistic regression. In this work, we propose a novel coreset construction via cardinality-constrained bilevel optimization. We show how our framework can efficiently generate coresets for deep neural networks, and demonstrate its empirical benefits in continual learning and in streaming settings.

Running nonlinear RNNs for T steps takes O(T) time. Our construction, called LDStack, approximately runs them in O(log T) parallel time, and obtains arbitrarily low error via repetition. First, we show nonlinear RNNs can be approximated by a stack of multiple-input, multiple-output (MIMO) LDS. This replaces nonlinearity across time with nonlinearity along depth. Next, we show that MIMO LDS can be approximated by an average or a concatenation of single-input, multiple-output (SIMO) LDS. Finally, we present an algorithm for running (and differentiating) SIMO LDS in O(log T) parallel time. On long sequences, LDStack is much faster than traditional RNNs, yet it achieves similar accuracy in our experiments. Furthermore, LDStack is amenable to linear systems theory. Therefore, it improves not only speed, but also interpretability and mathematical tractability.

Clustering is a ubiquitous task in data science. Compared to the commonly used k-means clustering, k-medoids clustering requires the cluster centers to be actual data points and supports arbitrary distance metrics, which permits greater interpretability and the clustering of structured objects. Current state-of-the-art k-medoids clustering algorithms, such as Partitioning Around Medoids (PAM), are iterative and are quadratic in the dataset size n for each iteration, being prohibitively expensive for large datasets. We propose BanditPAM, a randomized algorithm inspired by techniques from multi-armed bandits, that reduces the complexity of each PAM iteration from O(n^2) to O(nlogn) and returns the same results with high probability, under assumptions on the data that often hold in practice. As such, BanditPAM matches state-of-the-art clustering loss while reaching solutions much faster. We empirically validate our results on several large real-world datasets, including a coding exercise submissions dataset from Code.org, the 10x Genomics 68k PBMC single-cell RNA sequencing dataset, and the MNIST handwritten digits dataset. In these experiments, we observe that BanditPAM returns the same results as state-of-the-art PAM-like algorithms up to 4x faster while performing up to 200x fewer distance computations. The improvements demonstrated by BanditPAM enable k-medoids clustering on a wide range of applications, including identifying cell types in large-scale single-cell data and providing scalable feedback for students learning computer science online. We also release highly optimized Python and C++ implementations of our algorithm.

The sliding window model of computation captures scenarios in which data is arriving continuously, but only the latest $w$ elements should be used for analysis. The goal is to design algorithms that update the solution efficiently with each arrival rather than recomputing it from scratch. In this work, we focus on $k$-clustering problems such as $k$-means and $k$-median. In this setting, we provide simple and practical algorithms that offer stronger performance guarantees than previous results. Empirically, we show that our methods store only a small fraction of the data, are orders of magnitude faster, and find solutions with costs only slightly higher than those returned by algorithms with access to the full dataset.

$k$-means++ \cite{arthur2007k} is a widely used clustering algorithm that is easy to implement, has nice theoretical guarantees and strong empirical performance. Despite its wide adoption, $k$-means++ sometimes suffers from being slow on large data-sets so a natural question has been to obtain more efficient algorithms with similar guarantees. In this paper, we present such a near linear time algorithm for $k$-means++ seeding. Interestingly our algorithm obtains the same theoretical guarantees as $k$-means++ and significantly improves earlier results on fast $k$-means++ seeding. Moreover, we show empirically that our algorithm is significantly faster than $k$-means++ and obtains solutions of equivalent quality.

The presence of missing values makes supervised learning much more challenging. Indeed, previous work has shown that even when the response is a linear function of the complete data, the optimal predictor is a complex function of the observed entries and the missingness indicator. As a result, the computational or sample complexities of consistent approaches depend on the number of missing patterns, which can be exponential in the number of dimensions. In this work, we derive the analytical form of the optimal predictor under a linearity assumption and various missing data mechanisms including Missing at Random (MAR) and self-masking (Missing Not At Random). Based on a Neumann-series approximation of the optimal predictor, we propose a new principled architecture, named NeuMiss networks. Their originality and strength come from the use of a new type of non-linearity: the multiplication by the missingness indicator. We provide an upper bound on the Bayes risk of NeuMiss networks, and show that they have good predictive accuracy with both a number of parameters and a computational complexity independent of the number of missing data patterns. As a result they scale well to problems with many features, and remain statistically efficient for medium-sized samples. Moreover, we show that, contrary to procedures using EM or imputation, they are robust to the missing data mechanism, including difficult MNAR settings such as self-masking.

Stochastic gradient algorithm is a key ingredient of many machine learning methods, particularly appropriate for large-scale learning. However, a major caveat of large data is their incompleteness. We propose an averaged stochastic gradient algorithm handling missing values in linear models. This approach has the merit to be free from the need of any data distribution modeling and to account for heterogeneous missing proportion. In both streaming and finite-sample settings, we prove that this algorithm achieves convergence rate of $\mathcal{O}(\frac{1}{n})$ at the iteration $n$, the same as without missing values. We show the convergence behavior and the relevance of the algorithm not only on synthetic data but also on real data sets, including those collected from medical register.

Coreset is usually a small weighted subset of $n$ input points in $\mathbb{R}^d$, that provably approximates their loss function for a given set of queries (models, classifiers, etc.). Coresets become increasingly common in machine learning since existing heuristics or inefficient algorithms may be improved by running them possibly many times on the small coreset that can be maintained for streaming distributed data. Coresets can be obtained by sensitivity (importance) sampling, where its size is proportional to the total sum of sensitivities. Unfortunately, computing the sensitivity of each point is problem dependent and may be harder to compute than the original optimization problem at hand. We suggest a generic framework for computing sensitivities (and thus coresets) for wide family of loss functions which we call near-convex functions. This is by suggesting the $f$-SVD factorization that generalizes the SVD factorization of matrices to functions. Example applications include coresets that are either new or significantly improves previous results, such as SVM, Logistic regression, M-estimators, and $\ell_z$-regression. Experimental results and open source are also provided.

A central problem in learning from sequential data is representing cumulative history in an incremental fashion as more data is processed. We introduce a general framework (HiPPO) for the online compression of continuous signals and discrete time series by projection onto polynomial bases. Given a measure that specifies the importance of each time step in the past, HiPPO produces an optimal solution to a natural online function approximation problem. As special cases, our framework yields a short derivation of the recent Legendre Memory Unit (LMU) from first principles, and generalizes the ubiquitous gating mechanism of recurrent neural networks such as GRUs. This formal framework yields a new memory update mechanism (HiPPO-LegS) that scales through time to remember all history, avoiding priors on the timescale. HiPPO-LegS enjoys the theoretical benefits of timescale robustness, fast updates, and bounded gradients. By incorporating the memory dynamics into recurrent neural networks, HiPPO RNNs can empirically capture complex temporal dependencies. On the benchmark permuted MNIST dataset, HiPPO-LegS sets a new state-of-the-art accuracy of 98.3%. Finally, on a novel trajectory classification task testing robustness to out-of-distribution timescales and missing data, HiPPO-LegS outperforms RNN and neural ODE baselines by 25-40% accuracy.

In this paper, we provide an efficient approximation algorithm for finding the most likelihood configuration (MAP) of size $k$ for Determinantal Point Processes (DPP) in the online setting where the data points arrive in an arbitrary order and the algorithm cannot discard the selected elements from its local memory. Given a tolerance additive error $\eta$, our \online algorithm achieves a $k^{O(k)}$ multiplicative approximation guarantee with an additive error $\eta$, using a memory footprint independent of the size of the data stream. We note that the exponential dependence on $k$ in the approximation factor is unavoidable even in the offline setting. Our result readily implies a streaming algorithm with an improved memory bound compared to existing results.

Decision Trees (DTs) and Random Forests (RFs) are powerful discriminative learners and tools of central importance to the everyday machine learning practitioner and data scientist. Due to their discriminative nature, however, they lack principled methods to process inputs with missing features or to detect outliers, which requires pairing them with imputation techniques or a separate generative model. In this paper, we demonstrate that DTs and RFs can naturally be interpreted as generative models, by drawing a connection to Probabilistic Circuits, a prominent class of tractable probabilistic models. This reinterpretation equips them with a full joint distribution over the feature space and leads to Generative Decision Trees (GeDTs) and Generative Forests (GeFs), a family of novel hybrid generative-discriminative models. This family of models retains the overall characteristics of DTs and RFs while additionally being able to handle missing features by means of marginalisation. Under certain assumptions, frequently made for Bayes consistency results, we show that consistency in GeDTs and GeFs extend to any pattern of missing input features, if missing at random. Empirically, we show that our models often outperform common routines to treat missing data, such as K-nearest neighbour imputation, and moreover, that our models can naturally detect outliers by monitoring the marginal probability of input features.

Many modern data analyses benefit from explicitly modeling dependence structure in data -- such as measurements across time or space, ordered words in a sentence, or genes in a genome. A gold standard evaluation technique is structured cross-validation (CV), which leaves out some data subset (such as data within a time interval or data in a geographic region) in each fold. But CV here can be prohibitively slow due to the need to re-run already-expensive learning algorithms many times. Previous work has shown approximate cross-validation (ACV) methods provide a fast and provably accurate alternative in the setting of empirical risk minimization. But this existing ACV work is restricted to simpler models by the assumptions that (i) data across CV folds are independent and (ii) an exact initial model fit is available. In structured data analyses, both these assumptions are often untrue. In the present work, we address (i) by extending ACV to CV schemes with dependence structure between the folds. To address (ii), we verify -- both theoretically and empirically -- that ACV quality deteriorates smoothly with noise in the initial fit. We demonstrate the accuracy and computational benefits of our proposed methods on a diverse set of real-world applications.

Multivariate regression (or multi-task learning) concerns the task of predicting the value of multiple responses from a set of covariates. In this article, we propose a convex optimization formulation for high-dimensional multivariate linear regression under a general error covariance structure. The main difficulty with simultaneous estimation of the regression coefficients and the error covariance matrix lies in the fact that the negative log-likelihood function is not convex. To overcome this difficulty, a new parameterization is proposed, under which the negative log-likelihood function is proved to be convex. For faster computation, two other alternative loss functions are also considered, and proved to be convex under the proposed parameterization. This new parameterization is also useful for covariate-adjusted Gaussian graphical modeling in which the inverse of the error covariance matrix is of interest. A joint non-asymptotic analysis of the regression coefficients and the error covariance matrix is carried out under the new parameterization. In particular, we show that the proposed method recovers the oracle estimator under sharp scaling conditions, and rates of convergence in terms of vector $\ell_\infty$ norm are also established. Empirically, the proposed methods outperform existing high-dimensional multivariate linear regression methods that are based on either minimizing certain non-convex criteria or certain two-step procedures.

We study the low rank regression problem y = Mx + ε, where x and y are d1 and d2 dimensional vectors respectively. We consider the extreme high-dimensional setting where the number of observations n is less than d1 + d2. Existing algorithms are designed for settings where n is typically as large as rank(M)(d1+d2). This work provides an efficient algorithm which only involves two SVD, and establishes statistical guarantees on its performance. The algorithm decouples the problem by first estimating the precision matrix of the features, and then solving the matrix denoising problem. To complement the upper bound, we introduce new techniques for establishing lower bounds on the performance of any algorithm for this problem. Our preliminary experiments confirm that our algorithm often out-performs existing baseline, and is always at least competitive.

Knowledge distillation introduced in the deep learning context is a method to transfer knowledge from one architecture to another. In particular, when the architectures are identical, this is called self-distillation. The idea is to feed in predictions of the trained model as new target values for retraining (and iterate this loop possibly a few times). It has been empirically observed that the self-distilled model often achieves higher accuracy on held out data. Why this happens, however, has been a mystery: the self-distillation dynamics does not receive any new information about the task and solely evolves by looping over training. To the best of our knowledge, there is no rigorous understanding of why this happens. This work provides the first theoretical analysis of self-distillation. We focus on fitting a nonlinear function to training data, where the model space is Hilbert space and fitting is subject to L2 regularization in this function space. We show that self-distillation iterations modify regularization by progressively limiting the number of basis functions that can be used to represent the solution. This implies (as we also verify empirically) that while a few rounds of self-distillation may reduce over-fitting, further rounds may lead to under-fitting and thus worse performance.

Deep residual networks (ResNets) have demonstrated better generalization performance than deep feedforward networks (FFNets). However, the theory behind such a phenomenon is still largely unknown. This paper studies this fundamental problem in deep learning from a so-called ``neural tangent kernel'' perspective. Specifically, we first show that under proper conditions, as the width goes to infinity, training deep ResNets can be viewed as learning reproducing kernel functions with some kernel function. We then compare the kernel of deep ResNets with that of deep FFNets and discover that the class of functions induced by the kernel of FFNets is asymptotically not learnable, as the depth goes to infinity. In contrast, the class of functions induced by the kernel of ResNets does not exhibit such degeneracy. Our discovery partially justifies the advantages of deep ResNets over deep FFNets in generalization abilities. Numerical results are provided to support our claim.

Rectified linear unit (ReLU) activations can also be thought of as 'gates', which, either pass or stop their pre-activation input when they are 'on' (when the pre-activation input is positive) or 'off' (when the pre-activation input is negative) respectively. A deep neural network (DNN) with ReLU activations has many gates, and the on/off status of each gate changes across input examples as well as network weights. For a given input example, only a subset of gates are 'active', i.e., on, and the sub-network of weights connected to these active gates is responsible for producing the output. At randomised initialisation, the active sub-network corresponding to a given input example is random. During training, as the weights are learnt, the active sub-networks are also learnt, and could hold valuable information.

In this paper, we analytically characterise the role of gates and active sub-networks in deep learning. To this end, we encode the on/off state of the gates for a given input in a novel 'neural path feature' (NPF), and the weights of the DNN are encoded in a novel 'neural path value' (NPV). Further, we show that the output of network is indeed the inner product of NPF and NPV. The main result of the paper shows that the 'neural path kernel' associated with the NPF is a fundamental quantity that characterises the information stored in the gates of a DNN. We show via experiments (on MNIST and CIFAR-10) that in standard DNNs with ReLU activations NPFs are learnt during training and such learning is key for generalisation. Furthermore, NPFs and NPVs can be learnt in two separate networks and such learning also generalises well in experiments. In our experiments, we observe that almost all the information learnt by a DNN with ReLU activations is stored in the gates - a novel observation that underscores the need to investigate the role of the gates in DNNs.

We study the regularisation induced in neural networks by Gaussian noise injections (GNIs). Though such injections have been extensively studied when applied to data, there have been few studies on understanding the regularising effect they induce when applied to network activations. Here we derive the explicit regulariser of GNIs, obtained by marginalising out the injected noise, and show that it penalises functions with high-frequency components in the Fourier domain; particularly in layers closer to a neural network's output. We show analytically and empirically that such regularisation produces calibrated classifiers with large classification margins.

We consider neural networks with rational activation functions. The choice of the nonlinear activation function in deep learning architectures is crucial and heavily impacts the performance of a neural network. We establish optimal bounds in terms of network complexity and prove that rational neural networks approximate smooth functions more efficiently than ReLU networks with exponentially smaller depth. The flexibility and smoothness of rational activation functions make them an attractive alternative to ReLU, as we demonstrate with numerical experiments.

Recent theoretical work has shown that massively overparameterized neural networks are equivalent to kernel regressors that use Neural Tangent Kernels (NTKs). Experiments show that these kernel methods perform similarly to real neural networks. Here we show that NTK for fully connected networks with ReLU activation is closely related to the standard Laplace kernel. We show theoretically that for normalized data on the hypersphere both kernels have the same eigenfunctions and their eigenvalues decay polynomially at the same rate, implying that their Reproducing Kernel Hilbert Spaces (RKHS) include the same sets of functions. This means that both kernels give rise to classes of functions with the same smoothness properties. The two kernels differ for data off the hypersphere, but experiments indicate that when data is properly normalized these differences are not significant. Finally, we provide experiments on real data comparing NTK and the Laplace kernel, along with a larger class of $\gamma$-exponential kernels. We show that these perform almost identically. Our results suggest that much insight about neural networks can be obtained from analysis of the well-known Laplace kernel, which has a simple closed form.

In this work, we analyze the role of the network architecture in shaping the inductive bias of deep classifiers. To that end, we start by focusing on a very simple problem, i.e., classifying a class of linearly separable distributions, and show that, depending on the direction of the discriminative feature of the distribution, many state-of-the-art deep convolutional neural networks (CNNs) have a surprisingly hard time solving this simple task. We then define as neural anisotropy directions (NADs) the vectors that encapsulate the directional inductive bias of an architecture. These vectors, which are specific for each architecture and hence act as a signature, encode the preference of a network to separate the input data based on some particular features. We provide an efficient method to identify NADs for several CNN architectures and thus reveal their directional inductive biases. Furthermore, we show that, for the CIFAR-10 dataset, NADs characterize the features used by CNNs to discriminate between different classes.

We present a new paradigm for Neural ODE algorithms, called ODEtoODE, where time-dependent parameters of the main flow evolve according to a matrix flow on the orthogonal group O(d). This nested system of two flows, where the parameter-flow is constrained to lie on the compact manifold, provides stability and effectiveness of training and solves the gradient vanishing-explosion problem which is intrinsically related to training deep neural network architectures such as Neural ODEs. Consequently, it leads to better downstream models, as we show on the example of training reinforcement learning policies with evolution strategies, and in the supervised learning setting, by comparing with previous SOTA baselines. We provide strong convergence results for our proposed mechanism that are independent of the width of the network, supporting our empirical studies. Our results show an intriguing connection between the theory of deep neural networks and the field of matrix flows on compact manifolds.

As a popular approach to modeling the dynamics of training overparametrized neural networks (NNs), the neural tangent kernels (NTK) are known to fall behind real-world NNs in generalization ability. This performance gap is in part due to the \textit{label agnostic} nature of the NTK, which renders the resulting kernel not as \textit{locally elastic} as NNs~\citep{he2019local}. In this paper, we introduce a novel approach from the perspective of \emph{label-awareness} to reduce this gap for the NTK. Specifically, we propose two label-aware kernels that are each a superimposition of a label-agnostic part and a hierarchy of label-aware parts with increasing complexity of label dependence, using the Hoeffding decomposition. Through both theoretical and empirical evidence, we show that the models trained with the proposed kernels better simulate NNs in terms of generalization ability and local elasticity.

Self-attention architectures, which are rapidly pushing the frontier in natural language processing, demonstrate a surprising depth-inefficient behavior: previous works indicate that increasing the internal representation (network width) is just as useful as increasing the number of self-attention layers (network depth). We theoretically predict a width-dependent transition between depth-efficiency and depth-inefficiency in self-attention. We conduct systematic empirical ablations on networks of depths 6 to 48 that clearly reveal the theoretically predicted behaviors, and provide explicit quantitative suggestions regarding the optimal depth-to-width allocation for a given self-attention network size. The race towards beyond 1-Trillion parameter language models renders informed guidelines for increasing self-attention depth and width in tandem an essential ingredient. Our guidelines elucidate the depth-to-width trade-off in self-attention networks of sizes up to the scale of GPT3 (which is too deep for its size), and beyond, marking an unprecedented width of 30K as optimal for a 1-Trillion parameter self-attention network.

The goal of this work is to shed light on the remarkable phenomenon of "transition to linearity" of certain neural networks as their width approaches infinity. We show that the "transition to linearity'' of the model and, equivalently, constancy of the (neural) tangent kernel (NTK) result from the scaling properties of the norm of the Hessian matrix of the network as a function of the network width. We present a general framework for understanding the constancy of the tangent kernel via Hessian scaling applicable to the standard classes of neural networks. Our analysis provides a new perspective on the phenomenon of constant tangent kernel, which is different from the widely accepted "lazy training''. Furthermore, we show that the "transition to linearity" is not a general property of wide neural networks and does not hold when the last layer of the network is non-linear. It is also not necessary for successful optimization by gradient descent.

We provide a detailed asymptotic study of gradient flow trajectories and their implicit optimization bias when minimizing the exponential loss over "diagonal linear networks". This is the simplest model displaying a transition between "kernel" and non-kernel ("rich" or "active") regimes. We show how the transition is controlled by the relationship between the initialization scale and how accurately we minimize the training loss. Our results indicate that some limit behavior of gradient descent only kick in at ridiculous training accuracies (well beyond 10^-100). Moreover, the implicit bias at reasonable initialization scales and training accuracies is more complex and not captured by these limits.

In the light of the fact that the stochastic gradient descent (SGD) often finds a flat minimum valley in the training loss, we propose a novel directional pruning method which searches for a sparse minimizer in or close to that flat region. The proposed pruning method does not require retraining or the expert knowledge on the sparsity level. To overcome the computational formidability of estimating the flat directions, we propose to use a carefully tuned $\ell_1$ proximal gradient algorithm which can provably achieve the directional pruning with a small learning rate after sufficient training. The empirical results demonstrate the promising results of our solution in highly sparse regime (92% sparsity) among many existing pruning methods on the ResNet50 with the ImageNet, while using only a slightly higher wall time and memory footprint than the SGD. Using the VGG16 and the wide ResNet 28x10 on the CIFAR-10 and CIFAR-100, we demonstrate that our solution reaches the same minima valley as the SGD, and the minima found by our solution and the SGD do not deviate in directions that impact the training loss. The code that reproduces the results of this paper is available at https://github.com/donlan2710/gRDA-Optimizer/tree/master/directional_pruning.

The search for efficient, sparse deep neural network models is most prominently performed by pruning: training a dense, overparameterized network and removing parameters, usually via following a manually-crafted heuristic. Additionally, the recent Lottery Ticket Hypothesis conjectures that, for a typically-sized neural network, it is possible to find small sub-networks which, when trained from scratch on a comparable budget, match the performance of the original dense counterpart. We revisit fundamental aspects of pruning algorithms, pointing out missing ingredients in previous approaches, and develop a method, Continuous Sparsification, which searches for sparse networks based on a novel approximation of an intractable $\ell_0$ regularization. We compare against dominant heuristic-based methods on pruning as well as ticket search -- finding sparse subnetworks that can be successfully re-trained from an early iterate. Empirical results show that we surpass the state-of-the-art for both objectives, across models and datasets, including VGG trained on CIFAR-10 and ResNet-50 trained on ImageNet. In addition to setting a new standard for pruning, Continuous Sparsification also offers fast parallel ticket search, opening doors to new applications of the Lottery Ticket Hypothesis.

We consider the optimization problem associated with fitting two-layers ReLU networks with respect to the squared loss, where labels are generated by a target network. We leverage the rich symmetry structure to analytically characterize the Hessian at various families of spurious minima in the natural regime where the number of inputs $d$ and the number of hidden neurons $k$ is finite. In particular, we prove that for $d\ge k$ standard Gaussian inputs: (a) of the $dk$ eigenvalues of the Hessian, $dk - O(d)$ concentrate near zero, (b) $\Omega(d)$ of the eigenvalues grow linearly with $k$. Although this phenomenon of extremely skewed spectrum has been observed many times before, to our knowledge, this is the first time it has been established {rigorously}. Our analytic approach uses techniques, new to the field, from symmetry breaking and representation theory, and carries important implications for our ability to argue about statistical generalization through local curvature.

This paper shows that deep learning, i.e., neural networks trained by SGD, can learn in polytime any function class that can be learned in polytime by some algorithm, including parities. This universal result is further shown to be robust, i.e., it holds under possibly poly-noise on the gradients, which gives a separation between deep learning and statistical query algorithms, as the latter are not comparably universal due to cases like parities. This also shows that SGD-based deep learning does not suffer from the limitations of the perceptron discussed by Minsky-Papert '69. The paper further complement this result with a lower-bound on the generalization error of descent algorithms, which implies in particular that the robust universality breaks down if the gradients are averaged over large enough batches of samples as in full-GD, rather than fewer samples as in SGD.

Reservoir Computing is a class of simple yet efficient Recurrent Neural Networks where internal weights are fixed at random and only a linear output layer is trained. In the large size limit, such random neural networks have a deep connection with kernel methods. Our contributions are threefold: a) We rigorously establish the recurrent kernel limit of Reservoir Computing and prove its convergence. b) We test our models on chaotic time series prediction, a classic but challenging benchmark in Reservoir Computing, and show how the Recurrent Kernel is competitive and computationally efficient when the number of data points remains moderate. c) When the number of samples is too large, we leverage the success of structured Random Features for kernel approximation by introducing Structured Reservoir Computing. The two proposed methods, Recurrent Kernel and Structured Reservoir Computing, turn out to be much faster and more memory-efficient than conventional Reservoir Computing.

Ensemble is a general way of improving the accuracy and stability of learning models, especially for the generalization ability on small datasets. Compared with tree-based methods, relatively less works have been devoted to an in-depth study on effective ensemble design for neural networks. In this paper, we propose a principled ensemble technique by constructing the so-called diversified ensemble layer to combine multiple networks as individual modules. We theoretically show that each individual model in our ensemble layer corresponds to weights in the ensemble layer optimized in different directions. Meanwhile, the devised ensemble layer can be readily integrated into popular neural architectures, including CNNs, RNNs, and GCNs. Extensive experiments are conducted on public tabular datasets, images, and texts. By adopting weight sharing approach, the results show our method can notably improve the accuracy and stability of the original neural networks with ignorable extra time and space overhead.

Multi-task learning is an open and challenging problem in computer vision. The typical way of conducting multi-task learning with deep neural networks is either through handcrafted schemes that share all initial layers and branch out at an adhoc point, or through separate task-specific networks with an additional feature sharing/fusion mechanism. Unlike existing methods, we propose an adaptive sharing approach, calledAdaShare, that decides what to share across which tasks to achieve the best recognition accuracy, while taking resource efficiency into account. Specifically, our main idea is to learn the sharing pattern through a task-specific policy that selectively chooses which layers to execute for a given task in the multi-task network. We efficiently optimize the task-specific policy jointly with the network weights, using standard back-propagation. Experiments on several challenging and diverse benchmark datasets with a variable number of tasks well demonstrate the efficacy of our approach over state-of-the-art methods. Project page: https://cs-people.bu.edu/sunxm/AdaShare/project.html

Learning equivariant representations is a promising way to reduce sample and model complexity and improve the generalization performance of deep neural networks. The spherical CNNs are successful examples, producing SO(3)-equivariant representations of spherical inputs. There are two main types of spherical CNNs. The first type lifts the inputs to functions on the rotation group SO(3) and applies convolutions on the group, which are computationally expensive since SO(3) has one extra dimension. The second type applies convolutions directly on the sphere, which are limited to zonal (isotropic) filters, and thus have limited expressivity. In this paper, we present a new type of spherical CNN that allows anisotropic filters in an efficient way, without ever leaving the spherical domain. The key idea is to consider spin-weighted spherical functions, which were introduced in physics in the study of gravitational waves. These are complex-valued functions on the sphere whose phases change upon rotation. We define a convolution between spin-weighted functions and build a CNN based on it. The spin-weighted functions can also be interpreted as spherical vector fields, allowing applications to tasks where the inputs or outputs are vector fields. Experiments show that our method outperforms previous methods on tasks like classification of spherical images, classification of 3D shapes and semantic segmentation of spherical panoramas.

Autoencoders (AE) aim to reproduce the output from the input. They may hence tend to overfit towards learning the identity-function between the input and output, i.e., they may predict each feature in the output from itself in the input. This is not useful, however, when AEs are used for prediction tasks in the presence of noise in the data. It may seem intuitively evident that this kind of overfitting is prevented by training a denoising AE, as the dropped-out features have to be predicted from the other features. In this paper, we consider linear autoencoders, as they facilitate analytic solutions, and first show that denoising / dropout actually prevents the overfitting towards the identity-function only to the degree that it is penalized by the induced L2-norm regularization. In the main theorem of this paper, we show that the emphasized denoising AE is indeed capable of completely eliminating the overfitting towards the identity-function. Our derivations reveal several new insights, including the closed-form solution of the full-rank model, as well as a new (near-)orthogonality constraint in the low-rank model. While this constraint is conceptually very different from the regularizers recently proposed, their resulting effects on the learned embeddings are empirically similar. Our experiments on three well-known data-sets corroborate the various theoretical insights derived in this paper.

A central mechanism in machine learning is to identify, store, and recognize patterns. How to learn, access, and retrieve such patterns is crucial in Hopfield networks and the more recent transformer architectures. We show that the attention mechanism of transformer architectures is actually the update rule of modern Hopfield networks that can store exponentially many patterns. We exploit this high storage capacity of modern Hopfield networks to solve a challenging multiple instance learning (MIL) problem in computational biology: immune repertoire classification. In immune repertoire classification, a vast number of immune receptors are used to predict the immune status of an individual. This constitutes a MIL problem with an unprecedentedly massive number of instances, two orders of magnitude larger than currently considered problems, and with an extremely low witness rate. Accurate and interpretable machine learning methods solving this problem could pave the way towards new vaccines and therapies, which is currently a very relevant research topic intensified by the COVID-19 crisis. In this work, we present our novel method DeepRC that integrates transformer-like attention, or equivalently modern Hopfield networks, into deep learning architectures for massive MIL such as immune repertoire classification. We demonstrate that DeepRC outperforms all other methods with respect to predictive performance on large-scale experiments including simulated and real-world virus infection data and enables the extraction of sequence motifs that are connected to a given disease class. Source code and datasets: https://github.com/ml-jku/DeepRC

Signed distance field (SDF) is a prominent implicit representation of 3D meshes. Methods that are based on such representation achieved state-of-the-art 3D shape reconstruction quality. However, these methods struggle to reconstruct non-convex shapes. One remedy is to incorporate a constructive solid geometry framework (CSG) that represents a shape as a decomposition into primitives. It allows to embody a 3D shape of high complexity and non-convexity with a simple tree representation of Boolean operations. Nevertheless, existing approaches are supervised and require the entire CSG parse tree that is given upfront during the training process. On the contrary, we propose a model that extracts a CSG parse tree without any supervision - UCSG-Net. Our model predicts parameters of primitives and binarizes their SDF representation through differentiable indicator function. It is achieved jointly with discovering the structure of a Boolean operators tree. The model selects dynamically which operator combination over primitives leads to the reconstruction of high fidelity. We evaluate our method on 2D and 3D autoencoding tasks. We show that the predicted parse tree representation is interpretable and can be used in CAD software.

Most state-of-the-art deep geometric learning single-view reconstruction approaches rely on encoder-decoder architectures that output either shape parametrizations or implicit representations. However, these representations rarely preserve the Euclidean structure of the 3D space objects exist in. In this paper, we show that building a geometry preserving 3-dimensional latent space helps the network concurrently learn global shape regularities and local reasoning in the object coordinate space and, as a result, boosts performance.

We demonstrate both on ShapeNet synthetic images, which are often used for benchmarking purposes, and on real-world images that our approach outperforms state-of-the-art ones. Furthermore, the single-view pipeline naturally extends to multi-view reconstruction, which we also show.

While numerous approaches have been developed to embed graphs into either Euclidean or hyperbolic spaces, they do not fully utilize the information available in graphs, or lack the flexibility to model intrinsic complex graph geometry. To utilize the strength of both Euclidean and hyperbolic geometries, we develop a novel Geometry Interaction Learning (GIL) method for graphs, a well-suited and efficient alternative for learning abundant geometric properties in graph. GIL captures a more informative internal structural features with low dimensions while maintaining conformal invariance of each space. Furthermore, our method endows each node the freedom to determine the importance of each geometry space via a flexible dual feature interaction learning and probability assembling mechanism. Promising experimental results are presented for five benchmark datasets on node classification and link prediction tasks.

Feature importance ranking has become a powerful tool for explainable AI. However, its nature of combinatorial optimization poses a great challenge for deep learning. In this paper, we propose a novel dual-net architecture consisting of operator and selector for discovery of an optimal feature subset of a fixed size and ranking the importance of those features in the optimal subset simultaneously. During learning, the operator is trained for a supervised learning task via optimal feature subset candidates generated by the selector that learns predicting the learning performance of the operator working on different optimal subset candidates. We develop an alternate learning algorithm that trains two nets jointly and incorporates a stochastic local search procedure into learning to address the combinatorial optimization challenge. In deployment, the selector generates an optimal feature subset and ranks feature importance, while the operator makes predictions based on the optimal subset for test data. A thorough evaluation on synthetic, benchmark and real data sets suggests that our approach outperforms several state-of-the-art feature importance ranking and supervised feature selection methods. (Our source code is available: https://github.com/maksym33/FeatureImportanceDL)

Rather than performing inefficient local iterative routing between adjacent capsule layers, we propose an alternative global view based on representing the inherent uncertainty in part-object assignment. In our formulation, the local routing iterations are replaced with variational inference of part-object connections in a probabilistic capsule network, leading to a significant speedup without sacrificing performance. In this way, global context is also considered when routing capsules by introducing global latent variables that have direct influence on the objective function, and are updated discriminatively in accordance with the minimum description length (MDL) principle. We focus on enhancing capsule network properties, and perform a thorough evaluation on pose-aware tasks, observing improvements in performance over previous approaches whilst being more computationally efficient.

Several works have proposed Simplicity Bias (SB)---the tendency of standard training procedures such as Stochastic Gradient Descent (SGD) to find simple models---to justify why neural networks generalize well [Arpit et al. 2017, Nakkiran et al. 2019, Valle-Perez et al. 2019]. However, the precise notion of simplicity remains vague. Furthermore, previous settings [Soudry et al. 2018, Gunasekar et al. 2018] that use SB to theoretically justify why neural networks generalize well do not simultaneously capture the non-robustness of neural networks---a widely observed phenomenon in practice [Goodfellow et al. 2014, Jo and Bengio 2017]. We attempt to reconcile SB and the superior standard generalization of neural networks with the non-robustness observed in practice by introducing piecewise-linear and image-based datasets, which (a) incorporate a precise notion of simplicity, (b) comprise multiple predictive features with varying levels of simplicity, and (c) capture the non-robustness of neural networks trained on real data. Using theory and empirics on these datasets, we make four observations: (i) SB of SGD and variants can be extreme: neural networks can exclusively rely on the simplest feature and remain invariant to all predictive complex features. (ii) The extreme aspect of SB could explain why seemingly benign distribution shifts and small adversarial perturbations significantly degrade model performance. (iii) Contrary to conventional wisdom, SB can also hurt generalization on the same data distribution, as SB persists even when the simplest feature has less predictive power than the more complex features. (iv) Common approaches to improve generalization and robustness---ensembles and adversarial training---can fail in mitigating SB and its pitfalls. Given the role of SB in training neural networks, we hope that the proposed datasets and methods serve as an effective testbed to evaluate novel algorithmic approaches aimed at avoiding the pitfalls of SB.

Recent works in geometric deep learning have introduced neural networks that allow performing inference tasks on three-dimensional geometric data by defining convolution --and sometimes pooling-- operations on triangle meshes. These methods, however, either consider the input mesh as a graph, and do not exploit specific geometric properties of meshes for feature aggregation and downsampling, or are specialized for meshes, but rely on a rigid definition of convolution that does not properly capture the local topology of the mesh. We propose a method that combines the advantages of both types of approaches, while addressing their limitations: we extend a primal-dual framework drawn from the graph-neural-network literature to triangle meshes, and define convolutions on two types of graphs constructed from an input mesh. Our method takes features for both edges and faces of a 3D mesh as input, and dynamically aggregates them using an attention mechanism. At the same time, we introduce a pooling operation with a precise geometric interpretation, that allows handling variations in the mesh connectivity by clustering mesh faces in a task-driven fashion. We provide theoretical insights of our approach using tools from the mesh-simplification literature. In addition, we validate experimentally our method in the tasks of shape classification and shape segmentation, where we obtain comparable or superior performance to the state of the art.

This paper introduces a new method to build linear flows, by taking the exponential of a linear transformation. This linear transformation does not need to be invertible itself, and the exponential has the following desirable properties: it is guaranteed to be invertible, its inverse is straightforward to compute and the log Jacobian determinant is equal to the trace of the linear transformation. An important insight is that the exponential can be computed implicitly, which allows the use of convolutional layers. Using this insight, we develop new invertible transformations named convolution exponentials and graph convolution exponentials, which retain the equivariance of their underlying transformations. In addition, we generalize Sylvester Flows and propose Convolutional Sylvester Flows which are based on the generalization and the convolution exponential as basis change. Empirically, we show that the convolution exponential outperforms other linear transformations in generative flows on CIFAR10 and the graph convolution exponential improves the performance of graph normalizing flows. In addition, we show that Convolutional Sylvester Flows improve performance over residual flows as a generative flow model measured in log-likelihood.

Hierarchical multi-label classification (HMC) is a challenging classification task extending standard multi-label classification problems by imposing a hierarchy constraint on the classes. In this paper, we propose C-HMCNN(h), a novel approach for HMC problems, which, given a network h for the underlying multi-label classification problem, exploits the hierarchy information in order to produce predictions coherent with the constraint and improve performance. We conduct an extensive experimental analysis showing the superior performance of C-HMCNN(h) when compared to state-of-the-art models.

Finding the k largest or smallest elements from a collection of scores, i.e., top-k operation, is an important model component widely used in information retrieval, machine learning, and data mining. However, if the top-k operation is implemented in an algorithmic way, e.g., using bubble algorithm, the resulted model cannot be trained in an end-to-end way using prevalent gradient descent algorithms. This is because these implementations typically involve swapping indices, whose gradient cannot be computed. Moreover, the corresponding mapping from the input scores to the indicator vector of whether this element belongs to the top-k set is essentially discontinuous. To address the issue, we propose a smoothed approximation, namely SOFT (Scalable Optimal transport-based diFferenTiable) top-k operator. Specifically, our SOFT top-k operator approximates the output of top-k operation as the solution of an Entropic Optimal Transport (EOT) problem. The gradient of the SOFT operator can then be efficiently approximated based on the optimality conditions of EOT problem. We then apply the proposed operator to k-nearest neighbors algorithm and beam search algorithm. The numerical experiment demonstrates their achieve improved performance.

Underpinning the success of deep learning is effective regularizations that allow a variety of priors in data to be modeled. For example, robustness to adversarial perturbations, and correlations between multiple modalities. However, most regularizers are specified in terms of hidden layer outputs, which are not themselves optimization variables. In contrast to prevalent methods that optimize them indirectly through model weights, we propose inserting proximal mapping as a new layer to the deep network, which directly and explicitly produces well regularized hidden layer outputs. The resulting technique is shown well connected to kernel warping and dropout, and novel algorithms were developed for robust temporal learning and multiview modeling, both outperforming state-of-the-art methods.

The scalability of Distributed Stochastic Gradient Descent (SGD) is today limited by communication bottlenecks. We propose a novel SGD variant: \underline{C}ommunication-efficient \underline{S}GD with \underline{E}rror \underline{R}eset, or \underline{CSER}. The key idea in CSER is first a new technique called ``error reset'' that adapts arbitrary compressors for SGD, producing bifurcated local models with periodic reset of resulting local residual errors. Second we introduce partial synchronization for both the gradients and the models, leveraging advantages from them. We prove the convergence of CSER for smooth non-convex problems. Empirical results show that when combined with highly aggressive compressors, the CSER algorithms accelerate the distributed training by nearly $10\times$ for CIFAR-100, and by $4.5\times$ for ImageNet.

Lossy gradient compression has become a practical tool to overcome the communication bottleneck in centrally coordinated distributed training of machine learning models. However, algorithms for decentralized training with compressed communication over arbitrary connected networks have been more complicated, requiring additional memory and hyperparameters. We introduce a simple algorithm that directly compresses the model differences between neighboring workers using low-rank linear compressors. We prove that our method does not require any additional hyperparameters, converges faster than prior methods, and is asymptotically independent of both the network and the compression. Inspired the PowerSGD algorithm for centralized deep learning, we execute power iteration steps on model differences to maximize the information transferred per bit. Out of the box, these compressors perform on par with state-of-the-art tuned compression algorithms in a series of deep learning benchmarks.

Generative Adversarial Networks (GANs) are a powerful class of generative models in the deep learning community. Current practice on large-scale GAN training utilizes large models and distributed large-batch training strategies, and is implemented on deep learning frameworks (e.g., TensorFlow, PyTorch, etc.) designed in a centralized manner. In the centralized network topology, every worker needs to either directly communicate with the central node or indirectly communicate with all other workers in every iteration. However, when the network bandwidth is low or network latency is high, the performance would be significantly degraded. Despite recent progress on decentralized algorithms for training deep neural networks, it remains unclear whether it is possible to train GANs in a decentralized manner. The main difficulty lies at handling the nonconvex-nonconcave min-max optimization and the decentralized communication simultaneously. In this paper, we address this difficulty by designing the \textbf{first gradient-based decentralized parallel algorithm} which allows workers to have multiple rounds of communications in one iteration and to update the discriminator and generator simultaneously, and this design makes it amenable for the convergence analysis of the proposed decentralized algorithm. Theoretically, our proposed decentralized algorithm is able to solve a class of non-convex non-concave min-max problems with provable non-asymptotic convergence to first-order stationary point. Experimental results on GANs demonstrate the effectiveness of the proposed algorithm.

In this paper we study the problem of escaping from saddle points and achieving second-order optimality in a decentralized setting where a group of agents collaborate to minimize their aggregate objective function. We provide a non-asymptotic (finite-time) analysis and show that by following the idea of perturbed gradient descent, it is possible to converge to a second-order stationary point in a number of iterations which depends linearly on dimension and polynomially on the accuracy of second-order stationary point. Doing this in a communication-efficient manner requires overcoming several challenges, from identifying (first order) stationary points in a distributed manner, to adapting the perturbed gradient framework without prohibitive communication complexity. Our proposed Perturbed Decentralized Gradient Tracking (PDGT) method consists of two major stages: (i) a gradient-based step to find a first-order stationary point and (ii) a perturbed gradient descent step to escape from a first-order stationary point, if it is a saddle point with sufficient curvature. As a side benefit of our result, in the case that all saddle points are non-degenerate (strict), the proposed PDGT method finds a local minimum of the considered decentralized optimization problem in a finite number of iterations.

We develop a distributed second order optimization algorithm that is communication-efficient as well as robust against Byzantine failures of the worker machines. We propose an iterative approximate Newton-type algorithm, where the worker machines communicate \emph{only once} per iteration with the central machine. This is in sharp contrast with the state-of-the-art distributed second order algorithms like GIANT \cite{giant}, DINGO\cite{dingo}, where the worker machines send (functions of) local gradient and Hessian sequentially; thus ending up communicating twice with the central machine per iteration. Furthermore, we employ a simple norm based thresholding rule to filter-out the Byzantine worker machines. We establish the linear-quadratic rate of convergence of our proposed algorithm and establish that the communication savings and Byzantine resilience attributes only correspond to a small statistical error rate for arbitrary convex loss functions. To the best of our knowledge, this is the first work that addresses the issue of Byzantine resilience in second order distributed optimization. Furthermore, we validate our theoretical results with extensive experiments on synthetically generated and benchmark LIBSVM \cite{libsvm} data-set and demonstrate convergence guarantees.

We introduce a framework for designing primal methods under the decentralized optimization setting where local functions are smooth and strongly convex. Our approach consists of approximately solving a sequence of sub-problems induced by the accelerated augmented Lagrangian method, thereby providing a systematic way for deriving several well-known decentralized algorithms including EXTRA and SSDA. When coupled with accelerated gradient descent, our framework yields a novel primal algorithm whose convergence rate is optimal and matched by recently derived lower bounds. We provide experimental results that demonstrate the effectiveness of the proposed algorithm on highly ill-conditioned problems.

We consider the problem of training machine learning models on distributed data in a decentralized way. For finite-sum problems, fast single-machine algorithms for large datasets rely on stochastic updates combined with variance reduction. Yet, existing decentralized stochastic algorithms either do not obtain the full speedup allowed by stochastic updates, or require oracles that are more expensive than regular gradients. In this work, we introduce a Decentralized stochastic algorithm with Variance Reduction called DVR. DVR only requires computing stochastic gradients of the local functions, and is computationally as fast as a standard stochastic variance-reduced algorithms run on a $1/n$ fraction of the dataset, where $n$ is the number of nodes. To derive DVR, we use Bregman coordinate descent on a well-chosen dual problem, and obtain a dual-free algorithm using a specific Bregman divergence. We give an accelerated version of DVR based on the Catalyst framework, and illustrate its effectiveness with simulations on real data.

Motivated by federated learning, we consider the hub-and-spoke model of distributed optimization in which a central authority coordinates the computation of a solution among many agents while limiting communication. We first study some past procedures for federated optimization, and show that their fixed points need not correspond to stationary points of the original optimization problem, even in simple convex settings with deterministic updates. In order to remedy these issues, we introduce FedSplit, a class of algorithms based on operator splitting procedures for solving distributed convex minimization with additive structure. We prove that these procedures have the correct fixed points, corresponding to optima of the original optimization problem, and we characterize their convergence rates under different settings. Our theory shows that these methods are provably robust to inexact computation of intermediate local quantities. We complement our theory with some experiments that demonstrate the benefits of our methods in practice.

In this paper, we study communication efficient distributed algorithms for distributionally robust federated learning via periodic averaging with adaptive sampling. In contrast to standard empirical risk minimization, due to the minimax structure of the underlying optimization problem, a key difficulty arises from the fact that the global parameter that controls the mixture of local losses can only be updated infrequently on the global stage. To compensate for this, we propose a Distributionally Robust Federated Averaging (DRFA) algorithm that employs a novel snapshotting scheme to approximate the accumulation of history gradients of the mixing parameter. We analyze the convergence rate of DRFA in both convex-linear and nonconvex-linear settings. We also generalize the proposed idea to objectives with regularization on the mixture parameter and propose a proximal variant, dubbed as DRFA-Prox, with provable convergence rates. We also analyze an alternative optimization method for regularized case in strongly-convex-strongly-concave and non-convex (under PL condition)-strongly-concave settings. To the best of our knowledge, this paper is the first to solve distributionally robust federated learning with reduced communication, and to analyze the efficiency of local descent methods on distributed minimax problems. We give corroborating experimental evidence for our theoretical results in federated learning settings.

Federated learning (FL) is a decentralized and privacy-preserving machine learning technique in which a group of clients collaborate with a server to learn a global model without sharing clients' data. One challenge associated with FL is statistical diversity among clients, which restricts the global model from delivering good performance on each client's task. To address this, we propose an algorithm for personalized FL (pFedMe) using Moreau envelopes as clients' regularized loss functions, which help decouple personalized model optimization from the global model learning in a bi-level problem stylized for personalized FL. Theoretically, we show that pFedMe convergence rate is state-of-the-art: achieving quadratic speedup for strongly convex and sublinear speedup of order 2/3 for smooth nonconvex objectives. Experimentally, we verify that pFedMe excels at empirical performance compared with the vanilla FedAvg and Per-FedAvg, a meta-learning based personalized FL algorithm.

We analyze Local SGD (aka parallel or federated SGD) and Minibatch SGD in the heterogeneous distributed setting, where each machine has access to stochastic gradient estimates for a different, machine-specific, convex objective; the goal is to optimize w.r.t.~the average objective; and machines can only communicate intermittently. We argue that, (i) Minibatch SGD (even without acceleration) dominates all existing analysis of Local SGD in this setting, (ii) accelerated Minibatch SGD is optimal when the heterogeneity is high, and (iii) present the first upper bound for Local SGD that improves over Minibatch SGD in a non-homogeneous regime.

We extend the Approximate-Proximal Point (aProx) family of model-based methods for solving stochastic convex optimization problems, including stochastic subgradient, proximal point, and bundle methods, to the minibatch setting. To do this, we propose two minibatched algorithms for which we prove a non-asymptotic upper bound on the rate of convergence, revealing a linear speedup in minibatch size. In contrast to standard stochastic gradient methods, these methods may have linear speedup in the minibatch setting even for non-smooth functions. Our algorithms maintain the desirable traits characteristic of the aProx family, such as robustness to initial step size choice. Additionally, we show improved convergence rates for "interpolation" problems, which (for example) gives a new parallelization strategy for alternating projections. We corroborate our theoretical results with extensive empirical testing, which demonstrates the gains provided by accurate modeling and minibatching.

In Federated Learning, we aim to train models across multiple computing units (users), while users can only communicate with a common central server, without exchanging their data samples. This mechanism exploits the computational power of all users and allows users to obtain a richer model as their models are trained over a larger set of data points. However, this scheme only develops a common output for all the users, and, therefore, it does not adapt the model to each user. This is an important missing feature, especially given the heterogeneity of the underlying data distribution for various users. In this paper, we study a personalized variant of the federated learning in which our goal is to find an initial shared model that current or new users can easily adapt to their local dataset by performing one or a few steps of gradient descent with respect to their own data. This approach keeps all the benefits of the federated learning architecture, and, by structure, leads to a more personalized model for each user. We show this problem can be studied within the Model-Agnostic Meta-Learning (MAML) framework. Inspired by this connection, we study a personalized variant of the well-known Federated Averaging algorithm and evaluate its performance in terms of gradient norm for non-convex loss functions. Further, we characterize how this performance is affected by the closeness of underlying distributions of user data, measured in terms of distribution distances such as Total Variation and 1-Wasserstein metric.

This work proposes a novel smoothing method, called Bend, Mix and Release (BMR), that extends two well-known smooth approximations of the convex optimization literature: randomized smoothing and the Moreau envelope. The BMR smoothing method allows to trade-off between the computational simplicity of randomized smoothing (RS) and the approximation efficiency of the Moreau envelope (ME). More specifically, we show that BMR achieves up to a $\sqrt{d}$ multiplicative improvement compared to the approximation error of RS, where $d$ is the dimension of the search space, while being less computation intensive than the ME. For non-convex objectives, BMR also has the desirable property to widen local minima, allowing optimization methods to reach small cracks and crevices of extremely irregular and non-convex functions, while being well-suited to a distributed setting. This novel smoothing method is then used to improve first-order non-smooth optimization (both convex and non-convex) by allowing for a local exploration of the search space. More specifically, our analysis sheds light on the similarities between evolution strategies and BMR, creating a link between exploration strategies of zeroth-order methods and the regularity of first-order optimization problems. Finally, we evidence the impact of BMR through synthetic experiments.

Recently, there is a growing interest in the study of median-based algorithms for distributed non-convex optimization. Two prominent examples include signSGD with majority vote, an effective approach for communication reduction via 1-bit compression on the local gradients, and medianSGD, an algorithm recently proposed to ensure robustness against Byzantine workers. The convergence analyses for these algorithms critically rely on the assumption that all the distributed data are drawn iid from the same distribution. However, in applications such as Federated Learning, the data across different nodes or machines can be inherently heterogeneous, which violates such an iid assumption. This work analyzes signSGD and medianSGD in distributed settings with heterogeneous data. We show that these algorithms are non-convergent whenever there is some disparity between the expected median and mean over the local gradients. To overcome this gap, we provide a novel gradient correction mechanism that perturbs the local gradients with noise, which we show can provably close the gap between mean and median of the gradients. The proposed methods largely preserve nice properties of these median-based algorithms, such as the low per-iteration communication complexity of signSGD, and further enjoy global convergence to stationary solutions. Our perturbation technique can be of independent interest when one wishes to estimate mean through a median estimator.

In this paper, we propose a unified analysis of variants of distributed SGD with arbitrary compressions and delayed updates. Our framework is general enough to cover different variants of quantized SGD, Error-Compensated SGD (EC-SGD), and SGD with delayed updates (D-SGD). Via single theorem, we derive the complexity results for all the methods that fit our framework. For the existing methods, this theorem gives the best-known complexity results. Moreover, using our general scheme, we develop new variants of SGD that combine variance reduction or arbitrary sampling with error feedback and quantization and derive the convergence rates for these methods beating the state-of-the-art results. In order to illustrate the strength of our framework, we develop 16 new methods that fit this. In particular, we propose the first method called EC-SGD-DIANA that is based on error-feedback for biased compression operator and quantization of gradient differences and prove the convergence guarantees showing that EC-SGD-DIANA converges to the exact optimum asymptotically in expectation with constant learning rate for both convex and strongly convex objectives when workers compute full gradients of their loss functions. Moreover, for the case when the loss function of the worker has the form of finite sum, we modified the method and got a new one called EC-LSVRG-DIANA which is the first distributed stochastic method with error feedback and variance reduction that converges to the exact optimum asymptotically in expectation with constant learning rate.

We study the statistical problem of estimating a rank-one sparse tensor corrupted by additive gaussian noise, a Gaussian additive model also known as sparse tensor PCA. We show that for Bernoulli and Bernoulli-Rademacher distributed signals and \emph{for all} sparsity levels which are sublinear in the dimension of the signal, the sparse tensor PCA model exhibits a phase transition called the \emph{all-or-nothing phenomenon}. This is the property that for some signal-to-noise ratio (SNR) $\mathrm{SNR_c}$ and any fixed $\epsilon>0$, if the SNR of the model is below $\left(1-\epsilon\right)\mathrm{SNR_c}$, then it is impossible to achieve any arbitrarily small constant correlation with the hidden signal, while if the SNR is above $\left(1+\epsilon \right)\mathrm{SNR_c}$, then it is possible to achieve almost perfect correlation with the hidden signal. The all-or-nothing phenomenon was initially established in the context of sparse linear regression, and over the last year also in the context of sparse 2-tensor (matrix) PCA and Bernoulli group testing. Our results follow from a more general result showing that for any Gaussian additive model with a discrete uniform prior, the all-or-nothing phenomenon follows as a direct outcome of an appropriately defined ``near-orthogonality" property of the support of the prior distribution.

Flow models have recently made great progress at modeling ordinal discrete data such as images and audio. Due to the continuous nature of flow models, dequantization is typically applied when using them for such discrete data, resulting in lower bound estimates of the likelihood. In this paper, we introduce subset flows, a class of flows that can tractably transform finite volumes and thus allow exact computation of likelihoods for discrete data. Based on subset flows, we identify ordinal discrete autoregressive models, including WaveNets, PixelCNNs and Transformers, as single-layer flows. We use the flow formulation to compare models trained and evaluated with either the exact likelihood or its dequantization lower bound. Finally, we study multilayer flows composed of PixelCNNs and non-autoregressive coupling layers and demonstrate state-of-the-art results on CIFAR-10 for flow models trained with dequantization.

Algorithm configuration procedures optimize parameters of a given algorithm to perform well over a distribution of inputs. Recent theoretical work focused on the case of selecting between a small number of alternatives. In practice, parameter spaces are often very large or infinite, and so successful heuristic procedures discard parameters ``impatiently'', based on very few observations. Inspired by this idea, we introduce ImpatientCapsAndRuns, which quickly discards less promising configurations, significantly speeding up the search procedure compared to previous algorithms with theoretical guarantees, while still achieving optimal runtime up to logarithmic factors under mild assumptions. Experimental results demonstrate a practical improvement.

This paper tackles the modelling of large, complex and multivariate time series panels in a probabilistic setting. To this extent, we present a novel approach reconciling classical state space models with deep learning methods. By augmenting state space models with normalizing flows, we mitigate imprecisions stemming from idealized assumptions in state space models. The resulting model is highly flexible while still retaining many of the attractive properties of state space models, e.g., uncertainty and observation errors are properly accounted for, inference is tractable, sampling is efficient, good generalization performance is observed, even in low data regimes. We demonstrate competitiveness against state-of-the-art deep learning methods on the tasks of forecasting real world data and handling varying levels of missing data.

As power management has become a primary concern in modern data centers, computing resources are being scaled dynamically to minimize energy consumption. We initiate the study of a variant of the classic online speed scaling problem, in which machine learning predictions about the future can be integrated naturally. Inspired by recent work on learning-augmented online algorithms, we propose an algorithm which incorporates predictions in a black-box manner and outperforms any online algorithm if the accuracy is high, yet maintains provable guarantees if the prediction is very inaccurate. We provide both theoretical and experimental evidence to support our claims.