Designing expressive Graph Neural Networks (GNNs) is a central topic in learning graph-structured data. While numerous approaches have been proposed to improve GNNs with respect to the Weisfeiler-Lehman (WL) test, for most of them, there is still a lack of deep understanding of what additional power they can systematically and provably gain. In this paper, we take a fundamentally different perspective to study the expressive power of GNNs beyond the WL test. Specifically, we introduce a novel class of expressivity metrics via graph biconnectivity and highlight their importance in both theory and practice. As biconnectivity can be easily calculated using simple algorithms that have linear computational costs, it is natural to expect that popular GNNs can learn it easily as well. However, after a thorough review of prior GNN architectures, we surprisingly find that most of them are not expressive for any of these metrics. The only exception is the ESAN framework (Bevilacqua et al., 2022), for which we give a theoretical justification of its power. We proceed to introduce a principled and more efficient approach, called the Generalized Distance Weisfeiler-Lehman (GD-WL), which is provably expressive for all biconnectivity metrics. Practically, we show GD-WL can be implemented by a Transformer-like …

Animal navigation research posits that organisms build and maintain internal spa- tial representations, or maps, of their environment. We ask if machines – specifically, artificial intelligence (AI) navigation agents – also build implicit (or ‘mental’) maps. A positive answer to this question would (a) explain the surprising phenomenon in recent literature of ostensibly map-free neural-networks achieving strong performance, and (b) strengthen the evidence of mapping as a fundamental mechanism for navigation by intelligent embodied agents, whether they be biological or artificial. Unlike animal navigation, we can judiciously design the agent’s perceptual system and control the learning paradigm to nullify alternative navigation mechanisms. Specifically, we train ‘blind’ agents – with sensing limited to only egomotion and no other sensing of any kind – to perform PointGoal navigation (‘go to $\Delta$x, $\Delta$y’) via reinforcement learning. Our agents are composed of navigation-agnostic components (fully-connected and recurrent neural networks), and our experimental setup provides no inductive bias towards mapping. Despite these harsh conditions, we find that blind agents are (1) surprisingly effective navigators in new environments (∼95% success); (2) they utilize memory over long horizons (remembering ∼1,000 steps of past experience in an episode); (3) this memory enables them to exhibit intelligent behavior (following …

Dense prediction tasks are a fundamental class of problems in computer vision. As supervised methods suffer from high pixel-wise labeling cost, a few-shot learning solution that can learn any dense task from a few labeled images is desired. Yet, current few-shot learning methods target a restricted set of tasks such as semantic segmentation, presumably due to challenges in designing a general and unified model that is able to flexibly and efficiently adapt to arbitrary tasks of unseen semantics. We propose Visual Token Matching (VTM), a universal few-shot learner for arbitrary dense prediction tasks. It employs non-parametric matching on patch-level embedded tokens of images and labels that encapsulates all tasks. Also, VTM flexibly adapts to any task with a tiny amount of task-specific parameters that modulate the matching algorithm. We implement VTM as a powerful hierarchical encoder-decoder architecture involving ViT backbones where token matching is performed at multiple feature hierarchies. We experiment VTM on a challenging variant of Taskonomy dataset and observe that it robustly few-shot learns various unseen dense prediction tasks. Surprisingly, it is competitive with fully supervised baselines using only 10 labeled examples of novel tasks ($0.004\%$ of full supervision) and sometimes outperforms using $0.1\%$ of full supervision. Codes …

Animal navigation research posits that organisms build and maintain internal spa- tial representations, or maps, of their environment. We ask if machines – specifically, artificial intelligence (AI) navigation agents – also build implicit (or ‘mental’) maps. A positive answer to this question would (a) explain the surprising phenomenon in recent literature of ostensibly map-free neural-networks achieving strong performance, and (b) strengthen the evidence of mapping as a fundamental mechanism for navigation by intelligent embodied agents, whether they be biological or artificial. Unlike animal navigation, we can judiciously design the agent’s perceptual system and control the learning paradigm to nullify alternative navigation mechanisms. Specifically, we train ‘blind’ agents – with sensing limited to only egomotion and no other sensing of any kind – to perform PointGoal navigation (‘go to $\Delta$x, $\Delta$y’) via reinforcement learning. Our agents are composed of navigation-agnostic components (fully-connected and recurrent neural networks), and our experimental setup provides no inductive bias towards mapping. Despite these harsh conditions, we find that blind agents are (1) surprisingly effective navigators in new environments (∼95% success); (2) they utilize memory over long horizons (remembering ∼1,000 steps of past experience in an episode); (3) this memory enables them to exhibit intelligent behavior (following …

Designing expressive Graph Neural Networks (GNNs) is a central topic in learning graph-structured data. While numerous approaches have been proposed to improve GNNs with respect to the Weisfeiler-Lehman (WL) test, for most of them, there is still a lack of deep understanding of what additional power they can systematically and provably gain. In this paper, we take a fundamentally different perspective to study the expressive power of GNNs beyond the WL test. Specifically, we introduce a novel class of expressivity metrics via graph biconnectivity and highlight their importance in both theory and practice. As biconnectivity can be easily calculated using simple algorithms that have linear computational costs, it is natural to expect that popular GNNs can learn it easily as well. However, after a thorough review of prior GNN architectures, we surprisingly find that most of them are not expressive for any of these metrics. The only exception is the ESAN framework (Bevilacqua et al., 2022), for which we give a theoretical justification of its power. We proceed to introduce a principled and more efficient approach, called the Generalized Distance Weisfeiler-Lehman (GD-WL), which is provably expressive for all biconnectivity metrics. Practically, we show GD-WL can be implemented by a Transformer-like …

Dense prediction tasks are a fundamental class of problems in computer vision. As supervised methods suffer from high pixel-wise labeling cost, a few-shot learning solution that can learn any dense task from a few labeled images is desired. Yet, current few-shot learning methods target a restricted set of tasks such as semantic segmentation, presumably due to challenges in designing a general and unified model that is able to flexibly and efficiently adapt to arbitrary tasks of unseen semantics. We propose Visual Token Matching (VTM), a universal few-shot learner for arbitrary dense prediction tasks. It employs non-parametric matching on patch-level embedded tokens of images and labels that encapsulates all tasks. Also, VTM flexibly adapts to any task with a tiny amount of task-specific parameters that modulate the matching algorithm. We implement VTM as a powerful hierarchical encoder-decoder architecture involving ViT backbones where token matching is performed at multiple feature hierarchies. We experiment VTM on a challenging variant of Taskonomy dataset and observe that it robustly few-shot learns various unseen dense prediction tasks. Surprisingly, it is competitive with fully supervised baselines using only 10 labeled examples of novel tasks ($0.004\%$ of full supervision) and sometimes outperforms using $0.1\%$ of full supervision. Codes …

Recent breakthroughs in text-to-image synthesis have been driven by diffusion models trained on billions of image-text pairs. Adapting this approach to 3D synthesis would require large-scale datasets of labeled 3D or multiview data and efficient architectures for denoising 3D data, neither of which currently exist. In this work, we circumvent these limitations by using a pretrained 2D text-to-image diffusion model to perform text-to-3D synthesis. We introduce a loss based on probability density distillation that enables the use of a 2D diffusion model as a prior for optimization of a parametric image generator. Using this loss in a DeepDream-like procedure, we optimize a randomly-initialized 3D model (a Neural Radiance Field, or NeRF) via gradient descent such that its 2D renderings from random angles achieve a low loss. The resulting 3D model of the given text can be viewed from any angle, relit by arbitrary illumination, or composited into any 3D environment. Our approach requires no 3D training data and no modifications to the image diffusion model, demonstrating the effectiveness of pretrained image diffusion models as priors.

Antibody design is valuable for therapeutic usage and biological research. Existing deep-learning-based methods encounter several key issues: 1) incomplete context for Complementarity-Determining Regions (CDRs) generation; 2) incapability of capturing the entire 3D geometry of the input structure; 3) inefficient prediction of the CDR sequences in an autoregressive manner. In this paper, we propose Multi-channel Equivariant Attention Network (MEAN) to co-design 1D sequences and 3D structures of CDRs. To be specific, MEAN formulates antibody design as a conditional graph translation problem by importing extra components including the target antigen and the light chain of the antibody. Then, MEAN resorts to E(3)-equivariant message passing along with a proposed attention mechanism to better capture the geometrical correlation between different components. Finally, it outputs both the 1D sequences and 3D structure via a multi-round progressive full-shot scheme, which enjoys more efficiency and precision against previous autoregressive approaches. Our method significantly surpasses state-of-the-art models in sequence and structure modeling, antigen-binding CDR design, and binding affinity optimization. Specifically, the relative improvement to baselines is about 23\% in antigen-binding CDR design and 34\% for affinity optimization.

Recent approaches in self-supervised learning of image representations can be categorized into different families of methods and, in particular, can be divided into contrastive and non-contrastive approaches. While differences between the two families have been thoroughly discussed to motivate new approaches, we focus more on the theoretical similarities between them. By designing contrastive and covariance based non-contrastive criteria that can be related algebraically and shown to be equivalent under limited assumptions, we show how close those families can be. We further study popular methods and introduce variations of them, allowing us to relate this theoretical result to current practices and show the influence (or lack thereof) of design choices on downstream performance. Motivated by our equivalence result, we investigate the low performance of SimCLR and show how it can match VICReg's with careful hyperparameter tuning, improving significantly over known baselines. We also challenge the popular assumption that non-contrastive methods need large output dimensions. Our theoretical and quantitative results suggest that the numerical gaps between contrastive and non-contrastive methods in certain regimes can be closed given better network design choices and hyperparameter tuning. The evidence shows that unifying different SOTA methods is an important direction to build a better understanding of …

Neurons in the brain are often finely tuned for specific task variables. Moreover, such disentangled representations are highly sought after in machine learning. Here we mathematically prove that simple biological constraints on neurons, namely nonnegativity and energy efficiency in both activity and weights, promote such sought after disentangled representations by enforcing neurons to become selective for single factors of task variation. We demonstrate these constraints lead to disentanglement in a variety of tasks and architectures, including variational autoencoders. We also use this theory to explain why the brain partitions its cells into distinct cell types such as grid and object-vector cells, and also explain when the brain instead entangles representations in response to entangled task factors. Overall, this work provides a mathematical understanding of why single neurons in the brain often represent single human-interpretable factors, and steps towards an understanding task structure shapes the structure of brain representation.

Antibody design is valuable for therapeutic usage and biological research. Existing deep-learning-based methods encounter several key issues: 1) incomplete context for Complementarity-Determining Regions (CDRs) generation; 2) incapability of capturing the entire 3D geometry of the input structure; 3) inefficient prediction of the CDR sequences in an autoregressive manner. In this paper, we propose Multi-channel Equivariant Attention Network (MEAN) to co-design 1D sequences and 3D structures of CDRs. To be specific, MEAN formulates antibody design as a conditional graph translation problem by importing extra components including the target antigen and the light chain of the antibody. Then, MEAN resorts to E(3)-equivariant message passing along with a proposed attention mechanism to better capture the geometrical correlation between different components. Finally, it outputs both the 1D sequences and 3D structure via a multi-round progressive full-shot scheme, which enjoys more efficiency and precision against previous autoregressive approaches. Our method significantly surpasses state-of-the-art models in sequence and structure modeling, antigen-binding CDR design, and binding affinity optimization. Specifically, the relative improvement to baselines is about 23\% in antigen-binding CDR design and 34\% for affinity optimization.

No-press Diplomacy is a complex strategy game involving both cooperation and competition that has served as a benchmark for multi-agent AI research. While self-play reinforcement learning has resulted in numerous successes in purely adversarial games like chess, Go, and poker, self-play alone is insufficient for achieving optimal performance in domains involving cooperation with humans. We address this shortcoming by first introducing a planning algorithm we call DiL-piKL that regularizes a reward-maximizing policy toward a human imitation-learned policy. We prove that this is a no-regret learning algorithm under a modified utility function. We then show that DiL-piKL can be extended into a self-play reinforcement learning algorithm we call RL-DiL-piKL that provides a model of human play while simultaneously training an agent that responds well to this human model. We used RL-DiL-piKL to train an agent we name Diplodocus.In a 200-game no-press Diplomacy tournament involving 62 human participants spanning skill levels from beginner to expert, two Diplodocus agents both achieved a higher average score than all other participants who played more than two games, and ranked first and third according to an Elo ratings model.

We formally study how \emph{ensemble} of deep learning models can improve test accuracy, and how the superior performance of ensemble can be distilled into a single model using \emph{knowledge distillation}. We consider the challenging case where the ensemble is simply an average of the outputs of a few independently trained neural networks with the \emph{same} architecture, trained using the \emph{same} algorithm on the \emph{same} data set, and they only differ by the random seeds used in the initialization.We show that ensemble/knowledge distillation in \emph{deep learning} works very differently from traditional learning theory (such as boosting or NTKs). We develop a theory showing that when data has a structure we refer to as multi-view'', then ensemble of independently trained neural networks can provably improve test accuracy, and such superior test accuracy can also be provably distilled into a single model. Our result sheds light on how ensemble works in deep learning in a way that is completely different from traditional theorems, and how thedark knowledge'' is hidden in the outputs of the ensemble and can be used in distillation.

Neurons in the brain are often finely tuned for specific task variables. Moreover, such disentangled representations are highly sought after in machine learning. Here we mathematically prove that simple biological constraints on neurons, namely nonnegativity and energy efficiency in both activity and weights, promote such sought after disentangled representations by enforcing neurons to become selective for single factors of task variation. We demonstrate these constraints lead to disentanglement in a variety of tasks and architectures, including variational autoencoders. We also use this theory to explain why the brain partitions its cells into distinct cell types such as grid and object-vector cells, and also explain when the brain instead entangles representations in response to entangled task factors. Overall, this work provides a mathematical understanding of why single neurons in the brain often represent single human-interpretable factors, and steps towards an understanding task structure shapes the structure of brain representation.

We formally study how \emph{ensemble} of deep learning models can improve test accuracy, and how the superior performance of ensemble can be distilled into a single model using \emph{knowledge distillation}. We consider the challenging case where the ensemble is simply an average of the outputs of a few independently trained neural networks with the \emph{same} architecture, trained using the \emph{same} algorithm on the \emph{same} data set, and they only differ by the random seeds used in the initialization.We show that ensemble/knowledge distillation in \emph{deep learning} works very differently from traditional learning theory (such as boosting or NTKs). We develop a theory showing that when data has a structure we refer to as multi-view'', then ensemble of independently trained neural networks can provably improve test accuracy, and such superior test accuracy can also be provably distilled into a single model. Our result sheds light on how ensemble works in deep learning in a way that is completely different from traditional theorems, and how thedark knowledge'' is hidden in the outputs of the ensemble and can be used in distillation.

Recent approaches in self-supervised learning of image representations can be categorized into different families of methods and, in particular, can be divided into contrastive and non-contrastive approaches. While differences between the two families have been thoroughly discussed to motivate new approaches, we focus more on the theoretical similarities between them. By designing contrastive and covariance based non-contrastive criteria that can be related algebraically and shown to be equivalent under limited assumptions, we show how close those families can be. We further study popular methods and introduce variations of them, allowing us to relate this theoretical result to current practices and show the influence (or lack thereof) of design choices on downstream performance. Motivated by our equivalence result, we investigate the low performance of SimCLR and show how it can match VICReg's with careful hyperparameter tuning, improving significantly over known baselines. We also challenge the popular assumption that non-contrastive methods need large output dimensions. Our theoretical and quantitative results suggest that the numerical gaps between contrastive and non-contrastive methods in certain regimes can be closed given better network design choices and hyperparameter tuning. The evidence shows that unifying different SOTA methods is an important direction to build a better understanding of …