Convolutional Neural Networks (CNNs) have proved exceptional at learning representations for visual object categorization. However, CNNs do not explicitly encode objects, parts, and their physical properties, which has limited CNNs' success on tasks that require structured understanding of visual scenes. To overcome these limitations, we introduce the idea of ``Physical Scene Graphs'' (PSGs), which represent scenes as hierarchical graphs, with nodes in the hierarchy corresponding intuitively to object parts at different scales, and edges to physical connections between parts. Bound to each node is a vector of latent attributes that intuitively represent object properties such as surface shape and texture. We also describe PSGNet, a network architecture that learns to extract PSGs by reconstructing scenes through a PSG-structured bottleneck. PSGNet augments standard CNNs by including: recurrent feedback connections to combine low and high-level image information; graph pooling and vectorization operations that convert spatially-uniform feature maps into object-centric graph structures; and perceptual grouping principles to encourage the identification of meaningful scene elements. We show that PSGNet outperforms alternative self-supervised scene representation algorithms at scene segmentation tasks, especially on complex real-world images, and generalizes well to unseen object types and scene arrangements. PSGNet is also able learn from physical motion, enhancing scene estimates even for static images. We present a series of ablation studies illustrating the importance of each component of the PSGNet architecture, analyses showing that learned latent attributes capture intuitive scene properties, and illustrate the use of PSGs for compositional scene inference.

Variational mutual information (MI) estimators are widely used in unsupervised representation learning methods such as contrastive predictive coding (CPC). A lower bound on MI can be obtained from a multi-class classification problem, where a critic attempts to distinguish a positive sample drawn from the underlying joint distribution from (m-1) negative samples drawn from a suitable proposal distribution. Using this approach, MI estimates are bounded above by \log m, and could thus severely underestimate unless m is very large. To overcome this limitation, we introduce a novel estimator based on a multi-label classification problem, where the critic needs to jointly identify \emph{multiple} positive samples at the same time. We show that using the same amount of negative samples, multi-label CPC is able to exceed the \log m bound, while still being a valid lower bound of mutual information. We demonstrate that the proposed approach is able to lead to better mutual information estimation, gain empirical improvements in unsupervised representation learning, and beat the current state-of-the-art in knowledge distillation over 10 out of 13 tasks.

While using invariant and equivariant maps, it is possible to apply deep learning to a range of primitive data structures, a formalism for dealing with hierarchy is lacking. This is a significant issue because many practical structures are hierarchies of simple building blocks; some examples include sequences of sets, graphs of graphs, or multiresolution images. Observing that the symmetry of a hierarchical structure is the ``wreath product'' of symmetries of the building blocks, we express the equivariant map for the hierarchy using an intuitive combination of the equivariant linear layers of the building blocks. More generally, we show that any equivariant map for the hierarchy has this form. To demonstrate the effectiveness of this approach to model design, we consider its application in the semantic segmentation of point-cloud data. By voxelizing the point cloud, we impose a hierarchy of translation and permutation symmetries on the data and report state-of-the-art on {semantic3d}, {s3dis}, and {vkitti}, that include some of the largest real-world point-cloud benchmarks.

Alon et al. [2019] and Bun et al. [2020] recently showed that online learnability and private PAC learnability are equivalent in binary classification. We investigate whether this equivalence extends to multi-class classification and regression. First, we show that private learnability implies online learnability in both settings. Our extension involves studying a novel variant of the Littlestone dimension that depends on a tolerance parameter and on an appropriate generalization of the concept of threshold functions beyond binary classification. Second, we show that while online learnability continues to imply private learnability in multi-class classification, current proof techniques encounter significant hurdles in the regression setting. While the equivalence for regression remains open, we provide non-trivial sufficient conditions for an online learnable class to also be privately learnable.

We propose a framework that lifts the capabilities of graph convolutional networks (GCNs) to scenarios where no input graph is given and increases their robustness to adversarial attacks. We formulate a joint probabilistic model that considers a prior distribution over graphs along with a GCN-based likelihood and develop a stochastic variational inference algorithm to estimate the graph posterior and the GCN parameters jointly. To address the problem of propagating gradients through latent variables drawn from discrete distributions, we use their continuous relaxations known as Concrete distributions. We show that, on real datasets, our approach can outperform state-of-the-art Bayesian and non-Bayesian graph neural network algorithms on the task of semi-supervised classification in the absence of graph data and when the network structure is subjected to adversarial perturbations.

This paper explores useful modifications of the recent development in contrastive learning via novel probabilistic modeling. We derive a particular form of contrastive loss named Joint Contrastive Learning (JCL). JCL implicitly involves the simultaneous learning of an infinite number of query-key pairs, which poses tighter constraints when searching for invariant features. We derive an upper bound on this formulation that allows analytical solutions in an end-to-end training manner. While JCL is practically effective in numerous computer vision applications, we also theoretically unveil the certain mechanisms that govern the behavior of JCL. We demonstrate that the proposed formulation harbors an innate agency that strongly favors similarity within each instance-specific class, and therefore remains advantageous when searching for discriminative features among distinct instances. We evaluate these proposals on multiple benchmarks, demonstrating considerable improvements over existing algorithms. Code is publicly available at: https://github.com/caiqi/Joint-Contrastive-Learning.

Since its inception, the neural estimation of mutual information (MI) has demonstrated the empirical success of modeling expected dependency between high-dimensional random variables. However, MI is an aggregate statistic and cannot be used to measure point-wise dependency between different events. In this work, instead of estimating the expected dependency, we focus on estimating point-wise dependency (PD), which quantitatively measures how likely two outcomes co-occur. We show that we can naturally obtain PD when we are optimizing MI neural variational bounds. However, optimizing these bounds is challenging due to its large variance in practice. To address this issue, we develop two methods (free of optimizing MI variational bounds): Probabilistic Classifier and Density-Ratio Fitting. We demonstrate the effectiveness of our approaches in 1) MI estimation, 2) self-supervised representation learning, and 3) cross-modal retrieval task.

The rapid evolution of Graph Neural Networks (GNNs) has led to a growing number of new architectures as well as novel applications. However, current research focuses on proposing and evaluating specific architectural designs of GNNs, such as GCN, GIN, or GAT, as opposed to studying the more general design space of GNNs that consists of a Cartesian product of different design dimensions, such as the number of layers or the type of the aggregation function. Additionally, GNN designs are often specialized to a single task, yet few efforts have been made to understand how to quickly find the best GNN design for a novel task or a novel dataset. Here we define and systematically study the architectural design space for GNNs which consists of 315,000 different designs over 32 different predictive tasks. Our approach features three key innovations: (1) A general GNN design space; (2) a GNN task space with a similarity metric, so that for a given novel task/dataset, we can quickly identify/transfer the best performing architecture; (3) an efficient and effective design space evaluation method which allows insights to be distilled from a huge number of model-task combinations. Our key results include: (1) A comprehensive set of guidelines for designing well-performing GNNs; (2) while best GNN designs for different tasks vary significantly, the GNN task space allows for transferring the best designs across different tasks; (3) models discovered using our design space achieve state-of-the-art performance. Overall, our work offers a principled and scalable approach to transition from studying individual GNN designs for specific tasks, to systematically studying the GNN design space and the task space. Finally, we release GraphGym, a powerful platform for exploring different GNN designs and tasks. GraphGym features modularized GNN implementation, standardized GNN evaluation, and reproducible and scalable experiment management.

A prominent technique for self-supervised representation learning has been to contrast semantically similar and dissimilar pairs of samples. Without access to labels, dissimilar (negative) points are typically taken to be randomly sampled datapoints, implicitly accepting that these points may, in reality, actually have the same label. Perhaps unsurprisingly, we observe that sampling negative examples from truly different labels improves performance, in a synthetic setting where labels are available. Motivated by this observation, we develop a debiased contrastive objective that corrects for the sampling of same-label datapoints, even without knowledge of the true labels. Empirically, the proposed objective consistently outperforms the state-of-the-art for representation learning in vision, language, and reinforcement learning benchmarks. Theoretically, we establish generalization bounds for the downstream classification task.

Does a Variational AutoEncoder (VAE) consistently encode typical samples generated from its decoder? This paper shows that the perhaps surprising answer to this question is `No'; a (nominally trained) VAE does not necessarily amortize inference for typical samples that it is capable of generating. We study the implications of this behaviour on the learned representations and also the consequences of fixing it by introducing a notion of self consistency. Our approach hinges on an alternative construction of the variational approximation distribution to the true posterior of an extended VAE model with a Markov chain alternating between the encoder and the decoder. The method can be used to train a VAE model from scratch or given an already trained VAE, it can be run as a post processing step in an entirely self supervised way without access to the original training data. Our experimental analysis reveals that encoders trained with our self-consistency approach lead to representations that are robust (insensitive) to perturbations in the input introduced by adversarial attacks. We provide experimental results on the ColorMnist and CelebA benchmark datasets that quantify the properties of the learned representations and compare the approach with a baseline that is specifically trained for the desired property.

Unsupervised learning methods based on contrastive learning have drawn increasing attention and achieved promising results. Most of them aim to learn representations invariant to instance-level variations, which are provided by different views of the same instance. In this paper, we propose Invariance Propagation to focus on learning representations invariant to category-level variations, which are provided by different instances from the same category. Our method recursively discovers semantically consistent samples residing in the same high-density regions in representation space. We demonstrate a hard sampling strategy to concentrate on maximizing the agreement between the anchor sample and its hard positive samples, which provide more intra-class variations to help capture more abstract invariance. As a result, with a ResNet-50 as the backbone, our method achieves 71.3% top-1 accuracy on ImageNet linear classification and 78.2% top-5 accuracy fine-tuning on only 1% labels, surpassing previous results. We also achieve state-of-the-art performance on other downstream tasks, including linear classification on Places205 and Pascal VOC, and transfer learning on small scale datasets.