ICML 2023 论文列表

Graph Neural Networks (GNNs) had been demonstrated to be inherently susceptible to the problems of over-smoothing and over-squashing. These issues prohibit the ability of GNNs to model complex graph interactions by limiting their effectiveness in taking into account distant information. Our study reveals the key connection between the local graph geometry and the occurrence of both of these issues, thereby providing a unified framework for studying them at a local scale using the Ollivier-Ricci curvature. Specifically, we demonstrate that over-smoothing is linked to positive graph curvature while over-squashing is linked to negative graph curvature. Based on our theory, we propose the Batch Ollivier-Ricci Flow, a novel rewiring algorithm capable of simultaneously addressing both over-smoothing and over-squashing.

Self-supervised learning (SSL) has emerged as a powerful framework to learn representations from raw data without supervision. Yet in practice, engineers face issues such as instability in tuning optimizers and collapse of representations during training. Such challenges motivate the need for a theory to shed light on the complex interplay between the choice of data augmentation, network architecture, and training algorithm. % on the resulting performance in downstream tasks. We study such an interplay with a precise analysis of generalization performance on both pretraining and downstream tasks in kernel regimes, and highlight several insights for SSL practitioners that arise from our theory.

Mean-field theory is widely used in theoretical studies of neural networks. In this paper, we analyze the role of depth in the concentration of mean-field predictions for Gram matrices of hidden representations in deep multilayer perceptron (MLP) with batch normalization (BN) at initialization. It is postulated that the mean-field predictions suffer from layer-wise errors that amplify with depth. We demonstrate that BN avoids this error amplification with depth. When the chain of hidden representations is rapidly mixing, we establish a concentration bound for a mean-field model of Gram matrices. To our knowledge, this is the first concentration bound that does not become vacuous with depth for standard MLPs with a finite width.

Generative Flow Networks or GFlowNets are related to Monte-Carlo Markov chain methods (as they sample from a distribution specified by an energy function), reinforcement learning (as they learn a policy to sample composed objects through a sequence of steps), generative models (as they learn to represent and sample from a distribution) and amortized variational methods (as they can be used to learn to approximate and sample from an otherwise intractable posterior, given a prior and a likelihood). They are trained to generate an object $x$ through a sequence of steps with probability proportional to some reward function $R(x)$ (or $\exp(-\mathcal{E}(x))$ with $\mathcal{E}(x)$ denoting the energy function), given at the end of the generative trajectory. Like for other RL settings where the reward is only given at the end, the efficiency of training and credit assignment may suffer when those trajectories are longer. With previous GFlowNet work, no learning was possible from incomplete trajectories (lacking a terminal state and the computation of the associated reward). In this paper, we consider the case where the energy function can be applied not just to terminal states but also to intermediate states. This is for example achieved when the energy function is additive, with terms available along the trajectory. We show how to reparameterize the GFlowNet state flow function to take advantage of the partial reward already accrued at each state. This enables a training objective that can be applied to update parameters even with incomplete trajectories. Even when complete trajectories are available, being able to obtain more localized credit and gradients is found to speed up training convergence, as demonstrated across many simulations.

Minimax-fair machine learning minimizes the error for the worst-off group. However, empirical evidence suggests that when sophisticated models are trained with standard empirical risk minimization (ERM), they often have the same performance on the worst-off group as a minimax-trained model. Our work makes this counter-intuitive observation concrete. We prove that if the hypothesis class is sufficiently expressive and the group information is recoverable from the features, ERM and minimax-fairness learning formulations indeed have the same performance on the worst-off group. We provide additional empirical evidence of how this observation holds on a wide range of datasets and hypothesis classes. Since ERM is fundamentally easier than minimax optimization, our findings have implications on the practice of fair machine learning.

Understanding the impact of exploration on the behaviour of multi-agent learning has, so far, benefited from the restriction to potential, or network zero-sum games in which convergence to an equilibrium can be shown. Outside of these classes, learning dynamics rarely converge and little is known about the effect of exploration in the face of non-convergence. To progress this front, we study the smooth Q- Learning dynamics. We show that, in any network game, exploration by agents results in the convergence of Q-Learning to a neighbourhood of an equilibrium. This holds independently of whether the dynamics reach the equilibrium or display complex behaviours. We show that increasing the exploration rate decreases the size of this neighbourhood and also decreases the ability of all agents to improve their payoffs. Furthermore, in a broad class of games, the payoff performance of Q-Learning dynamics, measured by Social Welfare, decreases when the exploration rate increases. Our experiments show this to be a general phenomenon, namely that exploration leads to improved convergence of Q-Learning, at the cost of payoff performance.

As the issue of robustness in AI systems becomes vital, statistical learning techniques that are reliable even in presence of partly contaminated data have to be developed. Preference data, in the form of (complete) rankings in the simplest situations, are no exception and the demand for appropriate concepts and tools is all the more pressing given that technologies fed by or producing this type of data ($\textit{e.g.}$ search engines, recommending systems) are now massively deployed. However, the lack of vector space structure for the set of rankings ($\textit{i.e.}$ the symmetric group $\mathfrak{S}_n$) and the complex nature of statistics considered in ranking data analysis make the formulation of robustness objectives in this domain challenging. In this paper, we introduce notions of robustness, together with dedicated statistical methods, for $\textit{Consensus Ranking}$ the flagship problem in ranking data analysis, aiming at summarizing a probability distribution on $\mathfrak{S}_n$ by a $\textit{median}$ ranking. Precisely, we propose specific extensions of the popular concept of *breakdown point*, tailored to consensus ranking, and address the related computational issues. Beyond the theoretical contributions, the relevance of the approach proposed is supported by an experimental study.

Generalization in Reinforcement Learning (RL) aims to train an agent during training that generalizes to the target environment. In this work, we first point out that RL generalization is fundamentally different from the generalization in supervised learning, and fine-tuning on the target environment is necessary for good test performance. Therefore, we seek to answer the following question: how much can we expect pre-training over training environments to be helpful for efficient and effective fine-tuning? On one hand, we give a surprising result showing that asymptotically, the improvement from pre-training is at most a constant factor. On the other hand, we show that pre-training can be indeed helpful in the non-asymptotic regime by designing a policy collection-elimination (PCE) algorithm and proving a distribution-dependent regret bound that is independent of the state-action space. We hope our theoretical results can provide insight towards understanding pre-training and generalization in RL.

Understanding how the dynamics in biological and artificial neural networks implement the computations required for a task is a salient open question in machine learning and neuroscience. In particular, computations requiring complex memory storage and retrieval pose a significant challenge for these networks to implement or learn. Recently, a family of models described by neural ordinary differential equations (nODEs) has emerged as powerful dynamical neural network models capable of capturing complex dynamics. Here, we extend nODEs by endowing them with adaptive timescales using gating interactions. We refer to these as gated neural ODEs (gnODEs). Using a task that requires memory of continuous quantities, we demonstrate the inductive bias of the gnODEs to learn (approximate) continuous attractors. We further show how reduced-dimensional gnODEs retain their modeling power while greatly improving interpretability, even allowing explicit visualization of the structure of learned attractors. We introduce a novel measure of expressivity which probes the capacity of a neural network to generate complex trajectories. Using this measure, we explore how the phase-space dimension of the nODEs and the complexity of the function modeling the flow field contribute to expressivity. We see that a more complex function for modeling the flow field allows a lower-dimensional nODE to capture a given target dynamics. Finally, we demonstrate the benefit of gating in nODEs on several real-world tasks.

We study the task of agnostically learning halfspaces under the Gaussian distribution. Specifically, given labeled examples $(\\mathbf{x},y)$ from an unknown distribution on $\\mathbb{R}^n \\times \\{\pm 1 \\}$, whose marginal distribution on $\\mathbf{x}$ is the standard Gaussian and the labels $y$ can be arbitrary, the goal is to output a hypothesis with 0-1 loss $\\mathrm{OPT}+\\epsilon$, where $\\mathrm{OPT}$ is the 0-1 loss of the best-fitting halfspace. We prove a near-optimal computational hardness result for this task, under the widely believed sub-exponential time hardness of the Learning with Errors (LWE) problem. Prior hardness results are either qualitatively suboptimal or apply to restricted families of algorithms. Our techniques extend to yield near-optimal lower bounds for related problems, including ReLU regression.

Thompson sampling (TS) is widely used in sequential decision making due to its ease of use and appealing empirical performance. However, many existing analytical and empirical results for TS rely on restrictive assumptions on reward distributions, such as belonging to conjugate families, which limits their applicability in realistic scenarios. Moreover, sequential decision making problems are often carried out in a batched manner, either due to the inherent nature of the problem or to serve the purpose of reducing communication and computation costs. In this work, we jointly study these problems in two popular settings, namely, stochastic multi-armed bandits (MABs) and infinite-horizon reinforcement learning (RL), where TS is used to learn the unknown reward distributions and transition dynamics, respectively. We propose batched *Langevin Thompson Sampling* algorithms that leverage MCMC methods to sample from approximate posteriors with only logarithmic communication costs in terms of batches. Our algorithms are computationally efficient and maintain the same order-optimal regret guarantees of $\mathcal{O}(\log T)$ for stochastic MABs, and $\mathcal{O}(\sqrt{T})$ for RL. We complement our theoretical findings with experimental results.

Human knowledge is largely implicit and relational --- do we have a friend in common? can I walk from here to there? In this work, we leverage the combinatorial structure of graphs to quantify human priors over such relational data. Our experiments focus on two domains that have been continuously relevant over evolutionary timescales: social interaction and spatial navigation. We find that some features of the inferred priors are remarkably consistent, such as the tendency for sparsity as a function of graph size. Other features are domain-specific, such as the propensity for triadic closure in social interactions. More broadly, our work demonstrates how nonclassical statistical analysis of indirect behavioral experiments can be used to efficiently model latent biases in the data.

Additive models have been burgeoning in data analysis due to their flexible representation and desirable interpretability. However, most existing approaches are constructed under empirical risk minimization (ERM), and thus perform poorly in situations where average performance is not a suitable criterion for the problems of interest, e.g., data with complex non-Gaussian noise, imbalanced labels or both of them. In this paper, a novel class of sparse additive models is proposed under tilted empirical risk minimization (TERM), which addresses the deficiencies in ERM by imposing tilted impact on individual losses, and is flexibly capable of achieving a variety of learning objectives, e.g., variable selection, robust estimation, imbalanced classification and multiobjective learning. On the theoretical side, a learning theory analysis which is centered around the generalization bound and function approximation error bound (under some specific data distributions) is conducted rigorously. On the practical side, an accelerated optimization algorithm is designed by integrating Prox-SVRG and random Fourier acceleration technique. The empirical assessments verify the competitive performance of our approach on both synthetic and real data.

Concept bottleneck models (CBMs) are a class of interpretable neural network models that predict the target response of a given input based on its high-level concepts. Unlike the standard end-to-end models, CBMs enable domain experts to intervene on the predicted concepts and rectify any mistakes at test time, so that more accurate task predictions can be made at the end. While such intervenability provides a powerful avenue of control, many aspects of the intervention procedure remain rather unexplored. In this work, we develop various ways of selecting intervening concepts to improve the intervention effectiveness and conduct an array of in-depth analyses as to how they evolve under different circumstances. Specifically, we find that an informed intervention strategy can reduce the task error more than ten times compared to the current baseline under the same amount of intervention counts in realistic settings, and yet, this can vary quite significantly when taking into account different intervention granularity. We verify our findings through comprehensive evaluations, not only on the standard real datasets, but also on synthetic datasets that we generate based on a set of different causal graphs. We further discover some major pitfalls of the current practices which, without a proper addressing, raise concerns on reliability and fairness of the intervention procedure.

In this paper, we conduct an empirical study of the feature learning process in deep classifiers. Recent research has identified a training phenomenon called Neural Collapse (NC), in which the top-layer feature embeddings of samples from the same class tend to concentrate around their means, and the top layer's weights align with those features. Our study aims to investigate if these properties extend to intermediate layers. We empirically study the evolution of the covariance and mean of representations across different layers and show that as we move deeper into a trained neural network, the within-class covariance decreases relative to the between-class covariance. Additionally, we find that in the top layers, where the between-class covariance is dominant, the subspace spanned by the class means aligns with the subspace spanned by the most significant singular vector components of the weight matrix in the corresponding layer. Finally, we discuss the relationship between NC and Associative Memories (Willshaw et. al. 1969).

As with any machine learning problem with limited data, effective offline RL algorithms require careful regularization to avoid overfitting. One class of methods, known as one-step RL, perform just one step of policy improvement. These methods, which include advantage-weighted regression and conditional behavioral cloning, are thus simple and stable, but can have limited asymptotic performance. A second class of methods, known as critic regularization, perform many steps of policy improvement with a regularized objective. These methods typically require more compute but have appealing lower-bound guarantees. In this paper, we draw a connection between these methods: applying a multi-step critic regularization method with a regularization coefficient of 1 yields the same policy as one-step RL. While our theoretical results require assumptions (e.g., deterministic dynamics), our experiments nevertheless show that our analysis makes accurate, testable predictions about practical offline RL methods (CQL and one-step RL) with commonly-used hyperparameters.

Several recent studies have elucidated why knowledge distillation (KD) improves model performance. However, few have researched the other advantages of KD in addition to its improving model performance. In this study, we have attempted to show that KD enhances the interpretability as well as the accuracy of models. We measured the number of concept detectors identified in network dissection for a quantitative comparison of model interpretability. We attributed the improvement in interpretability to the class-similarity information transferred from the teacher to student models. First, we confirmed the transfer of class-similarity information from the teacher to student model via logit distillation. Then, we analyzed how class-similarity information affects model interpretability in terms of its presence or absence and degree of similarity information. We conducted various quantitative and qualitative experiments and examined the results on different datasets, different KD methods, and according to different measures of interpretability. Our research showed that KD models by large models could be used more reliably in various fields. The code is available at https://github.com/Rok07/KD_XAI.git.

We study Stochastic Gradient Descent with AdaGrad stepsizes: a popular adaptive (self-tuning) method for first-order stochastic optimization. Despite being well studied, existing analyses of this method suffer from various shortcomings: they either assume some knowledge of the problem parameters, impose strong global Lipschitz conditions, or fail to give bounds that hold with high probability. We provide a comprehensive analysis of this basic method without any of these limitations, in both the convex and non-convex (smooth) cases, that additionally supports a general ``affine variance'' noise model and provides sharp rates of convergence in both the low-noise and high-noise regimes.

In this paper, we consider federated Q-learning, which aims to learn an optimal Q-function by periodically aggregating local Q-estimates trained on local data alone. Focusing on infinite-horizon tabular Markov decision processes, we provide sample complexity guarantees for both the synchronous and asynchronous variants of federated Q-learning. In both cases, our bounds exhibit a linear speedup with respect to the number of agents and sharper dependencies on other salient problem parameters. Moreover, existing approaches to federated Q-learning adopt an equally-weighted averaging of local Q-estimates, which can be highly sub-optimal in the asynchronous setting since the local trajectories can be highly heterogeneous due to different local behavior policies. Existing sample complexity scales inverse proportionally to the minimum entry of the stationary state-action occupancy distributions over all agents, requiring that every agent covers the entire state-action space. Instead, we propose a novel importance averaging algorithm, giving larger weights to more frequently visited state-action pairs. The improved sample complexity scales inverse proportionally to the minimum entry of the average stationary state-action occupancy distribution of all agents, thus only requiring the agents collectively cover the entire state-action space, unveiling the blessing of heterogeneity.