Many latent-variable applications, including community detection, collaborative filtering, genomic analysis, and NLP, model data as generated by low-rank matrices. Yet despite considerable research, except for very special cases, the number of samples required to efficiently recover the underlying matrices has not been known. We determine the onset of learning in several common latent-variable settings. For all of them, we show that learning $k\times k$, rank-$r$, matrices to normalized $L_1$ distance $\epsilon$ requires $\Omega(\frac{kr}{\epsilon^2})$ samples, and propose an algorithm that uses ${\cal O}(\frac{kr}{\epsilon^2}\log^2\frac r\epsilon)$ samples, a number linear in the high dimension, and nearly linear in the, typically low, rank. The algorithm improves on existing spectral techniques and runs in polynomial time. The proofs establish new results on the rapid convergence of the spectral distance between the model and observation matrices, and may be of independent interest.

The accuracy of deep convolutional neural networks (CNNs) generally improves when fueled with high resolution images. However, this often comes at a high computational cost and high memory footprint. Inspired by the fact that not all regions in an image are task-relevant, we propose a novel framework that performs efficient image classification by processing a sequence of relatively small inputs, which are strategically selected from the original image with reinforcement learning. Such a dynamic decision process naturally facilitates adaptive inference at test time, i.e., it can be terminated once the model is sufficiently confident about its prediction and thus avoids further redundant computation. Notably, our framework is general and flexible as it is compatible with most of the state-of-the-art light-weighted CNNs (such as MobileNets, EfficientNets and RegNets), which can be conveniently deployed as the backbone feature extractor. Experiments on ImageNet show that our method consistently improves the computational efficiency of a wide variety of deep models. For example, it further reduces the average latency of the highly efficient MobileNet-V3 on an iPhone XS Max by 20% without sacrificing accuracy. Code and pre-trained models are available at https://github.com/blackfeather-wang/GFNet-Pytorch.

Various evaluation measures have been developed for multi-label classification, including Hamming Loss (HL), Subset Accuracy (SA) and Ranking Loss (RL). However, there is a gap between empirical results and the existing theories: 1) an algorithm often empirically performs well on some measure(s) while poorly on others, while a formal theoretical analysis is lacking; and 2) in small label space cases, the algorithms optimizing HL often have comparable or even better performance on the SA measure than those optimizing SA directly, while existing theoretical results show that SA and HL are conflicting measures. This paper provides an attempt to fill up this gap by analyzing the learning guarantees of the corresponding learning algorithms on both SA and HL measures. We show that when a learning algorithm optimizes HL with its surrogate loss, it enjoys an error bound for the HL measure independent of $c$ (the number of labels), while the bound for the SA measure depends on at most $O(c)$. On the other hand, when directly optimizing SA with its surrogate loss, it has learning guarantees that depend on $O(\sqrt{c})$ for both HL and SA measures. This explains the observation that when the label space is not large, optimizing HL with its surrogate loss can have promising performance for SA. We further show that our techniques are applicable to analyze the learning guarantees of algorithms on other measures, such as RL. Finally, the theoretical analyses are supported by experimental results.

Metric learning aims to learn a distance measure that can benefit distance-based methods such as the nearest neighbour (NN) classifier. While considerable efforts have been made to improve its empirical performance and analyze its generalization ability by focusing on the data structure and model complexity, an unresolved question is how choices of algorithmic parameters, such as the number of training iterations, affect metric learning as it is typically formulated as an optimization problem and nowadays more often as a non-convex problem. In this paper, we theoretically address this question and prove the agnostic Probably Approximately Correct (PAC) learnability for metric learning algorithms with non-convex objective functions optimized via gradient descent (GD); in particular, our theoretical guarantee takes the iteration number into account. We first show that the generalization PAC bound is a sufficient condition for agnostic PAC learnability and this bound can be obtained by ensuring the uniform convergence on a densely concentrated subset of the parameter space. We then show that, for classifiers optimized via GD, their generalizability can be guaranteed if the classifier and loss function are both Lipschitz smooth, and further improved by using fewer iterations. To illustrate and exploit the theoretical findings, we finally propose a novel metric learning method called Smooth Metric and representative Instance LEarning (SMILE), designed to satisfy the Lipschitz smoothness property and learned via GD with an early stopping mechanism for better discriminability and less computational cost of NN.

We consider the linear model $\vy=\vX\vbeta_{\star}+\vepsilon$ with $\vX\in \mathbb{R}^{n\times p}$ in the overparameterized regime $p>n$. We estimate $\vbeta_{\star}$ via generalized (weighted) ridge regression: $\hat{\vbeta}_{\lambda}=\left(\vX^{\t}\vX+\lambda\vSigma_w\right)^{\dagger}\vX^{\t}\vy$, where $\vSigma_w$ is the weighting matrix. Under a random design setting with general data covariance $\vSigma_x$ and anisotropic prior on the true coefficients $\bbE\vbeta_{\star}\vbeta_{\star}^{\t}=\vSigma_\beta$, we provide an exact characterization of the prediction risk $\mathbb{E}(y-\vx^{\t}\hat{\vbeta}_{\lambda})^2$ in the proportional asymptotic limit $p/n\rightarrow \gamma \in (1,\infty)$. Our general setup leads to a number of interesting findings. We outline precise conditions that decide the sign of the optimal setting $\lambda_{\opt}$ for the ridge parameter $\lambda$, which suggests an implicit $\ell_2$ regularization effect of overparameterization, and theoretically justifies the surprising empirical observation that $\lambda_{\opt}$ can be \textit{negative} in the overparameterized regime. We also characterize the double descent phenomenon for principal component regression (PCR) when $\vX$ and $\vbeta_{\star}$ are non-isotropic. Finally, we determine the optimal $\vSigma_w$ for both the ridgeless ($\lambda\to 0$) and optimally regularized ($\lambda = \lambda_{\opt}$) case, and demonstrate the advantage of the weighted objective over standard ridge regression and PCR.

Bregman divergences generalize measures such as the squared Euclidean distance and the KL divergence, and arise throughout many areas of machine learning. In this paper, we focus on the problem of approximating an arbitrary Bregman divergence from supervision, and we provide a well-principled approach to analyzing such approximations. We develop a formulation and algorithm for learning arbitrary Bregman divergences based on approximating their underlying convex generating function via a piecewise linear function. We provide theoretical approximation bounds using our parameterization and show that the generalization error $O_p(m^{-1/2})$ for metric learning using our framework matches the known generalization error in the strictly less general Mahalanobis metric learning setting. We further demonstrate empirically that our method performs well in comparison to existing metric learning methods, particularly for clustering and ranking problems.

We study the eigenvalue distributions of the Conjugate Kernel and Neural Tangent Kernel associated to multi-layer feedforward neural networks. In an asymptotic regime where network width is increasing linearly in sample size, under random initialization of the weights, and for input samples satisfying a notion of approximate pairwise orthogonality, we show that the eigenvalue distributions of the CK and NTK converge to deterministic limits. The limit for the CK is described by iterating the Marcenko-Pastur map across the hidden layers. The limit for the NTK is equivalent to that of a linear combination of the CK matrices across layers, and may be described by recursive fixed-point equations that extend this Marcenko-Pastur map. We demonstrate the agreement of these asymptotic predictions with the observed spectra for both synthetic and CIFAR-10 training data, and we perform a small simulation to investigate the evolutions of these spectra over training.

In suitably initialized wide networks, small learning rates transform deep neural networks (DNNs) into neural tangent kernel (NTK) machines, whose training dynamics is well-approximated by a linear weight expansion of the network at initialization. Standard training, however, diverges from its linearization in ways that are poorly understood. We study the relationship between the training dynamics of nonlinear deep networks, the geometry of the loss landscape, and the time evolution of a data-dependent NTK. We do so through a large-scale phenomenological analysis of training, synthesizing diverse measures characterizing loss landscape geometry and NTK dynamics. In multiple neural architectures and datasets, we find these diverse measures evolve in a highly correlated manner, revealing a universal picture of the deep learning process. In this picture, deep network training exhibits a highly chaotic rapid initial transient that within 2 to 3 epochs determines the final linearly connected basin of low loss containing the end point of training. During this chaotic transient, the NTK changes rapidly, learning useful features from the training data that enables it to outperform the standard initial NTK by a factor of 3 in less than 3 to 4 epochs. After this rapid chaotic transient, the NTK changes at constant velocity, and its performance matches that of full network training in 15\% to 45\% of training time. Overall, our analysis reveals a striking correlation between a diverse set of metrics over training time, governed by a rapid chaotic to stable transition in the first few epochs, that together poses challenges and opportunities for the development of more accurate theories of deep learning.

Total Variation (TV) is a popular regularization strategy that promotes piece-wise constant signals by constraining the ℓ1-norm of the first order derivative of the estimated signal. The resulting optimization problem is usually solved using iterative algorithms such as proximal gradient descent, primal-dual algorithms or ADMM. However, such methods can require a very large number of iterations to converge to a suitable solution. In this paper, we accelerate such iterative algorithms by unfolding proximal gradient descent solvers in order to learn their parameters for 1D TV regularized problems. While this could be done using the synthesis formulation, we demonstrate that this leads to slower performances. The main difficulty in applying such methods in the analysis formulation lies in proposing a way to compute the derivatives through the proximal operator. As our main contribution, we develop and characterize two approaches to do so, describe their benefits and limitations, and discuss the regime where they can actually improve over iterative procedures. We validate those findings with experiments on synthetic and real data.

We consider the classical setting of optimizing a nonsmooth Lipschitz continuous convex function over a convex constraint set, when having access to a (stochastic) first-order oracle (FO) for the function and a projection oracle (PO) for the constraint set. It is well known that to achieve $\epsilon$-suboptimality in high-dimensions, $\Theta(\epsilon^{-2})$ FO calls are necessary. This is achieved by the projected subgradient method (PGD). However, PGD also entails $O(\epsilon^{-2})$ PO calls, which may be computationally costlier than FO calls (e.g. nuclear norm constraints). Improving this PO calls complexity of PGD is largely unexplored, despite the fundamental nature of this problem and extensive literature. We present first such improvement. This only requires a mild assumption that the objective function, when extended to a slightly larger neighborhood of the constraint set, still remains Lipschitz and accessible via FO. In particular, we introduce MOPES method, which carefully combines Moreau-Yosida smoothing and accelerated first-order schemes. This is guaranteed to find a feasible $\epsilon$-suboptimal solution using only $O(\epsilon^{-1})$ PO calls and optimal $O(\epsilon^{-2})$ FO calls. Further, instead of a PO if we only have a linear minimization oracle (LMO, a la Frank-Wolfe) to access the constraint set, an extension of our method, MOLES, finds a feasible $\epsilon$-suboptimal solution using $O(\epsilon^{-2})$ LMO calls and FO calls---both match known lower bounds, resolving a question left open since White (1993). Our experiments confirm that these methods achieve significant speedups over the state-of-the-art, for a problem with costly PO and LMO calls.

Many results in recent years established polynomial time learnability of various models via neural networks algorithms (e.g. \cite{andoni2014learning, daniely2016toward, daniely2017sgd, cao2019generalization, ziwei2019polylogarithmic, zou2019improved, ma2019comparative, du2018gradient, arora2019fine, song2019quadratic, oymak2019towards, ge2019mildly, brutzkus2018sgd}). However, unless the model is linear separable~\cite{brutzkus2018sgd}, or the activation is a polynomial~\cite{ge2019mildly}, these results require very large networks -- much more than what is needed for the mere existence of a good predictor. In this paper we prove that SGD on depth two neural networks can memorize samples, learn polynomials with bounded weights, and learn certain kernel spaces, with {\em near optimal} network size, sample complexity, and runtime. In particular, we show that SGD on depth two network with $\tilde{O}\left(\frac{m}{d}\right)$ hidden neurons (and hence $\tilde{O}(m)$ parameters) can memorize $m$ random labeled points in $\sphere^{d-1}$.

Graphical models are powerful tools for modeling high-dimensional data, but learning graphical models in the presence of latent variables is well-known to be difficult. In this work we give new results for learning Restricted Boltzmann Machines, probably the most well-studied class of latent variable models. Our results are based on new connections to learning two-layer neural networks under $\ell_{\infty}$ bounded input; for both problems, we give nearly optimal results under the conjectured hardness of sparse parity with noise. Using the connection between RBMs and feedforward networks, we also initiate the theoretical study of {\em supervised RBMs} \citep{hinton2012practical}, a version of neural-network learning that couples distributional assumptions induced from the underlying graphical model with the architecture of the unknown function class. We then give an algorithm for learning a natural class of supervised RBMs with better runtime than what is possible for its related class of networks without distributional assumptions.

Gaussian Graphical Models (GGMs) have wide-ranging applications in machine learning and the natural and social sciences. In most of the settings in which they are applied, the number of observed samples is much smaller than the dimension and they are assumed to be sparse. While there are a variety of algorithms (e.g. Graphical Lasso, CLIME) that provably recover the graph structure with a logarithmic number of samples, to do so they require various assumptions on the well-conditioning of the precision matrix that are not information-theoretically necessary.

Here we give the first fixed polynomial-time algorithms for learning attractive GGMs and walk-summable GGMs with a logarithmic number of samples without any such assumptions. In particular, our algorithms can tolerate strong dependencies among the variables. Our result for structure recovery in walk-summable GGMs is derived from a more general result for efficient sparse linear regression in walk-summable models without any norm dependencies. We complement our results with experiments showing that many existing algorithms fail even in some simple settings where there are long dependency chains. Our algorithms do not.

We study the fixed-support Wasserstein barycenter problem (FS-WBP), which consists in computing the Wasserstein barycenter of $m$ discrete probability measures supported on a finite metric space of size $n$. We show first that the constraint matrix arising from the standard linear programming (LP) representation of the FS-WBP is \textit{not totally unimodular} when $m \geq 3$ and $n \geq 3$. This result resolves an open question pertaining to the relationship between the FS-WBP and the minimum-cost flow (MCF) problem since it proves that the FS-WBP in the standard LP form is not an MCF problem when $m \geq 3$ and $n \geq 3$. We also develop a provably fast \textit{deterministic} variant of the celebrated iterative Bregman projection (IBP) algorithm, named \textsc{FastIBP}, with a complexity bound of $\tilde{O}(mn^{7/3}\varepsilon^{-4/3})$, where $\varepsilon \in (0, 1)$ is the desired tolerance. This complexity bound is better than the best known complexity bound of $\tilde{O}(mn^2\varepsilon^{-2})$ for the IBP algorithm in terms of $\varepsilon$, and that of $\tilde{O}(mn^{5/2}\varepsilon^{-1})$ from accelerated alternating minimization algorithm or accelerated primal-dual adaptive gradient algorithm in terms of $n$. Finally, we conduct extensive experiments with both synthetic data and real images and demonstrate the favorable performance of the \textsc{FastIBP} algorithm in practice.

Projection robust Wasserstein (PRW) distance, or Wasserstein projection pursuit (WPP), is a robust variant of the Wasserstein distance. Recent work suggests that this quantity is more robust than the standard Wasserstein distance, in particular when comparing probability measures in high-dimensions. However, it is ruled out for practical application because the optimization model is essentially non-convex and non-smooth which makes the computation intractable. Our contribution in this paper is to revisit the original motivation behind WPP/PRW, but take the hard route of showing that, despite its non-convexity and lack of nonsmoothness, and even despite some hardness results proved by~\citet{Niles-2019-Estimation} in a minimax sense, the original formulation for PRW/WPP \textit{can} be efficiently computed in practice using Riemannian optimization, yielding in relevant cases better behavior than its convex relaxation. More specifically, we provide three simple algorithms with solid theoretical guarantee on their complexity bound (one in the appendix), and demonstrate their effectiveness and efficiency by conducing extensive experiments on synthetic and real data. This paper provides a first step into a computational theory of the PRW distance and provides the links between optimal transport and Riemannian optimization.

Contemporary machine learning applications often involve classification tasks with many classes. Despite their extensive use, a precise understanding of the statistical properties and behavior of classification algorithms is still missing, especially in modern regimes where the number of classes is rather large. In this paper, we take a step in this direction by providing the first asymptotically precise analysis of linear multiclass classification. Our theoretical analysis allows us to precisely characterize how the test error varies over different training algorithms, data distributions, problem dimensions as well as number of classes, inter/intra class correlations and class priors. Specifically, our analysis reveals that the classification accuracy is highly distribution-dependent with different algorithms achieving optimal performance for different data distributions and/or training/features sizes. Unlike linear regression/binary classification, the test error in multiclass classification relies on intricate functions of the trained model (e.g., correlation between some of the trained weights) whose asymptotic behavior is difficult to characterize. This challenge is already present in simple classifiers, such as those minimizing a square loss. Our novel theoretical techniques allow us to overcome some of these challenges. The insights gained may pave the way for a precise understanding of other classification algorithms beyond those studied in this paper.

We establish a new class of minimax prediction error bounds for generalized linear models. Our bounds significantly improve previous results when the design matrix is poorly structured, including natural cases where the matrix is wide or does not have full column rank. Apart from the typical $L_2$ risks, we study a class of entropic risks which recovers the usual $L_2$ prediction and estimation risks, and demonstrate that a tight analysis of Fisher information can uncover underlying structural dependency in terms of the spectrum of the design matrix. The minimax approach we take differs from the traditional metric entropy approach, and can be applied to many other settings.

We introduce a new theoretical framework to analyze deep learning optimization with connection to its generalization error. Existing frameworks such as mean field theory and neural tangent kernel theory for neural network optimization analysis typically require taking limit of infinite width of the network to show its global convergence. This potentially makes it difficult to directly deal with finite width network; especially in the neural tangent kernel regime, we cannot reveal favorable properties of neural networks {\it beyond kernel methods}. To realize more natural analysis, we consider a completely different approach in which we formulate the parameter training as a transportation map estimation and show its global convergence via the theory of the {\it infinite dimensional Langevin dynamics}. This enables us to analyze narrow and wide networks in a unifying manner. Moreover, we give generalization gap and excess risk bounds for the solution obtained by the dynamics. The excess risk bound achieves the so-called fast learning rate. In particular, we show an exponential convergence for a classification problem and a minimax optimal rate for a regression problem.

Experimental measurements of physical systems often have a limited number of independent channels, causing essential dynamical variables to remain unobserved. However, many popular methods for unsupervised inference of latent dynamics from experimental data implicitly assume that the measurements have higher intrinsic dimensionality than the underlying system---making coordinate identification a dimensionality reduction problem. Here, we study the opposite limit, in which hidden governing coordinates must be inferred from only a low-dimensional time series of measurements. Inspired by classical analysis techniques for partial observations of chaotic attractors, we introduce a general embedding technique for univariate and multivariate time series, consisting of an autoencoder trained with a novel latent-space loss function. We show that our technique reconstructs the strange attractors of synthetic and real-world systems better than existing techniques, and that it creates consistent, predictive representations of even stochastic systems. We conclude by using our technique to discover dynamical attractors in diverse systems such as patient electrocardiograms, household electricity usage, neural spiking, and eruptions of the Old Faithful geyser---demonstrating diverse applications of our technique for exploratory data analysis.

Training Neural Ordinary Differential Equations (ODEs) is often computationally expensive. Indeed, computing the forward pass of such models involves solving an ODE which can become arbitrarily complex during training. Recent works have shown that regularizing the dynamics of the ODE can partially alleviate this. In this paper we propose a new regularization technique: randomly sampling the end time of the ODE during training. The proposed regularization is simple to implement, has negligible overhead and is effective across a wide variety of tasks. Further, the technique is orthogonal to several other methods proposed to regularize the dynamics of ODEs and as such can be used in conjunction with them. We show through experiments on normalizing flows, time series models and image recognition that the proposed regularization can significantly decrease training time and even improve performance over baseline models.

Manifold learning is a fundamental problem in machine learning with numerous applications. Most of the existing methods directly learn the low-dimensional embedding of the data in some high-dimensional space, and usually lack the flexibility of being directly applicable to down-stream applications. In this paper, we propose the concept of implicit manifold learning, where manifold information is implicitly obtained by learning the associated heat kernel. A heat kernel is the solution of the corresponding heat equation, which describes how ``heat'' transfers on the manifold, thus containing ample geometric information of the manifold. We provide both practical algorithm and theoretical analysis of our framework. The learned heat kernel can be applied to various kernel-based machine learning models, including deep generative models (DGM) for data generation and Stein Variational Gradient Descent for Bayesian inference. Extensive experiments show that our framework can achieve the state-of-the-art results compared to existing methods for the two tasks.

Incorporating relational reasoning into neural networks has greatly expanded their capabilities and scope. One defining trait of relational reasoning is that it operates on a set of entities, as opposed to standard vector representations. Existing end-to-end approaches for relational reasoning typically extract entities from inputs by directly interpreting the latent feature representations as a set. We show that these approaches do not respect set permutational invariance and thus have fundamental representational limitations. To resolve this limitation, we propose a simple and general network module called Set Refiner Network (SRN). We first use synthetic image experiments to demonstrate how our approach effectively decomposes objects without explicit supervision. Then, we insert our module into existing relational reasoning models and show that respecting set invariance leads to substantial gains in prediction performance and robustness on several relational reasoning tasks. Code can be found at github.com/CUAI/BetterSetRepresentations.

Predicting calibrated confidence scores for multi-class deep networks is important for avoiding rare but costly mistakes. A common approach is to learn a post-hoc calibration function that transforms the output of the original network into calibrated confidence scores while maintaining the network's accuracy. However, previous post-hoc calibration techniques work only with simple calibration functions, potentially lacking sufficient representation to calibrate the complex function landscape of deep networks. In this work, we aim to learn general post-hoc calibration functions that can preserve the top-k predictions of any deep network. We call this family of functions intra order-preserving functions. We propose a new neural network architecture that represents a class of intra order-preserving functions by combining common neural network components. Additionally, we introduce order-invariant and diagonal sub-families, which can act as regularization for better generalization when the training data size is small. We show the effectiveness of the proposed method across a wide range of datasets and classifiers. Our method outperforms state-of-the-art post-hoc calibration methods, namely temperature scaling and Dirichlet calibration, in several evaluation metrics for the task.

This work addresses data-driven optimization problems, where the goal is to find an input that maximizes an unknown score or reward function given access to a dataset of inputs with corresponding scores. When the inputs are high-dimensional and valid inputs constitute a small subset of this space (e.g., valid protein sequences or valid natural images), such model-based optimization problems become exceptionally difficult, since the optimizer must avoid out-of-distribution and invalid inputs. We propose to address such problems with model inversion networks (MINs), which learn an inverse mapping from scores to inputs. MINs can scale to high-dimensional input spaces and leverage offline logged data for both contextual and non-contextual optimization problems. MINs can also handle both purely offline data sources and active data collection. We evaluate MINs on high- dimensional model-based optimization problems over images, protein designs, and neural network controller parameters, and bandit optimization from logged data.

In images of complex scenes, objects are often occluding each other which makes perception tasks such as object detection and tracking, or robotic control tasks such as planning, challenging. To facilitate downstream tasks, it is thus important to reason about the full extent of objects, i.e., seeing behind occlusion, typically referred to as amodal instance completion. In this paper, we propose a variational generative framework for amodal completion, referred to as AMODAL-VAE, which does not require any amodal labels at training time, as it is able to utilize widely available object instance masks. We showcase our approach on the downstream task of scene editing where the user is presented with interactive tools to complete and erase objects in photographs. Experiments on complex street scenes demonstrate state-of-the-art performance in amodal mask completion and showcase high-quality scene editing results. Interestingly, a user study shows that humans prefer object completions inferred by our model to the human-labeled ones.

We formalize and attack the problem of generating new images from old ones that are as diverse as possible, only allowing them to change without restrictions in certain parts of the image while remaining globally consistent. This encompasses the typical situation found in generative modelling, where we are happy with parts of the generated data, but would like to resample others (``I like this generated castle overall, but this tower looks unrealistic, I would like a new one''). In order to attack this problem we build from the best conditional and unconditional generative models to introduce a new network architecture, training procedure, and a new algorithm for resampling parts of the image as desired.

Recently, there has been a surge of interest in combining deep learning models with reasoning in order to handle more sophisticated learning tasks. In many cases, a reasoning task can be solved by an iterative algorithm. This algorithm is often unrolled, and used as a specialized layer in the deep architecture, which can be trained end-to-end with other neural components. Although such hybrid deep architectures have led to many empirical successes, the theoretical foundation of such architectures, especially the interplay between algorithm layers and other neural layers, remains largely unexplored. In this paper, we take an initial step towards an understanding of such hybrid deep architectures by showing that properties of the algorithm layers, such as convergence, stability, and sensitivity, are intimately related to the approximation and generalization abilities of the end-to-end model. Furthermore, our analysis matches closely our experimental observations under various conditions, suggesting that our theory can provide useful guidelines for designing deep architectures with reasoning modules (i.e., algorithm layers).

Deep learning models are computationally intense, and implementations often have to be highly optimized by experts or hardware vendors to be usable in practice. The DL compiler, together with Learning to Compile have proven to be a powerful technique for optimizing tensor programs. However, a limitation of this approach is that it still suffers from unbearably long overall optimization time.

In this paper, we present a new method, called AdaTune, that significantly reduces the optimization time of tensor programs for high-performance deep learning inference. In particular, we propose an adaptive evaluation method that statistically early terminates a costly hardware measurement without losing much accuracy. We further devise a surrogate model with uncertainty quantification that allows the optimization to adapt to hardware and model heterogeneity better. Finally, we introduce a contextual optimizer that provides adaptive control of the exploration and exploitation to improve the transformation space searching effectiveness. We evaluate and compare the levels of optimization obtained by a state-of-the-art DL compiler and AdaTune. The experiment results show that AdaTune obtains up to 115% higher GFLOPS than the baseline under the same optimization time budget. Furthermore, AdaTune provides 1.3--3.9X speedup in optimization time over the state-of-the-art to reach the same optimization quality for a range of models across different hardware architectures.

We present a novel discriminator for GANs that improves realness and diversity of generated samples by learning a structured hypersphere embedding space using spherical circles. The proposed discriminator learns to populate realistic samples around the longest spherical circle, i.e., a great circle, while pushing unrealistic samples toward the poles perpendicular to the great circle. Since longer circles occupy larger area on the hypersphere, they encourage more diversity in representation learning, and vice versa. Discriminating samples based on their corresponding spherical circles can thus naturally induce diversity to generated samples. We also extend the proposed method for conditional settings with class labels by creating a hypersphere for each category and performing class-wise discrimination and update. In experiments, we validate the effectiveness for both unconditional and conditional generation on standard benchmarks, achieving the state of the art.

Flow-based generative models are composed of invertible transformations between two random variables of the same dimension. Therefore, flow-based models cannot be adequately trained if the dimension of the data distribution does not match that of the underlying target distribution. In this paper, we propose SoftFlow, a probabilistic framework for training normalizing flows on manifolds. To sidestep the dimension mismatch problem, SoftFlow estimates a conditional distribution of the perturbed input data instead of learning the data distribution directly. We experimentally show that SoftFlow can capture the innate structure of the manifold data and generate high-quality samples unlike the conventional flow-based models. Furthermore, we apply the proposed framework to 3D point clouds to alleviate the difficulty of forming thin structures for flow-based models. The proposed model for 3D point clouds, namely SoftPointFlow, can estimate the distribution of various shapes more accurately and achieves state-of-the-art performance in point cloud generation.

Score-based generative models can produce high quality image samples comparable to GANs, without requiring adversarial optimization. However, existing training procedures are limited to images of low resolution (typically below 32 x 32), and can be unstable under some settings. We provide a new theoretical analysis of learning and sampling from score models in high dimensional spaces, explaining existing failure modes and motivating new solutions that generalize across datasets. To enhance stability, we also propose to maintain an exponential moving average of model weights. With these improvements, we can effortlessly scale score-based generative models to images with unprecedented resolutions ranging from 64 x 64 to 256 x 256. Our score-based models can generate high-fidelity samples that rival best-in-class GANs on various image datasets, including CelebA, FFHQ, and multiple LSUN categories.

Neural networks have been shown effective in deep steganography for hiding a full image in another. However, the reason for its success remains not fully clear. Under the existing cover ($C$) dependent deep hiding (DDH) pipeline, it is challenging to analyze how the secret ($S$) image is encoded since the encoded message cannot be analyzed independently. We propose a novel universal deep hiding (UDH) meta-architecture to disentangle the encoding of $S$ from $C$. We perform extensive analysis and demonstrate that the success of deep steganography can be attributed to a frequency discrepancy between $C$ and the encoded secret image. Despite $S$ being hidden in a cover-agnostic manner, strikingly, UDH achieves a performance comparable to the existing DDH. Beyond hiding one image, we push the limits of deep steganography. Exploiting its property of being \emph{universal}, we propose universal watermarking as a timely solution to address the concern of the exponentially increasing amount of images/videos. UDH is robust to a pixel intensity shift on the container image, which makes it suitable for challenging application of light field messaging (LFM). This is the first work demonstrating the success of (DNN-based) hiding a full image for watermarking and LFM. Code: \url{https://github.com/ChaoningZhang/Universal-Deep-Hiding}

A central problem in machine learning and statistics is to model joint densities of random variables from data. Copulas are joint cumulative distribution functions with uniform marginal distributions and are used to capture interdependencies in isolation from marginals. Copulas are widely used within statistics, but have not gained traction in the context of modern deep learning. In this paper, we introduce ACNet, a novel differentiable neural network architecture that enforces structural properties and enables one to learn an important class of copulas--Archimedean Copulas. Unlike Generative Adversarial Networks, Variational Autoencoders, or Normalizing Flow methods, which learn either densities or the generative process directly, ACNet learns a generator of the copula, which implicitly defines the cumulative distribution function of a joint distribution. We give a probabilistic interpretation of the network parameters of ACNet and use this to derive a simple but efficient sampling algorithm for the learned copula. Our experiments show that ACNet is able to both approximate common Archimedean Copulas and generate new copulas which may provide better fits to data.

We examine the problem of controlling divergences for latent space regularisation in variational autoencoders. Specifically, when aiming to reconstruct example $x\in\mathbb{R}^{m}$ via latent space $z\in\mathbb{R}^{n}$ ($n\leq m$), while balancing this against the need for generalisable latent representations. We present a regularisation mechanism based on the {\em skew-geometric Jensen-Shannon divergence} $\left(\textrm{JS}^{\textrm{G}_{\alpha}}\right)$. We find a variation in $\textrm{JS}^{\textrm{G}_{\alpha}}$, motivated by limiting cases, which leads to an intuitive interpolation between forward and reverse KL in the space of both distributions and divergences. We motivate its potential benefits for VAEs through low-dimensional examples, before presenting quantitative and qualitative results. Our experiments demonstrate that skewing our variant of $\textrm{JS}^{\textrm{G}_{\alpha}}$, in the context of $\textrm{JS}^{\textrm{G}_{\alpha}}$-VAEs, leads to better reconstruction and generation when compared to several baseline VAEs. Our approach is entirely unsupervised and utilises only one hyperparameter which can be easily interpreted in latent space.

Optimal transport (OT) is a powerful geometric and probabilistic tool for finding correspondences and measuring similarity between two distributions. Yet, its original formulation relies on the existence of a cost function between the samples of the two distributions, which makes it impractical when they are supported on different spaces. To circumvent this limitation, we propose a novel OT problem, named COOT for CO-Optimal Transport, that simultaneously optimizes two transport maps between both samples and features, contrary to other approaches that either discard the individual features by focusing on pairwise distances between samples or need to model explicitly the relations between them. We provide a thorough theoretical analysis of our problem, establish its rich connections with other OT-based distances and demonstrate its versatility with two machine learning applications in heterogeneous domain adaptation and co-clustering/data summarization, where COOT leads to performance improvements over the state-of-the-art methods.

We present an optimal transport framework for learning topics from textual data. While the celebrated Latent Dirichlet allocation (LDA) topic model and its variants have been applied to many disciplines, they mainly focus on word-occurrences and neglect to incorporate semantic regularities in language. Even though recent works have tried to exploit the semantic relationship between words to bridge this gap, however, these models which are usually extensions of LDA or Dirichlet Multinomial mixture (DMM) are tailored to deal effectively with either regular or short documents. The optimal transport distance provides an appealing tool to incorporate the geometry of word semantics into it. Moreover, recent developments on efficient computation of optimal transport distance also promote its application in topic modeling. In this paper we ground on optimal transport theory to naturally exploit the geometric structures of semantically related words in embedding spaces which leads to more interpretable learned topics. Comprehensive experiments illustrate that the proposed framework outperforms competitive approaches in terms of topic coherence on assorted text corpora which include both long and short documents. The representation of learned topic also leads to better accuracy on classification downstream tasks, which is considered as an extrinsic evaluation.

Subgroup analysis of treatment effects plays an important role in applications from medicine to public policy to recommender systems. It allows physicians (for example) to identify groups of patients for whom a given drug or treatment is likely to be effective and groups of patients for which it is not. Most of the current methods of subgroup analysis begin with a particular algorithm for estimating individualized treatment effects (ITE) and identify subgroups by maximizing the difference across subgroups of the average treatment effect in each subgroup. These approaches have several weaknesses: they rely on a particular algorithm for estimating ITE, they ignore (in)homogeneity within identified subgroups, and they do not produce good confidence estimates. This paper develops a new method for subgroup analysis, R2P, that addresses all these weaknesses. R2P uses an arbitrary, exogenously prescribed algorithm for estimating ITE and quantifies the uncertainty of the ITE estimation, using a construction that is more robust than other methods. Experiments using synthetic and semi-synthetic datasets (based on real data) demonstrate that R2P constructs partitions that are simultaneously more homogeneous within groups and more heterogeneous across groups than the partitions produced by other methods. Moreover, because R2P can employ any ITE estimator, it also produces much narrower confidence intervals with a prescribed coverage guarantee than other methods.

Although there is a vast body of literature related to methods for detecting change-points (CPs), less attention has been paid to assessing the statistical reliability of the detected CPs. In this paper, we introduce a novel method to perform statistical inference on the significance of the CPs, estimated by a Dynamic Programming (DP)-based optimal CP detection algorithm. Our main idea is to employ a Selective Inference (SI) approach---a new statistical inference framework that has recently received a lot of attention---to compute exact (non-asymptotic) valid p-values for the detected optimal CPs. Although it is well-known that SI has low statistical power because of over-conditioning, we address this drawback by introducing a novel method called parametric DP, which enables SI to be conducted with the minimum amount of conditioning, leading to high statistical power. We conduct experiments on both synthetic and real-world datasets, through which we offer evidence that our proposed method is more powerful than existing methods, has decent performance in terms of computational efficiency, and provides good results in many practical applications.

Variational Bayesian phylogenetic inference (VBPI) provides a promising general variational framework for efficient estimation of phylogenetic posteriors. However, the current diagonal Lognormal branch length approximation would significantly restrict the quality of the approximating distributions. In this paper, we propose a new type of VBPI, VBPI-NF, as a first step to empower phylogenetic posterior estimation with deep learning techniques. By handling the non-Euclidean branch length space of phylogenetic models with carefully designed permutation equivariant transformations, VBPI-NF uses normalizing flows to provide a rich family of flexible branch length distributions that generalize across different tree topologies. We show that VBPI-NF significantly improves upon the vanilla VBPI on a benchmark of challenging real data Bayesian phylogenetic inference problems. Further investigation also reveals that the structured parameterization in those permutation equivariant transformations can provide additional amortization benefit.

The state-of-the-art approximate nearest neighbor search (ANNS) algorithms face a fundamental tradeoff between query latency and accuracy, because of small main memory capacity: To store indices in main memory for short query latency, the ANNS algorithms have to limit dataset size or use a quantization scheme which hurts search accuracy. The emergence of heterogeneous memory (HM) brings a solution to significantly increase memory capacity and break the above tradeoff: Using HM, billions of data points can be placed in the main memory on a single machine without using any data compression. However, HM consists of both fast (but small) memory and slow (but large) memory, and using HM inappropriately slows down query significantly. In this work, we present a novel graph-based similarity search algorithm called HM-ANN, which takes both memory and data heterogeneity into consideration and enables billion-scale similarity search on a single node without using compression. On two billion-sized datasets BIGANN and DEEP1B, HM-ANN outperforms state-of-the-art compression-based solutions such as L&C and IMI+OPQ in recall-vs-latency by a large margin, obtaining 46% higher recall under the same search latency. We also extend existing graph-based methods such as HNSW and NSG with two strong baseline implementations on HM. At billion-point scale, HM-ANN is 2X and 5.8X faster than our HNSWand NSG baselines respectively to reach the same accuracy.

The log-likelihood of a generative model often involves both positive and negative terms. For a temporal multivariate point process, the negative term sums over all the possible event types at each time and also integrates over all the possible times. As a result, maximum likelihood estimation is expensive. We show how to instead apply a version of noise-contrastive estimation---a general parameter estimation method with a less expensive stochastic objective. Our specific instantiation of this general idea works out in an interestingly non-trivial way and has provable guarantees for its optimality, consistency and efficiency. On several synthetic and real-world datasets, our method shows benefits: for the model to achieve the same level of log-likelihood on held-out data, our method needs considerably fewer function evaluations and less wall-clock time.

Recent work suggests improving the performance of Bloom filter by incorporating a machine learning model as a binary classifier. However, such learned Bloom filter does not take full advantage of the predicted probability scores. We propose new algorithms that generalize the learned Bloom filter by using the complete spectrum of the score regions. We prove our algorithms have lower false positive rate (FPR) and memory usage compared with the existing approaches to learned Bloom filter. We also demonstrate the improved performance of our algorithms on real-world information filtering tasks over the web.

Deep learning (DL) frameworks take advantage of GPUs to improve the speed of DL inference and training. Ideally, DL frameworks should be able to fully utilize the computation power of GPUs such that the running time depends on the amount of computation assigned to GPUs. Yet, we observe that in scheduling GPU tasks, existing DL frameworks suffer from inefficiencies such as large scheduling overhead and unnecessary serial execution. To this end, we propose Nimble, a DL execution engine that runs GPU tasks in parallel with minimal scheduling overhead. Nimble introduces a novel technique called ahead-of-time (AoT) scheduling. Here, the scheduling procedure finishes before executing the GPU kernel, thereby removing most of the scheduling overhead during run time. Furthermore, Nimble automatically parallelizes the execution of GPU tasks by exploiting multiple GPU streams in a single GPU. Evaluation on a variety of neural networks shows that compared to PyTorch, Nimble speeds up inference and training by up to 22.34× and 3.61×, respectively. Moreover, Nimble outperforms state-of-the-art inference systems, TensorRT and TVM, by up to 2.81× and 1.70×, respectively.

In this paper, a Bayesian nonparametric (BNP) model for Baxter permutations (BPs), termed BP process (BPP) is proposed and applied to relational data analysis. The BPs are a well-studied class of permutations, and it has been demonstrated that there is one-to-one correspondence between BPs and several interesting objects including floorplan partitioning (FP), which constitutes a subset of rectangular partitioning (RP). Accordingly, the BPP can be used as an FP model. We combine the BPP with a multi-dimensional extension of the stick-breaking process called the {\it block-breaking process} to fill the gap between FP and RP, and obtain a stochastic process on arbitrary RPs. Compared with conventional BNP models for arbitrary RPs, the proposed model is simpler and has a high affinity with Bayesian inference.

Cooperative communication plays a central role in theories of human cognition, language, development, culture, and human-robot interaction. Prior models of cooperative communication are algorithmic in nature and do not shed light on why cooperation may yield effective belief transmission and what limitations may arise due to differences between beliefs of agents. Through a connection to the theory of optimal transport, we establishing a mathematical framework for cooperative communication. We derive prior models as special cases, statistical interpretations of belief transfer plans, and proofs of robustness and instability. Computational simulations support and elaborate our theoretical results, and demonstrate fit to human behavior. The results show that cooperative communication provably enables effective, robust belief transmission which is required to explain feats of human learning and improve human-machine interaction.

Loss functions are a cornerstone of machine learning and the starting point of most algorithms. Statistics and Bayesian decision theory have contributed, via properness, to elicit over the past decades a wide set of admissible losses in supervised learning, to which most popular choices belong (logistic, square, Matsushita, etc.). Rather than making a potentially biased ad hoc choice of the loss, there has recently been a boost in efforts to fit the loss to the domain at hand while training the model itself. The key approaches fit a canonical link, a function which monotonically relates the closed unit interval to R and can provide a proper loss via integration.

In this paper, we rely on a broader view of proper composite losses and a recent construct from information geometry, source functions, whose fitting alleviates constraints faced by canonical links. We introduce a trick on squared Gaussian Processes to obtain a random process whose paths are compliant source functions with many desirable properties in the context of link estimation. Experimental results demonstrate substantial improvements over the state of the art.

Modeling dependencies in multivariate discrete data is a challenging problem, especially in high dimensions. The Potts model is a versatile such model, suitable when each coordinate is a categorical variable. However, the full Potts model has too many parameters to be accurately fit when the number of categories is large. We introduce a variation on the Potts model that allows for general categorical marginals and Ising-type multivariate dependence. This reduces the number of parameters from $\Omega(d^2 K^2)$ in the full Potts model to $O(d^2 + Kd)$, where $K$ is the number of categories and $d$ is the dimension of the data. We show that the complexity of fitting this new Potts-Ising model is the same as that of an Ising model. In particular, adopting the neighborhood regression framework, the model can be fit by solving $d$ separate logistic regressions. We demonstrate the ability of the model to capture multivariate dependencies by comparing with existing approaches.

Incorporating the natural document-sentence-word structure into hierarchical Bayesian modeling, we propose convolutional Poisson gamma dynamical systems (PGDS) that introduce not only word-level probabilistic convolutions, but also sentence-level stochastic temporal transitions. With word-level convolutions capturing phrase-level topics and sentence-level transitions capturing how the topic usages evolve over consecutive sentences, we aggregate the topic proportions of all sentences of a document as its feature representation. To consider not only forward but also backward sentence-level information transmissions, we further develop a bidirectional convolutional PGDS to incorporate the full contextual information to represent each sentence. For efficient inference, we construct a convolutional-recurrent inference network, which provides both sentence-level and document-level representations, and introduce a hybrid Bayesian inference scheme combining stochastic-gradient MCMC and amortized variational inference. Experimental results on a variety of document corpora demonstrate that the proposed models can extract expressive multi-level latent representations, including interpretable phrase-level topics and sentence-level temporal transitions as well as discriminative document-level features, achieving state-of-the-art document categorization performance while being memory and computation efficient.

This paper studies the problem of approximately unlearning a Bayesian model from a small subset of the training data to be erased. We frame this problem as one of minimizing the Kullback-Leibler divergence between the approximate posterior belief of model parameters after directly unlearning from erased data vs. the exact posterior belief from retraining with remaining data. Using the variational inference (VI) framework, we show that it is equivalent to minimizing an evidence upper bound which trades off between fully unlearning from erased data vs. not entirely forgetting the posterior belief given the full data (i.e., including the remaining data); the latter prevents catastrophic unlearning that can render the model useless. In model training with VI, only an approximate (instead of exact) posterior belief given the full data can be obtained, which makes unlearning even more challenging. We propose two novel tricks to tackle this challenge. We empirically demonstrate our unlearning methods on Bayesian models such as sparse Gaussian process and logistic regression using synthetic and real-world datasets.

Despite its high search efficiency, differential architecture search (DARTS) often selects network architectures with dominated skip connections which lead to performance degradation. However, theoretical understandings on this issue remain absent, hindering the development of more advanced methods in a principled way. In this work, we solve this problem by theoretically analyzing the effects of various types of operations, e.g. convolution, skip connection and zero operation, to the network optimization. We prove that the architectures with more skip connections can converge faster than the other candidates, and thus are selected by DARTS. This result, for the first time, theoretically and explicitly reveals the impact of skip connections to fast network optimization and its competitive advantage over other types of operations in DARTS. Then we propose a theory-inspired path-regularized DARTS that consists of two key modules: (i) a differential group-structured sparse binary gate introduced for each operation to avoid unfair competition among operations, and (ii) a path-depth-wise regularization used to incite search exploration for deep architectures that often converge slower than shallow ones as shown in our theory and are not well explored during search. Experimental results on image classification tasks validate its advantages. Codes and models will be released.

One-shot weight sharing methods have recently drawn great attention in neural architecture search due to high efficiency and competitive performance. However, weight sharing across models has an inherent deficiency, i.e., insufficient training of subnetworks in the hypernetwork. To alleviate this problem, we present a simple yet effective architecture distillation method. The central idea is that subnetworks can learn collaboratively and teach each other throughout the training process, aiming to boost the convergence of individual models. We introduce the concept of prioritized path, which refers to the architecture candidates exhibiting superior performance during training. Distilling knowledge from the prioritized paths is able to boost the training of subnetworks. Since the prioritized paths are changed on the fly depending on their performance and complexity, the final obtained paths are the cream of the crop. We directly select the most promising one from the prioritized paths as the final architecture, without using other complex search methods, such as reinforcement learning or evolution algorithms. The experiments on ImageNet verify such path distillation method can improve the convergence ratio and performance of the hypernetwork, as well as boosting the training of subnetworks. The discovered architectures achieve superior performance compared to the recent MobileNetV3 and EfficientNet families under aligned settings. Moreover, the experiments on object detection and more challenging search space show the generality and robustness of the proposed method. Code and models are available at \url{https://github.com/neurips-20/cream.git}.

Recent works on One-Shot Neural Architecture Search (NAS) mostly adopt a bilevel optimization scheme to alternatively optimize the supernet weights and architecture parameters after relaxing the discrete search space into a differentiable space. However, the non-negligible incongruence in their relaxation methods is hard to guarantee the differentiable optimization in the continuous space is equivalent to the optimization in the discrete space. Differently, this paper utilizes a variational graph autoencoder to injectively transform the discrete architecture space into an equivalently continuous latent space, to resolve the incongruence. A probabilistic exploration enhancement method is accordingly devised to encourage intelligent exploration during the architecture search in the latent space, to avoid local optimal in architecture search. As the catastrophic forgetting in differentiable One-Shot NAS deteriorates supernet predictive ability and makes the bilevel optimization inefficient, this paper further proposes an architecture complementation method to relieve this deficiency. We analyze the effectiveness of the proposed method, and a series of experiments have been conducted to compare the proposed method with state-of-the-art One-Shot NAS methods.

Neural network architecture design mostly focuses on the new convolutional operator or special topological structure of network block, little attention is drawn to the configuration of stacking each block, called Block Stacking Style (BSS). Recent studies show that BSS may also have an unneglectable impact on networks, thus we design an efficient algorithm to search it automatically. The proposed method, AutoBSS, is a novel AutoML algorithm based on Bayesian optimization by iteratively refining and clustering Block Stacking Style Code (BSSC), which can find optimal BSS in a few trials without biased evaluation. On ImageNet classification task, ResNet50/MobileNetV2/EfficientNet-B0 with our searched BSS achieve 79.29%/74.5%/77.79%, which outperform the original baselines by a large margin. More importantly, experimental results on model compression, object detection and instance segmentation show the strong generalizability of the proposed AutoBSS, and further verify the unneglectable impact of BSS on neural networks.

Neural architecture search (NAS) relies on a good controller to generate better architectures or predict the accuracy of given architectures. However, training the controller requires both abundant and high-quality pairs of architectures and their accuracy, while it is costly to evaluate an architecture and obtain its accuracy. In this paper, we propose SemiNAS, a semi-supervised NAS approach that leverages numerous unlabeled architectures (without evaluation and thus nearly no cost). Specifically, SemiNAS 1) trains an initial accuracy predictor with a small set of architecture-accuracy data pairs; 2) uses the trained accuracy predictor to predict the accuracy of large amount of architectures (without evaluation); and 3) adds the generated data pairs to the original data to further improve the predictor. The trained accuracy predictor can be applied to various NAS algorithms by predicting the accuracy of candidate architectures for them. SemiNAS has two advantages: 1) It reduces the computational cost under the same accuracy guarantee. On NASBench-101 benchmark dataset, it achieves comparable accuracy with gradient-based method while using only 1/7 architecture-accuracy pairs. 2) It achieves higher accuracy under the same computational cost. It achieves 94.02% test accuracy on NASBench-101, outperforming all the baselines when using the same number of architectures. On ImageNet, it achieves 23.5% top-1 error rate (under 600M FLOPS constraint) using 4 GPU-days for search. We further apply it to LJSpeech text to speech task and it achieves 97% intelligibility rate in the low-resource setting and 15% test error rate in the robustness setting, with 9%, 7% improvements over the baseline respectively.

Existing Neural Architecture Search (NAS) methods either encode neural architectures using discrete encodings that do not scale well, or adopt supervised learning-based methods to jointly learn architecture representations and optimize architecture search on such representations which incurs search bias. Despite the widespread use, architecture representations learned in NAS are still poorly understood. We observe that the structural properties of neural architectures are hard to preserve in the latent space if architecture representation learning and search are coupled, resulting in less effective search performance. In this work, we find empirically that pre-training architecture representations using only neural architectures without their accuracies as labels improves the downstream architecture search efficiency. To explain this finding, we visualize how unsupervised architecture representation learning better encourages neural architectures with similar connections and operators to cluster together. This helps map neural architectures with similar performance to the same regions in the latent space and makes the transition of architectures in the latent space relatively smooth, which considerably benefits diverse downstream search strategies.

Neural architecture search (NAS) has been extensively studied in the past few years. A popular approach is to represent each neural architecture in the search space as a directed acyclic graph (DAG), and then search over all DAGs by encoding the adjacency matrix and list of operations as a set of hyperparameters. Recent work has demonstrated that even small changes to the way each architecture is encoded can have a significant effect on the performance of NAS algorithms.

In this work, we present the first formal study on the effect of architecture encodings for NAS, including a theoretical grounding and an empirical study. First we formally define architecture encodings and give a theoretical characterization on the scalability of the encodings we study. Then we identify the main encoding-dependent subroutines which NAS algorithms employ, running experiments to show which encodings work best with each subroutine for many popular algorithms. The experiments act as an ablation study for prior work, disentangling the algorithmic and encoding-based contributions, as well as a guideline for future work. Our results demonstrate that NAS encodings are an important design decision which can have a significant impact on overall performance. Our code is available at https://github.com/naszilla/naszilla.

Normalization layers and activation functions are fundamental components in deep networks and typically co-locate with each other. Here we propose to design them using an automated approach. Instead of designing them separately, we unify them into a single tensor-to-tensor computation graph, and evolve its structure starting from basic mathematical functions. Examples of such mathematical functions are addition, multiplication and statistical moments. The use of low-level mathematical functions, in contrast to the use of high-level modules in mainstream NAS, leads to a highly sparse and large search space which can be challenging for search methods. To address the challenge, we develop efficient rejection protocols to quickly filter out candidate layers that do not work well. We also use multi-objective evolution to optimize each layer's performance across many architectures to prevent overfitting. Our method leads to the discovery of EvoNorms, a set of new normalization-activation layers with novel, and sometimes surprising structures that go beyond existing design patterns. For example, some EvoNorms do not assume that normalization and activation functions must be applied sequentially, nor need to center the feature maps, nor require explicit activation functions. Our experiments show that EvoNorms work well on image classification models including ResNets, MobileNets and EfficientNets but also transfer well to Mask R-CNN with FPN/SpineNet for instance segmentation and to BigGAN for image synthesis, outperforming BatchNorm and GroupNorm based layers in many cases.

Knowledge graph (KG) embedding is well-known in learning representations of KGs. Many models have been proposed to learn the interactions between entities and relations of the triplets. However, long-term information among multiple triplets is also important to KG. In this work, based on the relational paths, which are composed of a sequence of triplets, we define the Interstellar as a recurrent neural architecture search problem for the short-term and long-term information along the paths. First, we analyze the difficulty of using a unified model to work as the Interstellar. Then, we propose to search for recurrent architecture as the Interstellar for different KG tasks. A case study on synthetic data illustrates the importance of the defined search problem. Experiments on real datasets demonstrate the effectiveness of the searched models and the efficiency of the proposed hybrid-search algorithm.

Attention modules have been demonstrated effective in strengthening the representation ability of a neural network via reweighting spatial or channel features or stacking both operations sequentially. However, designing the structures of different attention operations requires a bulk of computation and extensive expertise. In this paper, we devise an Auto Learning Attention (AutoLA) method, which is the first attempt on automatic attention design. Specifically, we define a novel attention module named high order group attention (HOGA) as a directed acyclic graph (DAG) where each group represents a node, and each edge represents an operation of heterogeneous attentions. A typical HOGA architecture can be searched automatically via the differential AutoLA method within 1 GPU day using the ResNet-20 backbone on CIFAR10. Further, the searched attention module can generalize to various backbones as a plug-and-play component and outperforms popular manually designed channel and spatial attentions for many vision tasks, including image classification on CIFAR100 and ImageNet, object detection and human keypoint detection on COCO dataset. The code will be released.

Most compilers for machine learning (ML) frameworks need to solve many correlated optimization problems to generate efficient machine code. Current ML compilers rely on heuristics based algorithms to solve these optimization problems one at a time. However, this approach is not only hard to maintain but often leads to sub-optimal solutions especially for newer model architectures. Existing learning based approaches in the literature are sample inefficient, tackle a single optimization problem, and do not generalize to unseen graphs making them infeasible to be deployed in practice. To address these limitations, we propose an end-to-end, transferable deep reinforcement learning method for computational graph optimization (GO), based on a scalable sequential attention mechanism over an inductive graph neural network. GO generates decisions on the entire graph rather than on each individual node autoregressively, drastically speeding up the search compared to prior methods. Moreover, we propose recurrent attention layers to jointly optimize dependent graph optimization tasks and demonstrate 33%-60% speedup on three graph optimization tasks compared to TensorFlow default optimization. On a diverse set of representative graphs consisting of up to 80,000 nodes, including Inception-v3, Transformer-XL, and WaveNet, GO achieves on average 21% improvement over human experts and 18% improvement over the prior state of the art with 15x faster convergence, on a device placement task evaluated in real systems.

Neural architecture search (NAS) has demonstrated impressive performance in automatically designing high-performance neural networks. The power of deep neural networks is to be unleashed for analyzing a large volume of data (e.g. ImageNet), but the architecture search is often executed on another smaller dataset (e.g. CIFAR-10) to finish it in a feasible time. However, it is hard to guarantee that the optimal architecture derived on the proxy task could maintain its advantages on another more challenging dataset. This paper aims to improve the generalization of neural architectures via domain adaptation. We analyze the generalization bounds of the derived architecture and suggest its close relations with the validation error and the data distribution distance on both domains. These theoretical analyses lead to AdaptNAS, a novel and principled approach to adapt neural architectures between domains in NAS. Our experimental evaluation shows that only a small part of ImageNet will be sufficient for AdaptNAS to extend its architecture success to the entire ImageNet and outperform state-of-the-art comparison algorithms.

Recent advances in neural architecture search inspire many channel number search algorithms~(CNS) for convolutional neural networks. To improve searching efficiency, parameter sharing is widely applied, which reuses parameters among different channel configurations. Nevertheless, it is unclear how parameter sharing affects the searching process. In this paper, we aim at providing a better understanding and exploitation of parameter sharing for CNS. Specifically, we propose affine parameter sharing~(APS) as a general formulation to unify and quantitatively analyze existing channel search algorithms. It is found that with parameter sharing, weight updates of one architecture can simultaneously benefit other candidates. However, it also results in less confidence in choosing good architectures. We thus propose a new strategy of parameter sharing towards a better balance between training efficiency and architecture discrimination. Extensive analysis and experiments demonstrate the superiority of the proposed strategy in channel configuration against many state-of-the-art counterparts on benchmark datasets.

Neuron-level structured pruning is a very effective technique to reduce the computation of neural networks without compromising prediction accuracy. In previous works, structured pruning is usually achieved by imposing L1 regularization on the scaling factors of neurons, and pruning the neurons whose scaling factors are below a certain threshold. The reasoning is that neurons with smaller scaling factors have weaker influence on network output. A scaling factor close to 0 actually suppresses a neuron. However, L1 regularization lacks discrimination between neurons because it pushes all scaling factors towards 0. A more reasonable pruning method is to only suppress unimportant neurons (with 0 scaling factors) and simultaneously keep important neurons intact (with larger scaling factor). To achieve this goal, we propose a new regularizer on scaling factors, namely polarization regularizer. Theoretically, we prove that polarization regularizer pushes some scaling factors to 0 and others to a value $a > 0$. Experimentally, we show that structured pruning using polarization regularizer achieves much better results than using L1 regularizer. Experiments on CIFAR and ImageNet datasets show that polarization pruning achieves the state-of-the-art result to date.

Quantization is an effective method for reducing memory footprint and inference time of Neural Networks. However, ultra low precision quantization could lead to significant degradation in model accuracy. A promising method to address this is to perform mixed-precision quantization, where more sensitive layers are kept at higher precision. However, the search space for a mixed-precision quantization is exponential in the number of layers. Recent work has proposed a novel Hessian based framework, with the aim of reducing this exponential search space by using second-order information. While promising, this prior work has three major limitations: (i) they only use a heuristic metric based on top Hessian eigenvalue as a measure of sensitivity and do not consider the rest of the Hessian spectrum; (ii) their approach only provides relative sensitivity of different layers and therefore requires a manual selection of the mixed-precision setting; and (iii) they do not consider mixed-precision activation quantization. Here, we present HAWQ-V2 which addresses these shortcomings. For (i), we theoretically prove that the right sensitivity metric is the average Hessian trace, instead of just top Hessian eigenvalue. For (ii), we develop a Pareto frontier based method for automatic bit precision selection of different layers without any manual intervention. For (iii), we develop the first Hessian based analysis for mixed-precision activation quantization, which is very beneficial for object detection. We show that HAWQ-V2 achieves new state-of-the-art results for a wide range of tasks. In particular, we present quantization results for InceptionV3, ResNet50, and SqueezeNext, all without any manual bit selection. Furthermore, we present results for object detection on Microsoft COCO, where we achieve 2.6 higher mAP than direct uniform quantization and 1.6 higher mAP than the recently proposed method of FQN, with a smaller model size of 17.9MB.

Machine learning on tiny IoT devices based on microcontroller units (MCU) is appealing but challenging: the memory of microcontrollers is 2-3 orders of magnitude smaller even than mobile phones. We propose MCUNet, a framework that jointly designs the efficient neural architecture (TinyNAS) and the lightweight inference engine (TinyEngine), enabling ImageNet-scale inference on microcontrollers. TinyNAS adopts a two-stage neural architecture search approach that first optimizes the search space to fit the resource constraints, then specializes the network architecture in the optimized search space. TinyNAS can automatically handle diverse constraints (i.e. device, latency, energy, memory) under low search costs. TinyNAS is co-designed with TinyEngine, a memory-efficient inference library to expand the search space and fit a larger model. TinyEngine adapts the memory scheduling according to the overall network topology rather than layer-wise optimization, reducing the memory usage by 3.4×, and accelerating the inference by 1.7-3.3× compared to TF-Lite Micro [3] and CMSIS-NN [28]. MCUNet is the first to achieves >70% ImageNet top1 accuracy on an off-the-shelf commercial microcontroller, using 3.5× less SRAM and 5.7× less Flash compared to quantized MobileNetV2 and ResNet-18. On visual&audio wake words tasks, MCUNet achieves state-of-the-art accuracy and runs 2.4-3.4× faster than Mo- bileNetV2 and ProxylessNAS-based solutions with 3.7-4.1× smaller peak SRAM. Our study suggests that the era of always-on tiny machine learning on IoT devices has arrived.

Variational Autoencoders (VAEs) have seen widespread use in learned image compression. They are used to learn expressive latent representations on which downstream compression methods can operate with high efficiency. Recently proposed 'bits-back' methods can indirectly encode the latent representation of images with codelength close to the relative entropy between the latent posterior and the prior. However, due to the underlying algorithm, these methods can only be used for lossless compression, and they only achieve their nominal efficiency when compressing multiple images simultaneously; they are inefficient for compressing single images. As an alternative, we propose a novel method, Relative Entropy Coding (REC), that can directly encode the latent representation with codelength close to the relative entropy for single images, supported by our empirical results obtained on the Cifar10, ImageNet32 and Kodak datasets. Moreover, unlike previous bits-back methods, REC is immediately applicable to lossy compression, where it is competitive with the state-of-the-art on the Kodak dataset.

Score matching (SM) provides a compelling approach to learn energy-based models (EBMs) by avoiding the calculation of partition function. However, it remains largely open to learn energy-based latent variable models (EBLVMs), except some special cases. This paper presents a bi-level score matching (BiSM) method to learn EBLVMs with general structures by reformulating SM as a bi-level optimization problem. The higher level introduces a variational posterior of the latent variables and optimizes a modified SM objective, and the lower level optimizes the variational posterior to fit the true posterior. To solve BiSM efficiently, we develop a stochastic optimization algorithm with gradient unrolling. Theoretically, we analyze the consistency of BiSM and the convergence of the stochastic algorithm. Empirically, we show the promise of BiSM in Gaussian restricted Boltzmann machines and highly nonstructural EBLVMs parameterized by deep convolutional neural networks. BiSM is comparable to the widely adopted contrastive divergence and SM methods when they are applicable; and can learn complex EBLVMs with intractable posteriors to generate natural images.

Normalizing flows, autoregressive models, variational autoencoders (VAEs), and deep energy-based models are among competing likelihood-based frameworks for deep generative learning. Among them, VAEs have the advantage of fast and tractable sampling and easy-to-access encoding networks. However, they are currently outperformed by other models such as normalizing flows and autoregressive models. While the majority of the research in VAEs is focused on the statistical challenges, we explore the orthogonal direction of carefully designing neural architectures for hierarchical VAEs. We propose Nouveau VAE (NVAE), a deep hierarchical VAE built for image generation using depth-wise separable convolutions and batch normalization. NVAE is equipped with a residual parameterization of Normal distributions and its training is stabilized by spectral regularization. We show that NVAE achieves state-of-the-art results among non-autoregressive likelihood-based models on the MNIST, CIFAR-10, CelebA 64, and CelebA HQ datasets and it provides a strong baseline on FFHQ. For example, on CIFAR-10, NVAE pushes the state-of-the-art from 2.98 to 2.91 bits per dimension, and it produces high-quality images on CelebA HQ. To the best of our knowledge, NVAE is the first successful VAE applied to natural images as large as 256x256 pixels. The source code is publicly available.

Generative adversarial nets (GANs) have become a preferred tool for tasks involving complicated distributions. To stabilise the training and reduce the mode collapse of GANs, one of their main variants employs the integral probability metric (IPM) as the loss function. This provides extensive IPM-GANs with theoretical support for basically comparing moments in an embedded domain of the \textit{critic}. We generalise this by comparing the distributions rather than their moments via a powerful tool, i.e., the characteristic function (CF), which uniquely and universally comprising all the information about a distribution. For rigour, we first establish the physical meaning of the phase and amplitude in CF, and show that this provides a feasible way of balancing the accuracy and diversity of generation. We then develop an efficient sampling strategy to calculate the CFs. Within this framework, we further prove an equivalence between the embedded and data domains when a reciprocal exists, where we naturally develop the GAN in an auto-encoder structure, in a way of comparing everything in the embedded space (a semantically meaningful manifold). This efficient structure uses only two modules, together with a simple training strategy, to achieve bi-directionally generating clear images, which is referred to as the reciprocal CF GAN (RCF-GAN). Experimental results demonstrate the superior performances of the proposed RCF-GAN in terms of both generation and reconstruction.

Stein discrepancies (SDs) monitor convergence and non-convergence in approximate inference when exact integration and sampling are intractable. However, the computation of a Stein discrepancy can be prohibitive if the Stein operator -- often a sum over likelihood terms or potentials -- is expensive to evaluate. To address this deficiency, we show that stochastic Stein discrepancies (SSDs) based on subsampled approximations of the Stein operator inherit the convergence control properties of standard SDs with probability 1. Along the way, we establish the convergence of Stein variational gradient descent (SVGD) on unbounded domains, resolving an open question of Liu (2017). In our experiments with biased Markov chain Monte Carlo (MCMC) hyperparameter tuning, approximate MCMC sampler selection, and stochastic SVGD, SSDs deliver comparable inferences to standard SDs with orders of magnitude fewer likelihood evaluations.

Probabilistic neural networks are typically modeled with independent weight priors, which do not capture weight correlations in the prior and do not provide a parsimonious interface to express properties in function space. A desirable class of priors would represent weights compactly, capture correlations between weights, facilitate calibrated reasoning about uncertainty, and allow inclusion of prior knowledge about the function space such as periodicity or dependence on contexts such as inputs. To this end, this paper introduces two innovations: (i) a Gaussian process-based hierarchical model for network weights based on unit priors that can flexibly encode correlated weight structures, and (ii) input-dependent versions of these weight priors that can provide convenient ways to regularize the function space through the use of kernels defined on contextual inputs. We show these models provide desirable test-time uncertainty estimates on out-of-distribution data and demonstrate cases of modeling inductive biases for neural networks with kernels which help both interpolation and extrapolation from training data.

Domains where supervised models are deployed often come with task-specific constraints, such as prior expert knowledge on the ground-truth function, or desiderata like safety and fairness. We introduce a novel probabilistic framework for reasoning with such constraints and formulate a prior that enables us to effectively incorporate them into Bayesian neural networks (BNNs), including a variant that can be amortized over tasks. The resulting Output-Constrained BNN (OC-BNN) is fully consistent with the Bayesian framework for uncertainty quantification and is amenable to black-box inference. Unlike typical BNN inference in uninterpretable parameter space, OC-BNNs widen the range of functional knowledge that can be incorporated, especially for model users without expertise in machine learning. We demonstrate the efficacy of OC-BNNs on real-world datasets, spanning multiple domains such as healthcare, criminal justice, and credit scoring.

Approximate inference techniques are the cornerstone of probabilistic methods based on Gaussian process priors. Despite this, most work approximately optimizes standard divergence measures such as the Kullback-Leibler (KL) divergence, which lack the basic desiderata for the task at hand, while chiefly offering merely technical convenience. We develop a new approximate inference method for Gaussian process models which overcomes the technical challenges arising from abandoning these convenient divergences. Our method---dubbed Quantile Propagation (QP)---is similar to expectation propagation (EP) but minimizes the $L_2$ Wasserstein distance (WD) instead of the KL divergence. The WD exhibits all the required properties of a distance metric, while respecting the geometry of the underlying sample space. We show that QP matches quantile functions rather than moments as in EP and has the same mean update but a smaller variance update than EP, thereby alleviating EP's tendency to over-estimate posterior variances. Crucially, despite the significant complexity of dealing with the WD, QP has the same favorable locality property as EP, and thereby admits an efficient algorithm. Experiments on classification and Poisson regression show that QP outperforms both EP and variational Bayes.

Hamiltonian Monte Carlo (HMC) has emerged as a powerful Markov Chain Monte Carlo (MCMC) method to sample from complex continuous distributions. However, a fundamental limitation of HMC is that it can not be applied to distributions with mixed discrete and continuous variables. In this paper, we propose mixed HMC (M-HMC) as a general framework to address this limitation. M-HMC is a novel family of MCMC algorithms that evolves the discrete and continuous variables in tandem, allowing more frequent updates of discrete variables while maintaining HMC's ability to suppress random-walk behavior. We establish M-HMC's theoretical properties, and present an efficient implementation with Laplace momentum that introduces minimal overhead compared to existing HMC methods. The superior performances of M-HMC over existing methods are demonstrated with numerical experiments on Gaussian mixture models (GMMs), variable selection in Bayesian logistic regression (BLR), and correlated topic models (CTMs).

Over-parameterized models, such as DeepNets and ConvNets, form a class of models that are routinely adopted in a wide variety of applications, and for which Bayesian inference is desirable but extremely challenging. Variational inference offers the tools to tackle this challenge in a scalable way and with some degree of flexibility on the approximation, but for overparameterized models this is challenging due to the over-regularization property of the variational objective. Inspired by the literature on kernel methods, and in particular on structured approximations of distributions of random matrices, this paper proposes Walsh-Hadamard Variational Inference (WHVI), which uses Walsh-Hadamardbased factorization strategies to reduce the parameterization and accelerate computations, thus avoiding over-regularization issues with the variational objective. Extensive theoretical and empirical analyses demonstrate that WHVI yields considerable speedups and model reductions compared to other techniques to carry out approximate inference for over-parameterized models, and ultimately show how advances in kernel methods can be translated into advances in approximate Bayesian inference for Deep Learning.

This paper introduces the f-divergence variational inference (f-VI) that generalizes variational inference to all f-divergences. Initiated from minimizing a crafty surrogate f-divergence that shares the statistical consistency with the f-divergence, the f-VI framework not only unifies a number of existing VI methods, e.g. Kullback–Leibler VI, Renyi's alpha-VI, and chi-VI, but offers a standardized toolkit for VI subject to arbitrary divergences from f-divergence family. A general f-variational bound is derived and provides a sandwich estimate of marginal likelihood (or evidence). The development of the f-VI unfolds with a stochastic optimization scheme that utilizes the reparameterization trick, importance weighting and Monte Carlo approximation; a mean-field approximation scheme that generalizes the well-known coordinate ascent variational inference (CAVI) is also proposed for f-VI. Empirical examples, including variational autoencoders and Bayesian neural networks, are provided to demonstrate the effectiveness and the wide applicability of f-VI.

Sparse models are desirable for many applications across diverse domains as they can perform automatic variable selection, aid interpretability, and provide regularization. When fitting sparse models in a Bayesian framework, however, analytically obtaining a posterior distribution over the parameters of interest is intractable for all but the simplest cases. As a result practitioners must rely on either sampling algorithms such as Markov chain Monte Carlo or variational methods to obtain an approximate posterior. Mean field variational inference is a particularly simple and popular framework that is often amenable to analytically deriving closed-form parameter updates. When all distributions in the model are members of exponential families and are conditionally conjugate, optimization schemes can often be derived by hand. Yet, I show that using standard mean field variational inference can fail to produce sensible results for models with sparsity-inducing priors, such as the spike-and-slab. Fortunately, such pathological behavior can be remedied as I show that mixtures of exponential family distributions with non-overlapping support form an exponential family. In particular, any mixture of an exponential family of diffuse distributions and a point mass at zero to model sparsity forms an exponential family. Furthermore, specific choices of these distributions maintain conditional conjugacy. I use two applications to motivate these results: one from statistical genetics that has connections to generalized least squares with a spike-and-slab prior on the regression coefficients; and sparse probabilistic principal component analysis. The theoretical results presented here are broadly applicable beyond these two examples.

The randomized midpoint method, proposed by (Shen and Lee, 2019), has emerged as an optimal discretization procedure for simulating the continuous time underdamped Langevin diffusion. In this paper, we analyze several probabilistic properties of the randomized midpoint discretization method, considering both overdamped and underdamped Langevin dynamics. We first characterize the stationary distribution of the discrete chain obtained with constant step-size discretization and show that it is biased away from the target distribution. Notably, the step-size needs to go to zero to obtain asymptotic unbiasedness. Next, we establish the asymptotic normality of numerical integration using the randomized midpoint method and highlight the relative advantages and disadvantages over other discretizations. Our results collectively provide several insights into the behavior of the randomized midpoint discretization method, including obtaining confidence intervals for numerical integrations.

In this work we study online rent-or-buy problems as a sequential decision making problem. We show how one can integrate predictions, typically coming from a machine learning (ML) setup, into this framework. Specifically, we consider the ski-rental problem and the dynamic TCP acknowledgment problem. We present new online algorithms and obtain explicit performance bounds in-terms of the accuracy of the prediction. Our algorithms are close to optimal with accurate predictions while hedging against less accurate predictions.

Modularity maximization has been a fundamental tool for understanding the community structure of a network, but the underlying optimization problem is nonconvex and NP-hard to solve. State-of-the-art algorithms like the Louvain or Leiden methods focus on different heuristics to help escape local optima, but they still depend on a greedy step that moves node assignment locally and is prone to getting trapped. In this paper, we propose a new class of low-cardinality algorithm that generalizes the local update to maximize a semidefinite relaxation derived from max-k-cut. This proposed algorithm is scalable, empirically achieves the global semidefinite optimality for small cases, and outperforms the state-of-the-art algorithms in real-world datasets with little additional time cost. From the algorithmic perspective, it also opens a new avenue for scaling-up semidefinite programming when the solutions are sparse instead of low-rank.

This paper presents competitive algorithms for a novel class of online optimization problems with memory. We consider a setting where the learner seeks to minimize the sum of a hitting cost and a switching cost that depends on the previous $p$ decisions. This setting generalizes Smoothed Online Convex Optimization. The proposed approach, Optimistic Regularized Online Balanced Descent, achieves a constant, dimension-free competitive ratio. Further, we show a connection between online optimization with memory and online control with adversarial disturbances. This connection, in turn, leads to a new constant-competitive policy for a rich class of online control problems.

In this paper, we develop a simple and fast online algorithm for solving a class of binary integer linear programs (LPs) arisen in the general resource allocation problem. The algorithm requires only one single pass through the input data and is free of doing any matrix inversion. It can be viewed as both an approximate algorithm for solving binary integer LPs and a fast algorithm for solving online LP problems. The algorithm is inspired by an equivalent form of the dual problem of the relaxed LP and it essentially performs (one-pass) projected stochastic subgradient descent in the dual space. We analyze the algorithm under two different models, stochastic input and random permutation, with minimal technical assumptions on the input data. The algorithm achieves $O\left(m \sqrt{n}\right)$ expected regret under the stochastic input model and $O\left((m+\log n)\sqrt{n}\right)$ expected regret under the random permutation model, and it achieves $O(m \sqrt{n})$ expected constraint violation under both models, where $n$ is the number of decision variables and $m$ is the number of constraints. In addition, we employ the notion of permutational Rademacher complexity and derive regret bounds for two earlier online LP algorithms for comparison. Both algorithms improve the regret bound with a factor of $\sqrt{m}$ by paying more computational cost. Furthermore, we demonstrate how to convert the possibly infeasible solution to a feasible one through a randomized procedure. Numerical experiments illustrate the general applicability and effectiveness of the algorithms.

In this paper, we consider an online optimization problem in which the reward functions are DR-submodular, and in addition to maximizing the total reward, the sequence of decisions must satisfy some convex constraints on average. Specifically, at each round $t\in\{1,\dots,T\}$, upon committing to an action $x_t$, a DR-submodular utility function $f_t(\cdot)$ and a convex constraint function $g_t(\cdot)$ are revealed, and the goal is to maximize the overall utility while ensuring the average of the constraint functions $\frac{1}{T}\sum_{t=1}^T g_t(x_t)$ is non-positive. Such cumulative constraints arise naturally in applications where the average resource consumption is required to remain below a prespecified threshold. We study this problem under an adversarial model and a stochastic model for the convex constraints, where the functions $g_t$ can vary arbitrarily or according to an i.i.d. process over time slots $t\in\{1,\dots,T\}$, respectively. We propose a single algorithm which achieves sub-linear (with respect to $T$) regret as well as sub-linear constraint violation bounds in both settings, without prior knowledge of the regime. Prior works have studied this problem in the special case of linear constraint functions. Our results not only improve upon the existing bounds under linear cumulative constraints, but also give the first sub-linear bounds for general convex long-term constraints.

The work studies how node-to-node communications over an Erd\H{o}s-R\'enyi random network influence distributed online convex optimization, which is vital in solving large-scale machine learning in antagonistic or changing environments. At per step, each node (computing unit) makes a local decision, experiences a loss evaluated with a convex function, and communicates the decision with other nodes over a network. The node-to-node communications are described by the Erd\H{o}s-R\'enyi rule, where independently each link takes place with a probability $p$ over a prescribed connected graph. The objective is to minimize the system-wide loss accumulated over a finite time horizon. We consider standard distributed gradient descents with full gradients, one-point bandits and two-points bandits for convex and strongly convex losses, respectively. We establish how the regret bounds scale with respect to time horizon $T$, network size $N$, decision dimension $d$, and an algebraic network connectivity. The regret bounds scaling with respect to $T$ match those obtained by state-of-the-art algorithms and fundamental limits in the corresponding centralized online optimization problems, e.g., $\mathcal{O}(\sqrt{T}) $ and $\mathcal{O}(\ln(T)) $ regrets are established for convex and strongly convex losses with full gradient feedback and two-points information, respectively. For classical Erd\H{o}s-R\'enyi networks over all-to-all possible node communications, the regret scalings with respect to the probability $p$ are analytically established, based on which the tradeoff between the communication overhead and computation accuracy is clearly demonstrated. Numerical studies have validated the theoretical findings.

L1 regularization has been broadly employed to pursue model sparsity. Despite the non-smoothness, people have developed efficient algorithms by leveraging the sparsity and convexity of the problems. In this paper, we propose a novel active incremental approach to further improve the efficiency of the solvers. We show that our method performs well even when the existing methods fail due to the low sparseness or high solution accuracy request. Theoretical analysis and experimental results on synthetic and real-world data sets validate the advantages of the method.

We study the problem of maximizing a non-monotone, non-negative submodular function subject to a matroid constraint. The prior best-known deterministic approximation ratio for this problem is $\frac{1}{4}-\epsilon$ under $\mathcal{O}(({n^4}/{\epsilon})\log n)$ time complexity. We show that this deterministic ratio can be improved to $\frac{1}{4}$ under $\mathcal{O}(nr)$ time complexity, and then present a more practical algorithm dubbed TwinGreedyFast which achieves $\frac{1}{4}-\epsilon$ deterministic ratio in nearly-linear running time of $\mathcal{O}(\frac{n}{\epsilon}\log\frac{r}{\epsilon})$. Our approach is based on a novel algorithmic framework of simultaneously constructing two candidate solution sets through greedy search, which enables us to get improved performance bounds by fully exploiting the properties of independence systems. As a byproduct of this framework, we also show that TwinGreedyFast achieves $\frac{1}{2p+2}-\epsilon$ deterministic ratio under a $p$-set system constraint with the same time complexity. To showcase the practicality of our approach, we empirically evaluated the performance of TwinGreedyFast on two network applications, and observed that it outperforms the state-of-the-art deterministic and randomized algorithms with efficient implementations for our problem.

The extension of classical online algorithms when provided with predictions is a new and active research area. In this paper, we extend the primal-dual method for online algorithms in order to incorporate predictions that advise the online algorithm about the next action to take. We use this framework to obtain novel algorithms for a variety of online covering problems. We compare our algorithms to the cost of the true and predicted offline optimal solutions and show that these algorithms outperform any online algorithm when the prediction is accurate while maintaining good guarantees when the prediction is misleading.

The task of maximizing a monotone submodular function under a cardinality constraint is at the core of many machine learning and data mining applications, including data summarization, sparse regression and coverage problems. We study this classic problem in the fully dynamic setting, where elements can be both inserted and removed. Our main result is a randomized algorithm that maintains an efficient data structure with a poly-logarithmic amortized update time and yields a $(1/2-epsilon)$-approximate solution. We complement our theoretical analysis with an empirical study of the performance of our algorithm.

In this paper, we introduce a novel technique for constrained submodular maximization, inspired by barrier functions in continuous optimization. This connection not only improves the running time for constrained submodular maximization but also provides the state of the art guarantee. More precisely, for maximizing a monotone submodular function subject to the combination of a $k$-matchoid and $\ell$-knapsack constraints (for $\ell\leq k$), we propose a potential function that can be approximately minimized. Once we minimize the potential function up to an $\epsilon$ error, it is guaranteed that we have found a feasible set with a $2(k+1+\epsilon)$-approximation factor which can indeed be further improved to $(k+1+\epsilon)$ by an enumeration technique. We extensively evaluate the performance of our proposed algorithm over several real-world applications, including a movie recommendation system, summarization tasks for YouTube videos, Twitter feeds and Yelp business locations, and a set cover problem.

We consider the problem of nonnegative submodular maximization in the online setting. At time step t, an algorithm selects a set St ∈ C ⊆ 2^V where C is a feasible family of sets. An adversary then reveals a submodular function ft. The goal is to design an efficient algorithm for minimizing the expected approximate regret. In this work, we give a general approach for improving regret bounds in online submodular maximization by exploiting “first-order” regret bounds for online linear optimization. - For monotone submodular maximization subject to a matroid, we give an efficient algorithm which achieves a (1 − c/e − ε)-regret of O(√kT ln(n/k)) where n is the size of the ground set, k is the rank of the matroid, ε > 0 is a constant, and c is the average curvature. Even without assuming any curvature (i.e., taking c = 1), this regret bound improves on previous results of Streeter et al. (2009) and Golovin et al. (2014). - For nonmonotone, unconstrained submodular functions, we give an algorithm with 1/2-regret O(√ nT), improving on the results of Roughgarden and Wang (2018). Our approach is based on Blackwell approachability; in particular, we give a novel first-order regret bound for the Blackwell instances that arise in this setting

Submodularity is an important property of set functions and has been extensively studied in the literature. It models set functions that exhibit a diminishing returns property, where the marginal value of adding an element to a set decreases as the set expands. This notion has been generalized to considering sequence functions, where the order of adding elements plays a crucial role and determines the function value; the generalized notion is called sequence (or string) submodularity. In this paper, we study a new problem of robust sequence submodular maximization with cardinality constraints. The robustness is against the removal of a subset of elements in the selected sequence (e.g., due to malfunctions or adversarial attacks). Compared to robust submodular maximization for set function, new challenges arise when sequence functions are concerned. Specifically, there are multiple definitions of submodularity for sequence functions, which exhibit subtle yet critical differences. Another challenge comes from two directions of monotonicity: forward monotonicity and backward monotonicity, both of which are important to proving performance guarantees. To address these unique challenges, we design two robust greedy algorithms: while one algorithm achieves a constant approximation ratio but is robust only against the removal of a subset of contiguous elements, the other is robust against the removal of an arbitrary subset of the selected elements but requires a stronger assumption and achieves an approximation ratio that depends on the number of the removed elements. Finally, we generalize the analyses to considering sequence functions under weaker assumptions based on approximate versions of sequence submodularity and backward monotonicity.

In this paper, we propose the first continuous optimization algorithms that achieve a constant factor approximation guarantee for the problem of monotone continuous submodular maximization subject to a linear constraint. We first prove that a simple variant of the vanilla coordinate ascent, called \COORDINATE-ASCENT+, achieves a $(\frac{e-1}{2e-1}-\eps)$-approximation guarantee while performing $O(n/\epsilon)$ iterations, where the computational complexity of each iteration is roughly $O(n/\sqrt{\epsilon}+n\log n)$ (here, $n$ denotes the dimension of the optimization problem). We then propose \COORDINATE-ASCENT++, that achieves the tight $(1-1/e-\eps)$-approximation guarantee while performing the same number of iterations, but at a higher computational complexity of roughly $O(n^3/\eps^{2.5} + n^3 \log n / \eps^2)$ per iteration. However, the computation of each round of \COORDINATE-ASCENT++ can be easily parallelized so that the computational cost per machine scales as $O(n/\sqrt{\epsilon}+n\log n)$.

We consider a natural model of online preference aggregation, where sets of preferred items R1, R2, ..., Rt, ..., along with a demand for kt items in each Rt, appear online. Without prior knowledge of (Rt, kt), the learner maintains a ranking \pit aiming that at least kt items from Rt appear high in \pi_t. This is a fundamental problem in preference aggregation with applications to e.g., ordering product or news items in web pages based on user scrolling and click patterns.

The widely studied Generalized Min-Sum-Set-Cover (GMSSC) problem serves as a formal model for the setting above. GMSSC is NP-hard and the standard application of no-regret online learning algorithms is computationally inefficient, because they operate in the space of rankings. In this work, we show how to achieve low regret for GMSSC in polynomial-time. We employ dimensionality reduction from rankings to the space of doubly stochastic matrices, where we apply Online Gradient Descent. A key step is to show how subgradients can be computed efficiently, by solving the dual of a configuration LP. Using deterministic and randomized rounding schemes, we map doubly stochastic matrices back to rankings with a small loss in the GMSSC objective.

We study the black-box attacks on graph neural networks (GNNs) under a novel and realistic constraint: attackers have access to only a subset of nodes in the network, and they can only attack a small number of them. A node selection step is essential under this setup. We demonstrate that the structural inductive biases of GNN models can be an effective source for this type of attacks. Specifically, by exploiting the connection between the backward propagation of GNNs and random walks, we show that the common gradient-based white-box attacks can be generalized to the black-box setting via the connection between the gradient and an importance score similar to PageRank. In practice, we find attacks based on this importance score indeed increase the classification loss by a large margin, but they fail to significantly increase the mis-classification rate. Our theoretical and empirical analyses suggest that there is a discrepancy between the loss and mis-classification rate, as the latter presents a diminishing-return pattern when the number of attacked nodes increases. Therefore, we propose a greedy procedure to correct the importance score that takes into account of the diminishing-return pattern. Experimental results show that the proposed procedure can significantly increase the mis-classification rate of common GNNs on real-world data without access to model parameters nor predictions.

Robustness of machine learning models to various adversarial and non-adversarial corruptions continues to be of interest. In this paper, we introduce the notion of the boundary thickness of a classifier, and we describe its connection with and usefulness for model robustness. Thick decision boundaries lead to improved performance, while thin decision boundaries lead to overfitting (e.g., measured by the robust generalization gap between training and testing) and lower robustness. We show that a thicker boundary helps improve robustness against adversarial examples (e.g., improving the robust test accuracy of adversarial training) as well as so-called out-of-distribution (OOD) transforms, and we show that many commonly-used regularization and data augmentation procedures can increase boundary thickness. On the theoretical side, we establish that maximizing boundary thickness during training is akin to the so-called mixup training. Using these observations, we show that noise-augmentation on mixup training further increases boundary thickness, thereby combating vulnerability to various forms of adversarial attacks and OOD transforms. We can also show that the performance improvement in several lines of recent work happens in conjunction with a thicker boundary.

As classifications datasets progressively get larger in terms of label space and number of examples, annotating them with all labels becomes non-trivial and expensive task. For example, annotating the entire OpenImage test set can cost $6.5M. Hence, in current large-scale benchmarks such as OpenImages and LVIS, less than 1\% of the labels are annotated across all images. Standard classification models are trained in a manner where these un-annotated labels are ignored. Ignoring these un-annotated labels result in loss of supervisory signal which reduces the performance of the classification models. Instead, in this paper, we exploit relationships among images and labels to derive more supervisory signal from the un-annotated labels. We study the effectiveness of our approach across several multi-label computer vision benchmarks, such as CIFAR100, MS-COCO panoptic segmentation, OpenImage and LVIS datasets. Our approach can outperform baselines by a margin of 2-10% across all the datasets on mean average precision (mAP) and mean F1 metrics.

The transition matrix, denoting the transition relationship from clean labels to noisy labels, is essential to build statistically consistent classifiers in label-noise learning. Existing methods for estimating the transition matrix rely heavily on estimating the noisy class posterior. However, the estimation error for noisy class posterior could be large because of the randomness of label noise. The estimation error would lead the transition matrix to be poorly estimated. Therefore in this paper, we aim to solve this problem by exploiting the divide-and-conquer paradigm. Specifically, we introduce an intermediate class to avoid directly estimating the noisy class posterior. By this intermediate class, the original transition matrix can then be factorized into the product of two easy-to-estimated transition matrices. We term the proposed method as the dual $T$-estimator. Both theoretical analyses and empirical results illustrate the effectiveness of the dual $T$-estimator for estimating transition matrices, leading to better classification performances.

Learning with the \textit{instance-dependent} label noise is challenging, because it is hard to model such real-world noise. Note that there are psychological and physiological evidences showing that we humans perceive instances by decomposing them into parts. Annotators are therefore more likely to annotate instances based on the parts rather than the whole instances, where a wrong mapping from parts to classes may cause the instance-dependent label noise. Motivated by this human cognition, in this paper, we approximate the instance-dependent label noise by exploiting \textit{part-dependent} label noise. Specifically, since instances can be approximately reconstructed by a combination of parts, we approximate the instance-dependent \textit{transition matrix} for an instance by a combination of the transition matrices for the parts of the instance. The transition matrices for parts can be learned by exploiting anchor points (i.e., data points that belong to a specific class almost surely). Empirical evaluations on synthetic and real-world datasets demonstrate our method is superior to the state-of-the-art approaches for learning from the instance-dependent label noise.

Graph Convolutional Networks (GCNs) have shown promising results in modeling graph-structured data. However, they have difficulty with processing digraphs because of two reasons: 1) transforming directed to undirected graph to guarantee the symmetry of graph Laplacian is not reasonable since it not only misleads message passing scheme to aggregate incorrect weights but also deprives the unique characteristics of digraph structure; 2) due to the fixed receptive field in each layer, GCNs fail to obtain multi-scale features that can boost their performance. In this paper, we theoretically extend spectral-based graph convolution to digraphs and derive a simplified form using personalized PageRank. Specifically, we present the Digraph Inception Convolutional Networks (DiGCN) which utilizes digraph convolution and kth-order proximity to achieve larger receptive fields and learn multi-scale features in digraphs. We empirically show that DiGCN can encode more structural information from digraphs than GCNs and help achieve better performance when generalized to other models. Moreover, experiments on various benchmarks demonstrate its superiority against the state-of-the-art methods.

Deep learning algorithms are well-known to have a propensity for fitting the training data very well and often fit even outliers and mislabeled data points. Such fitting requires memorization of training data labels, a phenomenon that has attracted significant research interest but has not been given a compelling explanation so far. A recent work of Feldman (2019) proposes a theoretical explanation for this phenomenon based on a combination of two insights. First, natural image and data distributions are (informally) known to be long-tailed, that is have a significant fraction of rare and atypical examples. Second, in a simple theoretical model such memorization is necessary for achieving close-to-optimal generalization error when the data distribution is long-tailed. However, no direct empirical evidence for this explanation or even an approach for obtaining such evidence were given.

In this work we design experiments to test the key ideas in this theory. The experiments require estimation of the influence of each training example on the accuracy at each test example as well as memorization values of training examples. Estimating these quantities directly is computationally prohibitive but we show that closely-related subsampled influence and memorization values can be estimated much more efficiently. Our experiments demonstrate the significant benefits of memorization for generalization on several standard benchmarks. They also provide quantitative and visually compelling evidence for the theory put forth in Feldman (2019).

We propose self-adaptive training---a new training algorithm that dynamically calibrates training process by model predictions without incurring extra computational cost---to improve generalization of deep learning for potentially corrupted training data. This problem is important to robustly learning from data that are corrupted by, e.g., random noises and adversarial examples. The standard empirical risk minimization (ERM) for such data, however, may easily overfit noises and thus suffers from sub-optimal performance. In this paper, we observe that model predictions can substantially benefit the training process: self-adaptive training significantly mitigates the overfitting issue and improves generalization over ERM under both random and adversarial noises. Besides, in sharp contrast to the recently-discovered double-descent phenomenon in ERM, self-adaptive training exhibits a single-descent error-capacity curve, indicating that such a phenomenon might be a result of overfitting of noises. Experiments on the CIFAR and ImageNet datasets verify the effectiveness of our approach in two applications: classification with label noise and selective classification. The code is available at \url{https://github.com/LayneH/self-adaptive-training}.

We investigate whether post-hoc model explanations are effective for diagnosing model errors--model debugging. In response to the challenge of explaining a model's prediction, a vast array of explanation methods have been proposed. Despite increasing use, it is unclear if they are effective. To start, we categorize \textit{bugs}, based on their source, into: ~\textit{data, model, and test-time} contamination bugs. For several explanation methods, we assess their ability to: detect spurious correlation artifacts (data contamination), diagnose mislabeled training examples (data contamination), differentiate between a (partially) re-initialized model and a trained one (model contamination), and detect out-of-distribution inputs (test-time contamination). We find that the methods tested are able to diagnose a spurious background bug, but not conclusively identify mislabeled training examples. In addition, a class of methods, that modify the back-propagation algorithm are invariant to the higher layer parameters of a deep network; hence, ineffective for diagnosing model contamination. We complement our analysis with a human subject study, and find that subjects fail to identify defective models using attributions, but instead rely, primarily, on model predictions. Taken together, our results provide guidance for practitioners and researchers turning to explanations as tools for model debugging.

Sparse sequences of neural spikes are posited to underlie aspects of working memory, motor production, and learning. Discovering these sequences in an unsupervised manner is a longstanding problem in statistical neuroscience. Promising recent work utilized a convolutive nonnegative matrix factorization model to tackle this challenge. However, this model requires spike times to be discretized, utilizes a sub-optimal least-squares criterion, and does not provide uncertainty estimates for model predictions or estimated parameters. We address each of these shortcomings by developing a point process model that characterizes fine-scale sequences at the level of individual spikes and represents sequence occurrences as a small number of marked events in continuous time. This ultra-sparse representation of sequence events opens new possibilities for spike train modeling. For example, we introduce learnable time warping parameters to model sequences of varying duration, which have been experimentally observed in neural circuits. We demonstrate these advantages on recordings from songbird higher vocal center and rodent hippocampus.

Feedforward networks (FFN) are ubiquitous structures in neural systems and have been studied to understand mechanisms of reliable signal and information transmission. In many FFNs, neurons in one layer have intrinsic properties that are distinct from those in their pre-/postsynaptic layers, but how this affects network-level information processing remains unexplored. Here we show that layer-to-layer heterogeneity arising from lamina-specific cellular properties facilitates signal and information transmission in FFNs. Specifically, we found that signal transformations, made by each layer of neurons on an input-driven spike signal, demodulate signal distortions introduced by preceding layers. This mechanism boosts information transfer carried by a propagating spike signal, and thereby supports reliable spike signal and information transmission in a deep FFN. Our study suggests that distinct cell types in neural circuits, performing different computational functions, facilitate information processing on the whole.

Reconstructing seeing images from fMRI recordings is an absorbing research area in neuroscience and provides a potential brain-reading technology. The challenge lies in that visual encoding in brain is highly complex and not fully revealed. Inspired by the theory that visual features are hierarchically represented in cortex, we propose to break the complex visual signals into multi-level components and decode each component separately. Specifically, we decode shape and semantic representations from the lower and higher visual cortex respectively, and merge the shape and semantic information to images by a generative adversarial network (Shape-Semantic GAN). This 'divide and conquer' strategy captures visual information more accurately. Experiments demonstrate that Shape-Semantic GAN improves the reconstruction similarity and image quality, and achieves the state-of-the-art image reconstruction performance.

A key challenge in understanding the sensory transformations of the visual system is to obtain a highly predictive model that maps natural images to neural responses. Deep neural networks (DNNs) provide a promising candidate for such a model. However, DNNs require orders of magnitude more training data than neuroscientists can collect because experimental recording time is severely limited. This motivates us to find images to train highly-predictive DNNs with as little training data as possible. We propose high-contrast, binarized versions of natural images---termed gaudy images---to efficiently train DNNs to predict higher-order visual cortical responses. In simulation experiments and analyses of real neural data, we find that training DNNs with gaudy images substantially reduces the number of training images needed to accurately predict responses to natural images. We also find that gaudy images, chosen before training, outperform images chosen during training by active learning algorithms. Thus, gaudy images overemphasize features of natural images that are the most important for efficiently training DNNs. We believe gaudy images will aid in the modeling of visual cortical neurons, potentially opening new scientific questions about visual processing.

Reinforcement learning (RL) is a powerful framework for learning to take actions to solve tasks. However, in many settings, an agent must winnow down the inconceivably large space of all possible tasks to the single task that it is currently being asked to solve. Can we instead constrain the space of tasks to those that are semantically meaningful? In this work, we introduce a framework for using weak supervision to automatically disentangle this semantically meaningful subspace of tasks from the enormous space of nonsensical "chaff" tasks. We show that this learned subspace enables efficient exploration and provides a representation that captures distance between states. On a variety of challenging, vision-based continuous control problems, our approach leads to substantial performance gains, particularly as the complexity of the environment grows.

The Predictive Information is the mutual information between the past and the future, I(Xpast; Xfuture). We hypothesize that capturing the predictive information is useful in RL, since the ability to model what will happen next is necessary for success on many tasks. To test our hypothesis, we train Soft Actor-Critic (SAC) agents from pixels with an auxiliary task that learns a compressed representation of the predictive information of the RL environment dynamics using a contrastive version of the Conditional Entropy Bottleneck (CEB) objective. We refer to these as Predictive Information SAC (PI-SAC) agents. We show that PI-SAC agents can substantially improve sample efficiency over challenging baselines on tasks from the DM Control suite of continuous control environments. We evaluate PI-SAC agents by comparing against uncompressed PI-SAC agents, other compressed and uncompressed agents, and SAC agents directly trained from pixels. Our implementation is given on GitHub.

Routing games are amongst the most studied classes of games in game theory. Their most well-known property is that learning dynamics typically converge to equilibria implying approximately optimal performance (low Price of Anarchy). We perform a stress test for these classic results by studying the ubiquitous learning dynamics, Multiplicative Weights Update (MWU), in different classes of congestion games, uncovering intricate non-equilibrium phenomena. We study MWU using the actual game costs without applying cost normalization to $[0,1]$. Although this non-standard assumption leads to large regret, it captures realistic agents' behaviors. Namely, as the total demand increases, agents respond more aggressively to unbearably large costs. We start with the illustrative case of non-atomic routing games with two paths of linear cost, and show that every system has a carrying capacity, above which it becomes unstable. If the equilibrium flow is a symmetric $50-50\%$ split, the system exhibits one period-doubling bifurcation. Although the Price of Anarchy is equal to one, in the large population limit the time-average social cost for all but a zero measure set of initial conditions converges to its worst possible value. For asymmetric equilibrium flows, increasing the demand eventually forces the system into Li-Yorke chaos with positive topological entropy and periodic orbits of all possible periods. Remarkably, in all non-equilibrating regimes, the time-average flows on the paths converge {\it exactly} to the equilibrium flows, a property akin to no-regret learning in zero-sum games. We extend our results to games with arbitrarily many strategies, polynomial cost functions, non-atomic as well as atomic routing games, and heterogenous users.

Prevailing methods for graphs require abundant label and edge information for learning. When data for a new task are scarce, meta-learning can learn from prior experiences and form much-needed inductive biases for fast adaption to new tasks. Here, we introduce G-Meta, a novel meta-learning algorithm for graphs. G-Meta uses local subgraphs to transfer subgraph-specific information and learn transferable knowledge faster via meta gradients. G-Meta learns how to quickly adapt to a new task using only a handful of nodes or edges in the new task and does so by learning from data points in other graphs or related, albeit disjoint, label sets. G-Meta is theoretically justified as we show that the evidence for a prediction can be found in the local subgraph surrounding the target node or edge. Experiments on seven datasets and nine baseline methods show that G-Meta outperforms existing methods by up to 16.3%. Unlike previous methods, G-Meta successfully learns in challenging, few-shot learning settings that require generalization to completely new graphs and never-before-seen labels. Finally, G-Meta scales to large graphs, which we demonstrate on a new Tree-of-Life dataset comprising 1,840 graphs, a two-orders of magnitude increase in the number of graphs used in prior work.

Representation learning of graph-structured data is challenging because both graph structure and node features carry important information. Graph Neural Networks (GNNs) provide an expressive way to fuse information from network structure and node features. However, GNNs are prone to adversarial attacks. Here we introduce Graph Information Bottleneck (GIB), an information-theoretic principle that optimally balances expressiveness and robustness of the learned representation of graph-structured data. Inheriting from the general Information Bottleneck (IB), GIB aims to learn the minimal sufficient representation for a given task by maximizing the mutual information between the representation and the target, and simultaneously constraining the mutual information between the representation and the input data. Different from the general IB, GIB regularizes the structural as well as the feature information. We design two sampling algorithms for structural regularization and instantiate the GIB principle with two new models: GIB-Cat and GIB-Bern, and demonstrate the benefits by evaluating the resilience to adversarial attacks. We show that our proposed models are more robust than state-of-the-art graph defense models. GIB-based models empirically achieve up to 31% improvement with adversarial perturbation of the graph structure as well as node features.

Current graph neural networks (GNNs) lack generalizability with respect to scales (graph sizes, graph diameters, edge weights, etc..) when solving many graph analysis problems. Taking the perspective of synthesizing graph theory programs, we propose several extensions to address the issue. First, inspired by the dependency of iteration number of common graph theory algorithms on graph size, we learn to terminate the message passing process in GNNs adaptively according to the computation progress. Second, inspired by the fact that many graph theory algorithms are homogeneous with respect to graph weights, we introduce homogeneous transformation layers that are universal homogeneous function approximators, to convert ordinary GNNs to be homogeneous. Experimentally, we show that our GNN can be trained from small-scale graphs but generalize well to large-scale graphs for a number of basic graph theory problems. It also shows generalizability for applications of multi-body physical simulation and image-based navigation problems.

Given data, finding a faithful low-dimensional hyperbolic embedding of the data is a key method by which we can extract hierarchical information or learn representative geometric features of the data. In this paper, we explore a new method for learning hyperbolic representations by taking a metric-first approach. Rather than determining the low-dimensional hyperbolic embedding directly, we learn a tree structure on the data. This tree structure can then be used directly to extract hierarchical information, embedded into a hyperbolic manifold using Sarkar's construction \cite{sarkar}, or used as a tree approximation of the original metric. To this end, we present a novel fast algorithm \textsc{TreeRep} such that, given a $\delta$-hyperbolic metric (for any $\delta \geq 0$), the algorithm learns a tree structure that approximates the original metric. In the case when $\delta = 0$, we show analytically that \textsc{TreeRep} exactly recovers the original tree structure. We show empirically that \textsc{TreeRep} is not only many orders of magnitude faster than previously known algorithms, but also produces metrics with lower average distortion and higher mean average precision than most previous algorithms for learning hyperbolic embeddings, extracting hierarchical information, and approximating metrics via tree metrics.

Graph Neural Networks (GNN) are an emerging field for learning on non-Euclidean data. Recently, there has been increased interest in designing GNN that scales to large graphs. Most existing methods use "graph sampling" or "layer-wise sampling" techniques to reduce training time; However, these methods still suffer from degrading performance and scalability problems when applying to graphs with billions of edges. In this paper, we present GBP, a scalable GNN that utilizes a localized bidirectional propagation process from both the feature vector and the training/testing nodes. Theoretical analysis shows that GBP is the first method that achieves sub-linear time complexity for both the precomputation and the training phases. An extensive empirical study demonstrates that GBP achieves state-of-the-art performance with significantly less training/testing time. Most notably, GBP is able to deliver superior performance on a graph with over 60 million nodes and 1.8 billion edges in less than 2,000 seconds on a single machine.

Message passing neural network (MPNN) has recently emerged as a successful framework by achieving state-of-the-art performances on many graph-based learning tasks. MPNN has also recently been extended to multi-relational graphs (each edge is labelled), and hypergraphs (each edge can connect any number of vertices). However, in real-world datasets involving text and knowledge, relationships are much more complex in which hyperedges can be multi-relational, recursive, and ordered. Such structures present several unique challenges because it is not clear how to adapt MPNN to variable-sized hyperedges in them.
In this work, we first unify exisiting MPNNs on different structures into G-MPNN (Generalised MPNN) framework. Motivated by real-world datasets, we then propose a novel extension of the framework, MPNN-R (MPNN-Recursive) to handle recursively-structured data. Experimental results demonstrate the effectiveness of proposed G-MPNN and MPNN-R.

Graph neural networks (GNNs) have been successful in learning representations from graphs. Many popular GNNs follow the pattern of aggregate-transform: they aggregate the neighbors' attributes and then transform the results of aggregation with a learnable function. Analyses of these GNNs explain which pairs of non-identical graphs have different representations. However, we still lack an understanding of how similar these representations will be. We adopt kernel distance and propose transform-sum-cat as an alternative to aggregate-transform to reflect the continuous similarity between the node neighborhoods in the neighborhood aggregation. The idea leads to a simple and efficient graph similarity, which we name Weisfeiler-Leman similarity (WLS). In contrast to existing graph kernels, WLS is easy to implement with common deep learning frameworks. In graph classification experiments, transform-sum-cat significantly outperforms other neighborhood aggregation methods from popular GNN models. We also develop a simple and fast GNN model based on transform-sum-cat, which obtains, in comparison with widely used GNN models, (1) a higher accuracy in node classification, (2) a lower absolute error in graph regression, and (3) greater stability in adversarial training of graph generation.

Graph Neural Networks (GNNs) are widely used deep learning models that learn meaningful representations from graph-structured data. Due to the finite nature of the underlying recurrent structure, current GNN methods may struggle to capture long-range dependencies in underlying graphs. To overcome this difficulty, we propose a graph learning framework, called Implicit Graph Neural Networks (IGNN), where predictions are based on the solution of a fixed-point equilibrium equation involving implicitly defined "state" vectors. We use the Perron-Frobenius theory to derive sufficient conditions that ensure well-posedness of the framework. Leveraging implicit differentiation, we derive a tractable projected gradient descent method to train the framework. Experiments on a comprehensive range of tasks show that IGNNs consistently capture long-range dependencies and outperform state-of-the-art GNN models.

Graph neural networks have shown superior performance in a wide range of applications providing a powerful representation of graph-structured data. Recent works show that the representation can be further improved by auxiliary tasks. However, the auxiliary tasks for heterogeneous graphs, which contain rich semantic information with various types of nodes and edges, have less explored in the literature. In this paper, to learn graph neural networks on heterogeneous graphs we propose a novel self-supervised auxiliary learning method using meta paths, which are composite relations of multiple edge types. Our proposed method is learning to learn a primary task by predicting meta-paths as auxiliary tasks. This can be viewed as a type of meta-learning. The proposed method can identify an effective combination of auxiliary tasks and automatically balance them to improve the primary task. Our methods can be applied to any graph neural networks in a plug-in manner without manual labeling or additional data. The experiments demonstrate that the proposed method consistently improves the performance of link prediction and node classification on heterogeneous graphs.

Recent years have seen increasing use of supervised learning methods for segmentation tasks. However, the predictive performance of these algorithms depends on the quality of labels. This problem is particularly pertinent in the medical image domain, where both the annotation cost and inter-observer variability are high. In a typical label acquisition process, different human experts provide their estimates of the ``true'' segmentation labels under the influence of their own biases and competence levels. Treating these noisy labels blindly as the ground truth limits the performance that automatic segmentation algorithms can achieve. In this work, we present a method for jointly learning, from purely noisy observations alone, the reliability of individual annotators and the true segmentation label distributions, using two coupled CNNs. The separation of the two is achieved by encouraging the estimated annotators to be maximally unreliable while achieving high fidelity with the noisy training data. We first define a toy segmentation dataset based on MNIST and study the properties of the proposed algorithm. We then demonstrate the utility of the method on three public medical imaging segmentation datasets with simulated (when necessary) and real diverse annotations: 1) MSLSC (multiple-sclerosis lesions); 2) BraTS (brain tumours); 3) LIDC-IDRI (lung abnormalities). In all cases, our method outperforms competing methods and relevant baselines particularly in cases where the number of annotations is small and the amount of disagreement is large. The experiments also show strong ability to capture the complex spatial characteristics of annotators' mistakes. Our code is available at \url{https://github.com/moucheng2017/LearnNoisyLabelsMedicalImages}.

Graph neural networks (GNNs) have been attracting increasing popularity due to their simplicity and effectiveness in a variety of fields. However, a large number of labeled data is generally required to train these networks, which could be very expensive to obtain in some domains. In this paper, we study active learning for GNNs, i.e., how to efficiently label the nodes on a graph to reduce the annotation cost of training GNNs. We formulate the problem as a sequential decision process on graphs and train a GNN-based policy network with reinforcement learning to learn the optimal query strategy. By jointly training on several source graphs with full labels, we learn a transferable active learning policy which can directly generalize to unlabeled target graphs. Experimental results on multiple datasets from different domains prove the effectiveness of the learned policy in promoting active learning performance in both settings of transferring between graphs in the same domain and across different domains.

We present the Open Graph Benchmark (OGB), a diverse set of challenging and realistic benchmark datasets to facilitate scalable, robust, and reproducible graph machine learning (ML) research. OGB datasets are large-scale, encompass multiple important graph ML tasks, and cover a diverse range of domains, ranging from social and information networks to biological networks, molecular graphs, source code ASTs, and knowledge graphs. For each dataset, we provide a unified evaluation protocol using meaningful application-specific data splits and evaluation metrics. In addition to building the datasets, we also perform extensive benchmark experiments for each dataset. Our experiments suggest that OGB datasets present significant challenges of scalability to large-scale graphs and out-of-distribution generalization under realistic data splits, indicating fruitful opportunities for future research. Finally, OGB provides an automated end-to-end graph ML pipeline that simplifies and standardizes the process of graph data loading, experimental setup, and model evaluation. OGB will be regularly updated and welcomes inputs from the community. OGB datasets as well as data loaders, evaluation scripts, baseline code, and leaderboards are publicly available at https://ogb.stanford.edu .

Graphs have been widely adopted to denote structural connections between entities. The relations are in many cases heterogeneous, but entangled together and denoted merely as a single edge between a pair of nodes. For example, in a social network graph, users in different latent relationships like friends and colleagues, are usually connected via a bare edge that conceals such intrinsic connections. In this paper, we introduce a novel graph convolutional network (GCN), termed as factorizable graph convolutional network (FactorGCN), that explicitly disentangles such intertwined relations encoded in a graph. FactorGCN takes a simple graph as input, and disentangles it into several factorized graphs, each of which represents a latent and disentangled relation among nodes. The features of the nodes are then aggregated separately in each factorized latent space to produce disentangled features, which further leads to better performances for downstream tasks. We evaluate the proposed FactorGCN both qualitatively and quantitatively on the synthetic and real-world datasets, and demonstrate that it yields truly encouraging results in terms of both disentangling and feature aggregation. Code is publicly available at https://github.com/ihollywhy/FactorGCN.PyTorch.

This paper considers the setting of jointly matching and clustering multiple graphs belonging to different groups, which naturally rises in many realistic problems. Both graph matching and clustering are challenging (NP-hard) and a joint solution is appealing due to the natural connection of the two tasks. In this paper, we resort to a graduated assignment procedure for soft matching and clustering over iterations, whereby the two-way constraint and clustering confidence are modulated by two separate annealing parameters, respectively. Our technique can be further utilized for end-to-end learning whose loss refers to the cross-entropy between two lines of matching pipelines, as such the keypoint feature extraction CNNs can be learned without ground-truth supervision. Experimental results on real-world benchmarks show our method outperforms learning-free algorithms and performs comparatively against two-graph based supervised graph matching approaches. Source code is publicly available as a module of ThinkMatch (https://github.com/Thinklab-SJTU/ThinkCO/tree/main/ThinkMatch).

A key requirement for graph neural networks is that they must process a graph in a way that does not depend on how the graph is described. Traditionally this has been taken to mean that a graph network must be equivariant to node permutations. Here we show that instead of equivariance, the more general concept of naturality is sufficient for a graph network to be well-defined, opening up a larger class of graph networks. We define global and local natural graph networks, the latter of which are as scalable as conventional message passing graph neural networks while being more flexible. We give one practical instantiation of a natural network on graphs which uses an equivariant message network parameterization, yielding good performance on several benchmarks.

It is known that the current graph neural networks (GNNs) are difficult to make themselves deep due to the problem known as over-smoothing. Multi-scale GNNs are a promising approach for mitigating the over-smoothing problem. However, there is little explanation of why it works empirically from the viewpoint of learning theory. In this study, we derive the optimization and generalization guarantees of transductive learning algorithms that include multi-scale GNNs. Using the boosting theory, we prove the convergence of the training error under weak learning-type conditions. By combining it with generalization gap bounds in terms of transductive Rademacher complexity, we show that a test error bound of a specific type of multi-scale GNNs that decreases corresponding to the number of node aggregations under some conditions. Our results offer theoretical explanations for the effectiveness of the multi-scale structure against the over-smoothing problem. We apply boosting algorithms to the training of multi-scale GNNs for real-world node prediction tasks. We confirm that its performance is comparable to existing GNNs, and the practical behaviors are consistent with theoretical observations. Code is available at https://github.com/delta2323/GB-GNN.

Over the last decade, a single algorithm has changed many facets of our lives - Stochastic Gradient Descent (SGD). In the era of ever decreasing loss functions, SGD and its various offspring have become the go-to optimization tool in machine learning and are a key component of the success of deep neural networks (DNNs). While SGD is guaranteed to converge to a local optimum (under loose assumptions), in some cases it may matter which local optimum is found, and this is often context-dependent. Examples frequently arise in machine learning, from shape-versus-texture-features to ensemble methods and zero-shot coordination. In these settings, there are desired solutions which SGD on standard' loss functions will not find, since it instead converges to theeasy' solutions. In this paper, we present a different approach. Rather than following the gradient, which corresponds to a locally greedy direction, we instead follow the eigenvectors of the Hessian. By iteratively following and branching amongst the ridges, we effectively span the loss surface to find qualitatively different solutions. We show both theoretically and experimentally that our method, called Ridge Rider (RR), offers a promising direction for a variety of challenging problems.

We consider the problem of minimizing a functional over a parametric family of probability measures, where the parameterization is characterized via a push-forward structure. 
An important application of this problem is in training generative adversarial networks.  
In this regard, we propose a novel Sinkhorn Natural Gradient (SiNG) algorithm which acts as a steepest descent method on the probability space endowed with the Sinkhorn divergence.
We show that the Sinkhorn information matrix (SIM), a key component of SiNG, has an explicit expression and can be evaluated accurately in complexity that scales logarithmically with respect to the desired accuracy. This is in sharp contrast to  existing natural gradient methods that can only be carried out approximately.
Moreover, in practical applications when only Monte-Carlo type integration is available, we design an empirical estimator for SIM and provide the stability analysis.
In our experiments, we quantitatively compare SiNG with state-of-the-art SGD-type solvers on generative tasks to demonstrate its efficiency and efficacy of our method.

In this paper, we consider the problem of learning a sparse graph from the Laplacian constrained Gaussian graphical model. This problem can be formulated as a penalized maximum likelihood estimation of the precision matrix under Laplacian structural constraints. Like in the classical graphical lasso problem, recent works made use of the $\ell_1$-norm with the goal of promoting sparsity in the Laplacian constrained precision matrix estimation. However, through empirical evidence, we observe that the $\ell_1$-norm is not effective in imposing a sparse solution in this problem. From a theoretical perspective, we prove that a large regularization parameter will surprisingly lead to a solution representing a complete graph, i.e., every pair of vertices is connected by an edge. To address this issue, we propose a nonconvex penalized maximum likelihood estimation method, and establish the order of the statistical error. Numerical experiments involving synthetic and real-world data sets demonstrate the effectiveness of the proposed method. An open source $\mathsf{R}$ package is available at {\color{blue} \url{https://github.com/mirca/sparseGraph}}.

Given a sufficiently large amount of labeled data, the nonconvex low-rank matrix recovery problem contains no spurious local minima, so a local optimization algorithm is guaranteed to converge to a global minimum starting from any initial guess. However, the actual amount of data needed by this theoretical guarantee is very pessimistic, as it must prevent spurious local minima from existing anywhere, including at adversarial locations. In contrast, prior work based on good initial guesses have more realistic data requirements, because they allow spurious local minima to exist outside of a neighborhood of the solution. In this paper, we quantify the relationship between the quality of the initial guess and the corresponding reduction in data requirements. Using the restricted isometry constant as a surrogate for sample complexity, we compute a sharp “threshold” number of samples needed to prevent each specific point on the optimization landscape from becoming a spurious local minima. Optimizing the threshold over regions of the landscape, we see that, for initial points not too close to the ground truth, a linear improvement in the quality of the initial guess amounts to a constant factor improvement in the sample complexity.

We propose a new randomized algorithm for solving L2-regularized least-squares problems based on sketching. We consider two of the most popular random embeddings, namely, Gaussian embeddings and the Subsampled Randomized Hadamard Transform (SRHT). While current randomized solvers for least-squares optimization prescribe an embedding dimension at least greater than the data dimension, we show that the embedding dimension can be reduced to the effective dimension of the optimization problem, and still preserve high-probability convergence guarantees. In this regard, we derive sharp matrix deviation inequalities over ellipsoids for both Gaussian and SRHT embeddings. Specifically, we improve on the constant of a classical Gaussian concentration bound whereas, for SRHT embeddings, our deviation inequality involves a novel technical approach. Leveraging these bounds, we are able to design a practical and adaptive algorithm which does not require to know the effective dimension beforehand. Our method starts with an initial embedding dimension equal to 1 and, over iterations, increases the embedding dimension up to the effective one at most. Hence, our algorithm improves the state-of-the-art computational complexity for solving regularized least-squares problems. Further, we show numerically that it outperforms standard iterative solvers such as the conjugate gradient method and its pre-conditioned version on several standard machine learning datasets.

Linear programming (LP) is used in many machine learning applications, such as $\ell_1$-regularized SVMs, basis pursuit, nonnegative matrix factorization, etc. Interior Point Methods (IPMs) are one of the most popular methods to solve LPs both in theory and in practice. Their underlying complexity is dominated by the cost of solving a system of linear equations at each iteration. In this paper, we consider \emph{infeasible} IPMs for the special case where the number of variables is much larger than the number of constraints (i.e., wide), or vice-versa (i.e., tall) by taking the dual. Using tools from Randomized Linear Algebra, we present a preconditioning technique that, when combined with the Conjugate Gradient iterative solver, provably guarantees that infeasible IPM algorithms (suitably modified to account for the error incurred by the approximate solver), converge to a feasible, approximately optimal solution, without increasing their iteration complexity. Our empirical evaluations verify our theoretical results on both real and synthetic data.

In distributed second order optimization, a standard strategy is to average many local estimates, each of which is based on a small sketch or batch of the data. However, the local estimates on each machine are typically biased, relative to the full solution on all of the data, and this can limit the effectiveness of averaging. Here, we introduce a new technique for debiasing the local estimates, which leads to both theoretical and empirical improvements in the convergence rate of distributed second order methods. Our technique has two novel components: (1) modifying standard sketching techniques to obtain what we call a surrogate sketch; and (2) carefully scaling the global regularization parameter for local computations. Our surrogate sketches are based on determinantal point processes, a family of distributions for which the bias of an estimate of the inverse Hessian can be computed exactly. Based on this computation, we show that when the objective being minimized is $l_2$-regularized with parameter $\lambda$ and individual machines are each given a sketch of size $m$, then to eliminate the bias, local estimates should be computed using a shrunk regularization parameter given by $\lambda^\prime=\lambda(1-\frac{d_\lambda}{m})$, where $d_\lambda$ is the $\lambda$-effective dimension of the Hessian (or, for quadratic problems, the data matrix).

We study the question of obtaining last-iterate convergence rates for no-regret learning algorithms in multi-player games. We show that the optimistic gradient (OG) algorithm with a constant step-size, which is no-regret, achieves a last-iterate rate of O(1/√T) with respect to the gap function in smooth monotone games. This result addresses a question of Mertikopoulos & Zhou (2018), who asked whether extra-gradient approaches (such as OG) can be applied to achieve improved guarantees in the multi-agent learning setting. The proof of our upper bound uses a new technique centered around an adaptive choice of potential function at each iteration. We also show that the O(1/√T) rate is tight for all p-SCLI algorithms, which includes OG as a special case. As a byproduct of our lower bound analysis we additionally present a proof of a conjecture of Arjevani et al. (2015) which is more direct than previous approaches.

This paper studies how to design abstractions of large-scale combinatorial optimization problems that can leverage existing state-of-the-art solvers in general-purpose ways, and that are amenable to data-driven design. The goal is to arrive at new approaches that can reliably outperform existing solvers in wall-clock time. We focus on solving integer programs and ground our approach in the large neighborhood search (LNS) paradigm, which iteratively chooses a subset of variables to optimize while leaving the remainder fixed. The appeal of LNS is that it can easily use any existing solver as a subroutine, and thus can inherit the benefits of carefully engineered heuristic approaches and their software implementations. We also show that one can learn a good neighborhood selector from training data. Through an extensive empirical validation, we demonstrate that our LNS framework can significantly outperform, in wall-clock time, compared to state-of-the-art commercial solvers such as Gurobi.

In this paper, we consider the problem of computing the barycenter of a set of probability distributions under the Sinkhorn divergence. This problem has recently found applications across various domains, including graphics, learning, and vision, as it provides a meaningful mechanism to aggregate knowledge. Unlike previous approaches which directly operate in the space of probability measures, we recast the Sinkhorn barycenter problem as an instance of unconstrained functional optimization and develop a novel functional gradient descent method named \texttt{Sinkhorn Descent} (\texttt{SD}). We prove that \texttt{SD} converges to a stationary point at a sublinear rate, and under reasonable assumptions, we further show that it asymptotically finds a global minimizer of the Sinkhorn barycenter problem. Moreover, by providing a mean-field analysis, we show that \texttt{SD} preserves the {weak convergence} of empirical measures. Importantly, the computational complexity of \texttt{SD} scales linearly in the dimension $d$ and we demonstrate its scalability by solving a $100$-dimensional Sinkhorn barycenter problem.

Gradient clipping is commonly used in training deep neural networks partly due to its practicability in relieving the exploding gradient problem. Recently, \citet{zhang2019gradient} show that clipped (stochastic) Gradient Descent (GD) converges faster than vanilla GD via introducing a new assumption called $(L_0, L_1)$-smoothness, which characterizes the violent fluctuation of gradients typically encountered in deep neural networks. However, their iteration complexities on the problem-dependent parameters are rather pessimistic, and theoretical justification of clipping combined with other crucial techniques, e.g. momentum acceleration, are still lacking. In this paper, we bridge the gap by presenting a general framework to study the clipping algorithms, which also takes momentum methods into consideration.We provide convergence analysis of the framework in both deterministic and stochastic setting, and demonstrate the tightness of our results by comparing them with existing lower bounds. Our results imply that the efficiency of clipping methods will not degenerate even in highly non-smooth regions of the landscape. Experiments confirm the superiority of clipping-based methods in deep learning tasks.

We analyze continuous-time mirror descent applied to sparse phase retrieval, which is the problem of recovering sparse signals from a set of magnitude-only measurements. We apply mirror descent to the unconstrained empirical risk minimization problem (batch setting), using the square loss and square measurements. We provide a full convergence analysis of the algorithm in this non-convex setting and prove that, with the hypentropy mirror map, mirror descent recovers any $k$-sparse vector $\mathbf{x}^\star\in\mathbb{R}^n$ with minimum (in modulus) non-zero entry on the order of $\| \mathbf{x}^\star \|_2/\sqrt{k}$ from $k^2$ Gaussian measurements, modulo logarithmic terms. This yields a simple algorithm which, unlike most existing approaches to sparse phase retrieval, adapts to the sparsity level, without including thresholding steps or adding regularization terms. Our results also provide a principled theoretical understanding for Hadamard Wirtinger flow [54], as Euclidean gradient descent applied to the empirical risk problem with Hadamard parametrization can be recovered as a first-order approximation to mirror descent in discrete time.

We propose Federated Accelerated Stochastic Gradient Descent (FedAc), a principled acceleration of Federated Averaging (FedAvg, also known as Local SGD) for distributed optimization. FedAc is the first provable acceleration of FedAvg that improves convergence speed and communication efficiency on various types of convex functions. For example, for strongly convex and smooth functions, when using M workers, the previous state-of-the-art FedAvg analysis can achieve a linear speedup in M if given M rounds of synchronization, whereas FedAc only requires M^⅓ rounds. Moreover, we prove stronger guarantees for FedAc when the objectives are third-order smooth. Our technique is based on a potential-based perturbed iterate analysis, a novel stability analysis of generalized accelerated SGD, and a strategic tradeoff between acceleration and stability.

Most popular optimizers for deep learning can be broadly categorized as adaptive methods (e.g.~Adam) and accelerated schemes (e.g.~stochastic gradient descent (SGD) with momentum). For many models such as convolutional neural networks (CNNs), adaptive methods typically converge faster but generalize worse compared to SGD; for complex settings such as generative adversarial networks (GANs), adaptive methods are typically the default because of their stability. We propose AdaBelief to simultaneously achieve three goals: fast convergence as in adaptive methods, good generalization as in SGD, and training stability. The intuition for AdaBelief is to adapt the stepsize according to the "belief" in the current gradient direction. Viewing the exponential moving average (EMA) of the noisy gradient as the prediction of the gradient at the next time step, if the observed gradient greatly deviates from the prediction, we distrust the current observation and take a small step; if the observed gradient is close to the prediction, we trust it and take a large step. We validate AdaBelief in extensive experiments, showing that it outperforms other methods with fast convergence and high accuracy on image classification and language modeling. Specifically, on ImageNet, AdaBelief achieves comparable accuracy to SGD. Furthermore, in the training of a GAN on Cifar10, AdaBelief demonstrates high stability and improves the quality of generated samples compared to a well-tuned Adam optimizer. Code is available athttps://github.com/juntang-zhuang/Adabelief-Optimizer

We study without-replacement SGD for solving finite-sum optimization problems. Specifically, depending on how the indices of the finite-sum are shuffled, we consider the RandomShuffle (shuffle at the beginning of each epoch) and SingleShuffle (shuffle only once) algorithms. First, we establish minimax optimal convergence rates of these algorithms up to poly-log factors. Notably, our analysis is general enough to cover gradient dominated nonconvex costs, and does not rely on the convexity of individual component functions unlike existing optimal convergence results. Secondly, assuming convexity of the individual components, we further sharpen the tight convergence results for RandomShuffle by removing the drawbacks common to all prior arts: large number of epochs required for the results to hold, and extra poly-log factor gaps to the lower bound.

Understanding the behavior of no-regret dynamics in general N-player games is a fundamental question in online learning and game theory. A folk result in the field states that, in finite games, the empirical frequency of play under no-regret learning converges to the game’s set of coarse correlated equilibria. By contrast, our understanding of how the day-to-day behavior of the dynamics correlates to the game’s Nash equilibria is much more limited, and only partial results are known for certain classes of games (such as zero-sum or congestion games). In this paper, we study the dynamics of follow the regularized leader (FTRL), arguably the most well-studied class of no-regret dynamics, and we establish a sweeping negative result showing that the notion of mixed Nash equilibrium is antithetical to no-regret learning. Specifically, we show that any Nash equilibrium which is not strict (in that every player has a unique best response) cannot be stable and attracting under the dynamics of FTRL. This result has significant implications for predicting the outcome of a learning process as it shows unequivocally that only strict (and hence, pure) Nash equilibria can emerge as stable limit points thereof.

Leverage score sampling is a powerful technique that originates from theoretical computer science, which can be used to speed up a large number of fundamental questions, e.g. linear regression, linear programming, semi-definite programming, cutting plane method, graph sparsification, maximum matching and max-flow. Recently, it has been shown that leverage score sampling helps to accelerate kernel methods [Avron, Kapralov, Musco, Musco, Velingker and Zandieh 17]. In this work, we generalize the results in [Avron, Kapralov, Musco, Musco, Velingker and Zandieh 17] to a broader class of kernels. We further bring the leverage score sampling into the field of deep learning theory. 1. We show the connection between the initialization for neural network training and approximating the neural tangent kernel with random features. 2. We prove the equivalence between regularized neural network and neural tangent kernel ridge regression under the initialization of both classical random Gaussian and leverage score sampling.

Despite tremendous success in many application scenarios, deep learning faces serious intellectual property (IP) infringement threats. Considering the cost of designing and training a good model, infringements will significantly infringe the interests of the original model owner. Recently, many impressive works have emerged for deep model IP protection. However, they either are vulnerable to ambiguity attacks, or require changes in the target network structure by replacing its original normalization layers and hence cause significant performance drops. To this end, we propose a new passport-aware normalization formulation, which is generally applicable to most existing normalization layers and only needs to add another passport-aware branch for IP protection. This new branch is jointly trained with the target model but discarded in the inference stage. Therefore it causes no structure change in the target model. Only when the model IP is suspected to be stolen by someone, the private passport-aware branch is added back for ownership verification. Through extensive experiments, we verify its effectiveness in both image and 3D point recognition models. It is demonstrated to be robust not only to common attack techniques like fine-tuning and model compression, but also to ambiguity attacks. By further combining it with trigger-set based methods, both black-box and white-box verification can be achieved for enhanced security of deep learning models deployed in real systems.

To obtain excellent deep neural architectures, a series of techniques are carefully designed in EfficientNets. The giant formula for simultaneously enlarging the resolution, depth and width provides us a Rubik's cube for neural networks. So that we can find networks with high efficiency and excellent performance by twisting the three dimensions. This paper aims to explore the twisting rules for obtaining deep neural networks with minimum model sizes and computational costs. Different from the network enlarging, we observe that resolution and depth are more important than width for tiny networks. Therefore, the original method, \ie the compound scaling in EfficientNet is no longer suitable. To this end, we summarize a tiny formula for downsizing neural architectures through a series of smaller models derived from the EfficientNet-B0 with the FLOPs constraint. Experimental results on the ImageNet benchmark illustrate that our TinyNet performs much better than the smaller version of EfficientNets using the inversed giant formula. For instance, our TinyNet-E achieves a 59.9\% Top-1 accuracy with only 24M FLOPs, which is about 1.9\% higher than that of the previous best MobileNetV3 with similar computational cost. Code will be available at {\small\url{https://github.com/huawei-noah/ghostnet/tree/master/tinynetpytorch}}, and {\small\url{https://gitee.com/mindspore/mindspore/tree/master/modelzoo/research/cv/tinynet}}.

Previous literature offers limited clues on how to learn a periodic function using modern neural networks. We start with a study of the extrapolation properties of neural networks; we prove and demonstrate experimentally that the standard activations functions, such as ReLU, tanh, sigmoid, along with their variants, all fail to learn to extrapolate simple periodic functions. We hypothesize that this is due to their lack of a ``periodic" inductive bias. As a fix of this problem, we propose a new activation, namely, $x + \sin^2(x)$, which achieves the desired periodic inductive bias to learn a periodic function while maintaining a favorable optimization property of the $\relu$-based activations. Experimentally, we apply the proposed method to temperature and financial data prediction.

We perform a careful, thorough, and large scale empirical study of the correspondence between wide neural networks and kernel methods. By doing so, we resolve a variety of open questions related to the study of infinitely wide neural networks. Our experimental results include: kernel methods outperform fully-connected finite-width networks, but underperform convolutional finite width networks; neural network Gaussian process (NNGP) kernels frequently outperform neural tangent (NT) kernels; centered and ensembled finite networks have reduced posterior variance and behave more similarly to infinite networks; weight decay and the use of a large learning rate break the correspondence between finite and infinite networks; the NTK parameterization outperforms the standard parameterization for finite width networks; diagonal regularization of kernels acts similarly to early stopping; floating point precision limits kernel performance beyond a critical dataset size; regularized ZCA whitening improves accuracy; finite network performance depends non-monotonically on width in ways not captured by double descent phenomena; equivariance of CNNs is only beneficial for narrow networks far from the kernel regime. Our experiments additionally motivate an improved layer-wise scaling for weight decay which improves generalization in finite-width networks. Finally, we develop improved best practices for using NNGP and NT kernels for prediction, including a novel ensembling technique. Using these best practices we achieve state-of-the-art results on CIFAR-10 classification for kernels corresponding to each architecture class we consider.

Natural Gradient Descent (NGD) helps to accelerate the convergence of gradient descent dynamics, but it requires approximations in large-scale deep neural networks because of its high computational cost. Empirical studies have confirmed that some NGD methods with approximate Fisher information converge sufficiently fast in practice. Nevertheless, it remains unclear from the theoretical perspective why and under what conditions such heuristic approximations work well. In this work, we reveal that, under specific conditions, NGD with approximate Fisher information achieves the same fast convergence to global minima as exact NGD. We consider deep neural networks in the infinite-width limit, and analyze the asymptotic training dynamics of NGD in function space via the neural tangent kernel. In the function space, the training dynamics with the approximate Fisher information are identical to those with the exact Fisher information, and they converge quickly. The fast convergence holds in layer-wise approximations; for instance, in block diagonal approximation where each block corresponds to a layer as well as in block tri-diagonal and K-FAC approximations. We also find that a unit-wise approximation achieves the same fast convergence under some assumptions. All of these different approximations have an isotropic gradient in the function space, and this plays a fundamental role in achieving the same convergence properties in training. Thus, the current study gives a novel and unified theoretical foundation with which to understand NGD methods in deep learning.

Modern neural network performance typically improves as model size increases. A recent line of research on the Neural Tangent Kernel (NTK) of over-parameterized networks indicates that the improvement with size increase is a product of a better conditioned loss landscape. In this work, we investigate a form of over-parameterization achieved through ensembling, where we define collegial ensembles (CE) as the aggregation of multiple independent models with identical architectures, trained as a single model. We show that the optimization dynamics of CE simplify dramatically when the number of models in the ensemble is large, resembling the dynamics of wide models, yet scale much more favorably. We use recent theoretical results on the finite width corrections of the NTK to perform efficient architecture search in a space of finite width CE that aims to either minimize capacity, or maximize trainability under a set of constraints. The resulting ensembles can be efficiently implemented in practical architectures using group convolutions and block diagonal layers. Finally, we show how our framework can be used to analytically derive optimal group convolution modules originally found using expensive grid searches, without having to train a single model.

Recently, Transformer-based language models have demonstrated remarkable performance across many NLP domains. However, the unsupervised pre-training step of these models suffers from unbearable overall computational expenses. Current methods for accelerating the pre-training either rely on massive parallelism with advanced hardware or are not applicable to language models.

In this work, we propose a method based on progressive layer dropping that speeds the training of Transformer-based language models, not at the cost of excessive hardware resources but from model architecture change and training technique boosted efficiency. Extensive experiments on BERT show that the proposed method achieves a 25% reduction of computation cost in FLOPS and a 24% reduction in the end-to-end wall-clock training time. Furthermore, we show that our pre-trained models are equipped with strong knowledge transferability, achieving similar or even higher accuracy in downstream tasks to baseline models.

We introduce a simple (one line of code) modification to the Generative Adversarial Network (GAN) training algorithm that materially improves results with no increase in computational cost. When updating the generator parameters, we simply zero out the gradient contributions from the elements of the batch that the critic scores as least realistic'. Through experiments on many different GAN variants, we show that thistop-k update' procedure is a generally applicable improvement. In order to understand the nature of the improvement, we conduct extensive analysis on a simple mixture-of-Gaussians dataset and discover several interesting phenomena. Among these is that, when gradient updates are computed using the worst-scoring batch elements, samples can actually be pushed further away from the their nearest mode. We also apply our method to state-of-the-art GAN models including BigGAN and improve state-of-the-art FID for conditional generation on CIFAR-10 from 9.21 to 8.57.

It is not clear yet why ADAM-alike adaptive gradient algorithms suffer from worse generalization performance than SGD despite their faster training speed. This work aims to provide understandings on this generalization gap by analyzing their local convergence behaviors. Specifically, we observe the heavy tails of gradient noise in these algorithms. This motivates us to analyze these algorithms through their Levy-driven stochastic differential equations (SDEs) because of the similar convergence behaviors of an algorithm and its SDE. Then we establish the escaping time of these SDEs from a local basin. The result shows that (1) the escaping time of both SGD and ADAM~depends on the Radon measure of the basin positively and the heaviness of gradient noise negatively; (2) for the same basin, SGD enjoys smaller escaping time than ADAM, mainly because (a) the geometry adaptation in ADAM~via adaptively scaling each gradient coordinate well diminishes the anisotropic structure in gradient noise and results in larger Radon measure of a basin; (b) the exponential gradient average in ADAM~smooths its gradient and leads to lighter gradient noise tails than SGD. So SGD is more locally unstable than ADAM~at sharp minima defined as the minima whose local basins have small Radon measure, and can better escape from them to flatter ones with larger Radon measure. As flat minima here which often refer to the minima at flat or asymmetric basins/valleys often generalize better than sharp ones~\cite{keskar2016large,he2019asymmetric}, our result explains the better generalization performance of SGD over ADAM. Finally, experimental results confirm our heavy-tailed gradient noise assumption and theoretical affirmation.

A recent breakthrough in deep learning theory shows that the training of over-parameterized deep neural networks can be characterized by a kernel function called \textit{neural tangent kernel} (NTK). However, it is known that this type of results does not perfectly match the practice, as NTK-based analysis requires the network weights to stay very close to their initialization throughout training, and cannot handle regularizers or gradient noises. In this paper, we provide a generalized neural tangent kernel analysis and show that noisy gradient descent with weight decay can still exhibit a ``kernel-like'' behavior. This implies that the training loss converges linearly up to a certain accuracy. We also establish a novel generalization error bound for two-layer neural networks trained by noisy gradient descent with weight decay.

Hyperparameter optimization of neural networks can be elegantly formulated as a bilevel optimization problem. While research on bilevel optimization of neural networks has been dominated by implicit differentiation and unrolling, hypernetworks such as Self-Tuning Networks (STNs) have recently gained traction due to their ability to amortize the optimization of the inner objective. In this paper, we diagnose several subtle pathologies in the training of STNs. Based on these observations, we propose the Delta-STN, an improved hypernetwork architecture which stabilizes training and optimizes hyperparameters much more efficiently than STNs. The key idea is to focus on accurately approximating the best-response Jacobian rather than the full best-response function; we achieve this by reparameterizing the hypernetwork and linearizing the network around the current parameters. We demonstrate empirically that our Delta-STN can tune regularization hyperparameters (e.g. weight decay, dropout, number of cutout holes) with higher accuracy, faster convergence, and improved stability compared to existing approaches.

Modern neural networks have the capacity to overfit noisy labels frequently found in real-world datasets. Although great progress has been made, existing techniques are limited in providing theoretical guarantees for the performance of the neural networks trained with noisy labels. Here we propose a novel approach with strong theoretical guarantees for robust training of deep networks trained with noisy labels. The key idea behind our method is to select weighted subsets (coresets) of clean data points that provide an approximately low-rank Jacobian matrix. We then prove that gradient descent applied to the subsets do not overfit the noisy labels. Our extensive experiments corroborate our theory and demonstrate that deep networks trained on our subsets achieve a significantly superior performance compared to state-of-the art, e.g., 6% increase in accuracy on CIFAR-10 with 80% noisy labels, and 7% increase in accuracy on mini Webvision.

Feature attribution methods, which explain an individual prediction made by a model as a sum of attributions for each input feature, are an essential tool for understanding the behavior of complex deep learning models. However, ensuring that models produce meaningful explanations, rather than ones that rely on noise, is not straightforward. Exacerbating this problem is the fact that attribution methods do not provide insight as to why features are assigned their attribution values, leading to explanations that are difficult to interpret. In real-world problems we often have sets of additional information for each feature that are predictive of that feature's importance to the task at hand. Here, we propose the deep attribution prior (DAPr) framework to exploit such information to overcome the limitations of attribution methods. Our framework jointly learns a relationship between prior information and feature importance, as well as biases models to have explanations that rely on features predicted to be important. We find that our framework both results in networks that generalize better to out of sample data and admits new methods for interpreting model behavior.

We introduce a method called TracIn that computes the influence of a training example on a prediction made by the model. The idea is to trace how the loss on the test point changes during the training process whenever the training example of interest was utilized. We provide a scalable implementation of TracIn via: (a) a first-order gradient approximation to the exact computation, (b) saved checkpoints of standard training procedures, and (c) cherry-picking layers of a deep neural network. In contrast with previously proposed methods, TracIn is simple to implement; all it needs is the ability to work with gradients, checkpoints, and loss functions. The method is general. It applies to any machine learning model trained using stochastic gradient descent or a variant of it, agnostic of architecture, domain and task. We expect the method to be widely useful within processes that study and improve training data.

In this paper, we show that under over-parametrization several standard stochastic optimization algorithms escape saddle-points and converge to local-minimizers much faster. One of the fundamental aspects of over-parametrized models is that they are capable of interpolating the training data. We show that, under interpolation-like assumptions satisfied by the stochastic gradients in an over-parametrization setting, the first-order oracle complexity of Perturbed Stochastic Gradient Descent (PSGD) algorithm to reach an $\epsilon$-local-minimizer, matches the corresponding deterministic rate of $O(1/\epsilon^{2})$. We next analyze Stochastic Cubic-Regularized Newton (SCRN) algorithm under interpolation-like conditions, and show that the oracle complexity to reach an $\epsilon$-local-minimizer under interpolation-like conditions, is $O(1/\epsilon^{2.5})$. While this obtained complexity is better than the corresponding complexity of either PSGD, or SCRN without interpolation-like assumptions, it does not match the rate of $O(1/\epsilon^{1.5})$ corresponding to deterministic Cubic-Regularized Newton method. It seems further Hessian-based interpolation-like assumptions are necessary to bridge this gap. We also discuss the corresponding improved complexities in the zeroth-order settings.

Data augmentation has been actively studied for robust neural networks. Most of the recent data augmentation methods focus on augmenting datasets during the training phase. At the testing phase, simple transformations are still widely used for test-time augmentation. This paper proposes a novel instance-level test- time augmentation that efficiently selects suitable transformations for a test input. Our proposed method involves an auxiliary module to predict the loss of each possible transformation given the input. Then, the transformations having lower predicted losses are applied to the input. The network obtains the results by averaging the prediction results of augmented inputs. Experimental results on several image classification benchmarks show that the proposed instance-aware test- time augmentation improves the model’s robustness against various corruptions.

Many recent breakthroughs in deep learning were achieved by training increasingly larger models on massive datasets. However, training such models can be prohibitively expensive. For instance, the cluster used to train GPT-3 costs over $250 million. As a result, most researchers cannot afford to train state of the art models and contribute to their development. Hypothetically, a researcher could crowdsource the training of large neural networks with thousands of regular PCs provided by volunteers. The raw computing power of a hundred thousand $2500 desktops dwarfs that of a $250M server pod, but one cannot utilize that power efficiently with conventional distributed training methods. In this work, we propose Learning@home: a novel neural network training paradigm designed to handle large amounts of poorly connected participants. We analyze the performance, reliability, and architectural constraints of this paradigm and compare it against existing distributed training techniques.

The strong correlation between neurons or filters can significantly weaken the generalization ability of neural networks. Inspired by the well-known Tammes problem, we propose a novel diversity regularization method to address this issue, which makes the normalized weight vectors of neurons or filters distributed on a hypersphere as uniformly as possible, through maximizing the minimal pairwise angles (MMA). This method can easily exert its effect by plugging the MMA regularization term into the loss function with negligible computational overhead. The MMA regularization is simple, efficient, and effective. Therefore, it can be used as a basic regularization method in neural network training. Extensive experiments demonstrate that MMA regularization is able to enhance the generalization ability of various modern models and achieves considerable performance improvements on CIFAR100 and TinyImageNet datasets. In addition, experiments on face verification show that MMA regularization is also effective for feature learning. Code is available at: https://github.com/wznpub/MMA_Regularization.

Triplet loss with batch hard mining (TriHard loss) is an important variation of triplet loss inspired by the idea that hard triplets improve the performance of metric leaning networks. However, there is a dilemma in the training process. The hard negative samples contain various quite similar characteristics compared with anchors and positive samples in a batch. Features of these characteristics should be clustered between anchors and positive samples while are also utilized to repel between anchors and hard negative samples. It is harmful for learning mutual features within classes. Several methods to alleviate the dilemma are designed and tested. In the meanwhile, an element-weighted TriHard loss is emphatically proposed to enlarge the distance between partial elements of feature vectors selectively which represent the different characteristics between anchors and hard negative samples. Extensive evaluations are conducted on Market1501 and MSMT17 datasets and the results achieve state-of-the-art on public baselines.

Normalization operations are widely used to train deep neural networks, and they can improve both convergence and generalization in most tasks. The theories for normalization's effectiveness and new forms of normalization have always been hot topics in research. To better understand normalization, one question can be whether normalization is indispensable for training deep neural network? In this paper, we study what would happen when normalization layers are removed from the network, and show how to train deep neural networks without normalization layers and without performance degradation. Our proposed method can achieve the same or even slightly better performance in a variety of tasks: image classification in ImageNet, object detection and segmentation in MS-COCO, video classification in Kinetics, and machine translation in WMT English-German, etc. Our study may help better understand the role of normalization layers and can be a competitive alternative to normalization layers. Codes are available.

This paper proposes a reliable neural network pruning algorithm by setting up a scientific control. Existing pruning methods have developed various hypotheses to approximate the importance of filters to the network and then execute filter pruning accordingly. To increase the reliability of the results, we prefer to have a more rigorous research design by including a scientific control group as an essential part to minimize the effect of all factors except the association between the filter and expected network output. Acting as a control group, knockoff feature is generated to mimic the feature map produced by the network filter, but they are conditionally independent of the example label given the real feature map. We theoretically suggest that the knockoff condition can be approximately preserved given the information propagation of network layers. Besides the real feature map on an intermediate layer, the corresponding knockoff feature is brought in as another auxiliary input signal for the subsequent layers. Redundant filters can be discovered in the adversarial process of different features. Through experiments, we demonstrate the superiority of the proposed algorithm over state-of-the-art methods. For example, our method can reduce 57.8% parameters and 60.2% FLOPs of ResNet-101 with only 0.01% top-1 accuracy loss on ImageNet. The code is available at https://github.com/huawei-noah/Pruning/tree/master/SCOP_NeurIPS2020.

What makes untrained deep neural networks (DNNs) different from the trained performant ones? By zooming into the weights in well-trained DNNs, we found that it is the location of weights that holds most of the information encoded by the training. Motivated by this observation, we hypothesized that weights in DNNs trained using stochastic gradient-based methods can be separated into two dimensions: the location of weights, and their exact values. To assess our hypothesis, we propose a novel method called lookahead permutation (LaPerm) to train DNNs by reconnecting the weights. We empirically demonstrate LaPerm's versatility while producing extensive evidence to support our hypothesis: when the initial weights are random and dense, our method demonstrates speed and performance similar to or better than that of regular optimizers, e.g., Adam. When the initial weights are random and sparse (many zeros), our method changes the way neurons connect, achieving accuracy comparable to that of a well-trained dense network. When the initial weights share a single value, our method finds a weight agnostic neural network with far-better-than-chance accuracy.

Deep metric learning has attracted much attention in recent years, due to seamlessly combining the distance metric learning and deep neural network. Many endeavors are devoted to design different pair-based angular loss functions, which decouple the magnitude and direction information for embedding vectors and ensure the training and testing measure consistency. However, these traditional angular losses cannot guarantee that all the sample embeddings are on the surface of the same hypersphere during the training stage, which would result in unstable gradient in batch optimization and may influence the quick convergence of the embedding learning. In this paper, we first investigate the effect of the embedding norm for deep metric learning with angular distance, and then propose a spherical embedding constraint (SEC) to regularize the distribution of the norms. SEC adaptively adjusts the embeddings to fall on the same hypersphere and performs more balanced direction update. Extensive experiments on deep metric learning, face recognition, and contrastive self-supervised learning show that the SEC-based angular space learning strategy significantly improves the performance of the state-of-the-art.

Adder Neural Networks (ANNs) which only contain additions bring us a new way of developing deep neural networks with low energy consumption. Unfortunately, there is an accuracy drop when replacing all convolution filters by adder filters. The main reason here is the optimization difficulty of ANNs using $\ell_1$-norm, in which the estimation of gradient in back propagation is inaccurate. In this paper, we present a novel method for further improving the performance of ANNs without increasing the trainable parameters via a progressive kernel based knowledge distillation (PKKD) method. A convolutional neural network (CNN) with the same architecture is simultaneously initialized and trained as a teacher network, features and weights of ANN and CNN will be transformed to a new space to eliminate the accuracy drop. The similarity is conducted in a higher-dimensional space to disentangle the difference of their distributions using a kernel based method. Finally, the desired ANN is learned based on the information from both the ground-truth and teacher, progressively. The effectiveness of the proposed method for learning ANN with higher performance is then well-verified on several benchmarks. For instance, the ANN-50 trained using the proposed PKKD method obtains a 76.8\% top-1 accuracy on ImageNet dataset, which is 0.6\% higher than that of the ResNet-50.

Sparse neural networks are becoming increasingly important as the field seeks to improve the performance of existing models by scaling them up, while simultaneously trying to reduce power consumption and computational footprint. Unfortunately, most existing methods for inducing performant sparse models still entail the instantiation of dense parameters, or dense gradients in the backward-pass, during training. For very large models this requirement can be prohibitive. In this work we propose Top-KAST, a method that preserves constant sparsity throughout training (in both the forward and backward-passes). We demonstrate the efficacy of our approach by showing that it performs comparably to or better than previous works when training models on the established ImageNet benchmark, whilst fully maintaining sparsity. In addition to our ImageNet results, we also demonstrate our approach in the domain of language modeling where the current best performing architectures tend to have tens of billions of parameters and scaling up does not yet seem to have saturated performance. Sparse versions of these architectures can be run with significantly fewer resources, making them more widely accessible and applicable. Furthermore, in addition to being effective, our approach is straightforward and can easily be implemented in a wide range of existing machine learning frameworks with only a few additional lines of code. We therefore hope that our contribution will help enable the broader community to explore the potential held by massive models, without incurring massive computational cost.

Feature distillation, a primary method in knowledge distillation, always leads to significant accuracy improvements. Most existing methods distill features in the teacher network through a manually designed transformation. In this paper, we propose a novel distillation method named task-oriented feature distillation (TOFD) where the transformation is convolutional layers that are trained in a data-driven manner by task loss. As a result, the task-oriented information in the features can be captured and distilled to students. Moreover, an orthogonal loss is applied to the feature resizing layer in TOFD to improve the performance of knowledge distillation. Experiments show that TOFD outperforms other distillation methods by a large margin on both image classification and 3D classification tasks. Codes have been released in Github.

Binary Neural Network (BNN) shows its predominance in reducing the complexity of deep neural networks. However, it suffers severe performance degradation. One of the major impediments is the large quantization error between the full-precision weight vector and its binary vector. Previous works focus on compensating for the norm gap while leaving the angular bias hardly touched. In this paper, for the first time, we explore the influence of angular bias on the quantization error and then introduce a Rotated Binary Neural Network (RBNN), which considers the angle alignment between the full-precision weight vector and its binarized version. At the beginning of each training epoch, we propose to rotate the full-precision weight vector to its binary vector to reduce the angular bias. To avoid the high complexity of learning a large rotation matrix, we further introduce a bi-rotation formulation that learns two smaller rotation matrices. In the training stage, we devise an adjustable rotated weight vector for binarization to escape the potential local optimum. Our rotation leads to around 50% weight flips which maximize the information gain. Finally, we propose a training-aware approximation of the sign function for the gradient backward. Experiments on CIFAR-10 and ImageNet demonstrate the superiorities of RBNN over many state-of-the-arts. Our source code, experimental settings, training logs and binary models are available at https://github.com/lmbxmu/RBNN.

Distilling knowledge from an ensemble of teacher models is expected to have a more promising performance than that from a single one. Current methods mainly adopt a vanilla average rule, i.e., to simply take the average of all teacher losses for training the student network. However, this approach treats teachers equally and ignores the diversity among them. When conflicts or competitions exist among teachers, which is common, the inner compromise might hurt the distillation performance. In this paper, we examine the diversity of teacher models in the gradient space and regard the ensemble knowledge distillation as a multi-objective optimization problem so that we can determine a better optimization direction for the training of student network. Besides, we also introduce a tolerance parameter to accommodate disagreement among teachers. In this way, our method can be seen as a dynamic weighting method for each teacher in the ensemble. Extensive experiments validate the effectiveness of our method for both logits-based and feature-based cases.

Neural network training is computationally and memory intensive. Sparse training can reduce the burden on emerging hardware platforms designed to accelerate sparse computations, but it can also affect network convergence. In this work, we propose a novel CNN training algorithm called Sparse Weight Activation Training (SWAT). SWAT is more computation and memory-efficient than conventional training. SWAT modifies back-propagation based on the empirical insight that convergence during training tends to be robust to the elimination of (i) small magnitude weights during the forward pass and (ii) both small magnitude weights and activations during the backward pass. We evaluate SWAT on recent CNN architectures such as ResNet, VGG, DenseNet and WideResNet using CIFAR-10, CIFAR-100 and ImageNet datasets. For ResNet-50 on ImageNet SWAT reduces total floating-point operations (FLOPs) during training by 80% resulting in a 3.3x training speedup when run on a simulated sparse learning accelerator representative of emerging platforms while incurring only 1.63% reduction in validation accuracy. Moreover, SWAT reduces memory footprint during the backward pass by 23% to 50% for activations and 50% to 90% for weights. Code is available at https://github.com/AamirRaihan/SWAT.

Recurrent neural networks are the foundation of many sequence-to-sequence models in machine learning, such as machine translation and speech synthesis. With applied quantum computing in its infancy, there already exist quantum machine learning models such as variational quantum eigensolvers which have been used e.g. in the context of energy minimization tasks. Yet, to date, no viable recurrent quantum network has been proposed.

In this work we construct the first quantum recurrent neural network (QRNN) with demonstrable performance on non-trivial tasks such as sequence learning and integer digit classification. The QRNN cell is built from parametrized quantum neurons, which, in conjunction with amplitude amplification, creates a nonlinear activation of polynomials of its inputs and hidden state, and allows the extraction of a probability distribution over predicted classes at each step.

To study the model's performance, we provide an implementation in pytorch, which allows the relatively efficient optimization of parametrized quantum circuits with tens of thousands of parameters, and which demonstrates that model does not appear to suffer from the vanishing gradient problem that plagues many exting quantum classifiers and classical RNNs. We establish a QRNN training setup by benchmarking optimization hyperparameters, and analyse suitable network topologies for simple memorisation and sequence prediction tasks from Elman's seminal paper (1990).  We then proceed to evaluate the QRNN on MNIST classification, by feeding the QRNN each image pixel-by-pixel; with a network utilizing only 12 qubits we reach a test set accuracy over 98\% when discriminating between the digits `0' and `1'.

Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep learning algorithms are lacking of theoretical supports. On the other hand, another line of works have proposed theoretical frameworks that are computationally infeasible. In this paper, we train sparse deep neural networks with a fully Bayesian treatment under spike-and-slab priors, and develop a set of computationally efficient variational inferences via continuous relaxation of Bernoulli distribution. The variational posterior contraction rate is provided, which justifies the consistency of the proposed variational Bayes method. Interestingly, our empirical results demonstrate that this variational procedure provides uncertainty quantification in terms of Bayesian predictive distribution and is also capable to accomplish consistent variable selection by training a sparse multi-layer neural network.