ICML 2023 Papers

Recent efforts at explaining the interplay of memorization and generalization in deep overparametrized networks have posited that neural networks *memorize* ``hard'' examples in the final few layers of the model. Memorization refers to the ability to correctly predict on *atypical* examples of the training set. In this work, we show that rather than being confined to individual layers, memorization is a phenomenon confined to a small set of neurons in various layers of the model. First, via three experimental sources of converging evidence, we find that most layers are redundant for the memorization of examples and the layers that contribute to example memorization are, in general, not the final layers. The three sources are *gradient accounting* (measuring the contribution to the gradient norms from memorized and clean examples), *layer rewinding* (replacing specific model weights of a converged model with previous training checkpoints), and *retraining* (training rewound layers only on clean examples). Second, we ask a more generic question: can memorization be localized *anywhere* in a model? We discover that memorization is often confined to a small number of neurons or channels (around 5) of the model. Based on these insights we propose a new form of dropout---*example-tied dropout* that enables us to direct the memorization of examples to an aprior determined set of neurons. By dropping out these neurons, we are able to reduce the accuracy on memorized examples from 100% to 3%, while also reducing the generalization gap.

We study the efficient estimation of predictive confidence intervals for black-box predictors when the common data exchangeability (e.g., i.i.d.) assumption is violated due to potentially feedback-induced shifts in the input data distribution. That is, we focus on standard and feedback covariate shift (FCS), where the latter allows for feedback dependencies between train and test data that occur in many decision-making scenarios like experimental design. Whereas prior conformal prediction methods for this problem are in general either extremely computationally demanding or make inefficient use of labeled data, we propose a collection of methods based on the jackknife+ that achieve a practical balance of computational and statistical efficiency. Theoretically, our proposed JAW-FCS method extends the rigorous, finite-sample coverage guarantee of the jackknife+ to FCS. We moreover propose two tunable relaxations to JAW-FCS's computation that maintain finite-sample guarantees: one using only $K$ leave-one-out models (JAW-$K$LOO) and a second building on $K$-fold cross validation+ (WCV+). Practically, we demonstrate that JAW-FCS and its computational relaxations outperform state-of-the-art baselines on a variety of real-world datasets under standard and feedback covariate shift, including for biomolecular design and active learning tasks.

We consider the neural contextual bandit problem. In contrast to the existing work which primarily focuses on ReLU neural nets, we consider a general set of smooth activation functions. Under this more general setting, (i) we derive non-asymptotic error bounds on the difference between an overparameterized neural net and its corresponding neural tangent kernel, (ii) we propose an algorithm with a provable sublinear regret bound that is also efficient in the finite regime as demonstrated by empirical studies. The non-asymptotic error bounds may be of broader interests as a tool to establish the relation between the smoothness of the activation functions in neural contextual bandits and the smoothness of the kernels in kernel bandits.

Recently, remarkable progress has been made by approximating Nash equilibrium (NE), correlated equilibrium (CE), and coarse correlated equilibrium (CCE) through function approximation that trains a neural network to predict equilibria from game representations. Furthermore, equivariant architectures are widely adopted in designing such equilibrium approximators in normal-form games. In this paper, we theoretically characterize the benefits and limitations of equivariant equilibrium approximators. For the benefits, we show that they enjoy better generalizability than general ones and can achieve better approximations when the payoff distribution is permutation-invariant. For the limitations, we discuss their drawbacks in terms of equilibrium selection and social welfare. Together, our results help to understand the role of equivariance in equilibrium approximators.

Offline reinforcement learning (RL) aims to find an optimal policy for sequential decision-making using a pre-collected dataset, without further interaction with the environment. Recent theoretical progress has focused on developing sample-efficient offline RL algorithms with various relaxed assumptions on data coverage and function approximators, especially to handle the case with excessively large state-action spaces. Among them, the framework based on the linear-programming (LP) reformulation of Markov decision processes has shown promise: it enables sample-efficient offline RL with function approximation, under only partial data coverage and realizability assumptions on the function classes, with favorable computational tractability. In this work, we revisit the LP framework for offline RL, and provide a new reformulation that advances the existing results in several aspects, relaxing certain assumptions and achieving optimal statistical rates in terms of sample size. Our key enabler is to introduce proper constraints in the reformulation, instead of using any regularization as in the literature, also with careful choices of the function classes and initial state distributions. We hope our insights bring into light the use of LP formulations and the induced primal-dual minimax optimization, in offline RL.

We study offline multi-agent reinforcement learning (RL) in Markov games, where the goal is to learn an approximate equilibrium---such as Nash equilibrium and (Coarse) Correlated Equilibrium---from an offline dataset pre-collected from the game. Existing works consider relatively restricted tabular or linear models and handle each equilibria separately. In this work, we provide the first framework for sample-efficient offline learning in Markov games under general function approximation, handling all 3 equilibria in a unified manner. By using Bellman-consistent pessimism, we obtain interval estimation for policies' returns, and use both the upper and the lower bounds to obtain a relaxation on the gap of a candidate policy, which becomes our optimization objective. Our results generalize prior works and provide several additional insights. Importantly, we require a data coverage condition that improves over the recently proposed ``unilateral concentrability''. Our condition allows selective coverage of deviation policies that optimally trade-off between their greediness (as approximate best responses) and coverage, and we show scenarios where this leads to significantly better guarantees. As a new connection, we also show how our algorithmic framework can subsume seemingly different solution concepts designed for the special case of two-player zero-sum games.

The neural operator has emerged as a powerful tool in learning mappings between function spaces in PDEs. However, when faced with real-world physical data, which are often highly non-uniformly distributed, it is challenging to use mesh-based techniques such as the FFT. To address this, we introduce the Non-Uniform Neural Operator (NUNO), a comprehensive framework designed for efficient operator learning with non-uniform data. Leveraging a K-D tree-based domain decomposition, we transform non-uniform data into uniform grids while effectively controlling interpolation error, thereby paralleling the speed and accuracy of learning from non-uniform data. We conduct extensive experiments on 2D elasticity, (2+1)D channel flow, and a 3D multi-physics heatsink, which, to our knowledge, marks a novel exploration into 3D PDE problems with complex geometries. Our framework has reduced error rates by up to 60% and enhanced training speeds by 2x to 30x. The code is now available at https://github.com/thu-ml/NUNO .

General function approximation is a powerful tool to handle large state and action spaces in a broad range of reinforcement learning (RL) scenarios. However, theoretical understanding of non-stationary MDPs with general function approximation is still limited. In this paper, we make the first such an attempt. We first propose a new complexity metric called dynamic Bellman Eluder (DBE) dimension for non-stationary MDPs, which subsumes majority of existing tractable RL problems in static MDPs as well as non-stationary MDPs. Based on the proposed complexity metric, we propose a novel confidence-set based model-free algorithm called SW-OPEA, which features a sliding window mechanism and a new confidence set design for non-stationary MDPs. We then establish an upper bound on the dynamic regret for the proposed algorithm, and show that SW-OPEA is provably efficient as long as the variation budget is not significantly large. We further demonstrate via examples of non-stationary linear and tabular MDPs that our algorithm performs better in small variation budget scenario than the existing UCB-type algorithms. To the best of our knowledge, this is the first dynamic regret analysis in non-stationary MDPs with general function approximation.

Learning partial differential equations' (PDEs) solution operators is an essential problem in machine learning. However, there are several challenges for learning operators in practical applications like the irregular mesh, multiple input functions, and complexity of the PDEs' solution. To address these challenges, we propose a general neural operator transformer (GNOT), a scalable and effective transformer-based framework for learning operators. By designing a novel heterogeneous normalized attention layer, our model is highly flexible to handle multiple input functions and irregular meshes. Besides, we introduce a geometric gating mechanism which could be viewed as a soft domain decomposition to solve the multi-scale problems. The large model capacity of the transformer architecture grants our model the possibility to scale to large datasets and practical problems. We conduct extensive experiments on multiple challenging datasets from different domains and achieve a remarkable improvement compared with alternative methods. Our code and data are publicly available at https://github.com/thu-ml/GNOT.

Decentralized stochastic gradient descent (D-SGD) allows collaborative learning on massive devices simultaneously without the control of a central server. However, existing theories claim that decentralization invariably undermines generalization. In this paper, we challenge the conventional belief and present a completely new perspective for understanding decentralized learning. We prove that D-SGD implicitly minimizes the loss function of an average-direction Sharpness-aware minimization (SAM) algorithm under general non-convex non-$\beta$-smooth settings. This surprising asymptotic equivalence reveals an intrinsic regularization-optimization trade-off and three advantages of decentralization: (1) there exists a free uncertainty evaluation mechanism in D-SGD to improve posterior estimation; (2) D-SGD exhibits a gradient smoothing effect; and (3) the sharpness regularization effect of D-SGD does not decrease as total batch size increases, which justifies the potential generalization benefit of D-SGD over centralized SGD (C-SGD) in large-batch scenarios.

We present a shape-guided expert-learning framework to tackle the problem of unsupervised 3D anomaly detection. Our method is established on the effectiveness of two specialized expert models and their synergy to localize anomalous regions from color and shape modalities. The first expert utilizes geometric information to probe 3D structural anomalies by modeling the implicit distance fields around local shapes. The second expert considers the 2D RGB features associated with the first expert to identify color appearance irregularities on the local shapes. We use the two experts to build the dual memory banks from the anomaly-free training samples and perform shape-guided inference to pinpoint the defects in the testing samples. Owing to the per-point 3D representation and the effective fusion scheme of complementary modalities, our method efficiently achieves state-of-the-art performance on the MVTec 3D-AD dataset with better recall and lower false positive rates, as preferred in real applications.

We make two contributions in the field of AI fairness over continuous protected attributes. First, we show that the Hirschfeld-Gebelein-Renyi (HGR) indicator (the only one currently available for such a case) is valuable but subject to a few crucial limitations regarding semantics, interpretability, and robustness. Second, we introduce a family of indicators that are: 1) complementary to HGR in terms of semantics; 2) fully interpretable and transparent; 3) robust over finite samples; 4) configurable to suit specific applications. Our approach also allows us to define fine-grained constraints to permit certain types of dependence and forbid others selectively. By expanding the available options for continuous protected attributes, our approach represents a significant contribution to the area of fair artificial intelligence.

An abundance of recent impossibility results establish that regret minimization in Markov games with adversarial opponents is both statistically and computationally intractable. Nevertheless, none of these results preclude the possibility of regret minimization under the assumption that all parties adopt the same learning procedure. In this work, we present the first (to our knowledge) algorithm for learning in general-sum Markov games that provides sublinear regret guarantees when executed by all agents. The bounds we obtain are for $\textit{swap regret}$, and thus, along the way, imply convergence to a $\textit{correlated}$ equilibrium. Our algorithm is decentralized, computationally efficient, and does not require any communication between agents. Our key observation is that online learning via policy optimization in Markov games essentially reduces to a form of $\textit{weighted}$ regret minimization, with $\textit{unknown}$ weights determined by the path length of the agents' policy sequence. Consequently, controlling the path length leads to weighted regret objectives for which sufficiently adaptive algorithms provide sublinear regret guarantees.

The task of mixture proportion estimation (MPE) is to estimate the weight of a component distribution in a mixture, given observations from both the component and mixture. Previous work on MPE adopts the *irreducibility* assumption, which ensures identifiablity of the mixture proportion. In this paper, we propose a more general sufficient condition that accommodates several settings of interest where irreducibility does not hold. We further present a resampling-based meta-algorithm that takes any existing MPE algorithm designed to work under irreducibility and adapts it to work under our more general condition. Our approach empirically exhibits improved estimation performance relative to baseline methods and to a recently proposed regrouping-based algorithm.

Although graph neural networks (GNNs) have achieved impressive achievements in graph classification, they often need abundant task-specific labels, which could be extensively costly to acquire. A credible solution is to explore additional labeled graphs to enhance unsupervised learning on the target domain. However, how to apply GNNs to domain adaptation remains unsolved owing to the insufficient exploration of graph topology and the significant domain discrepancy. In this paper, we propose Coupled Contrastive Graph Representation Learning (CoCo), which extracts the topological information from coupled learning branches and reduces the domain discrepancy with coupled contrastive learning. CoCo contains a graph convolutional network branch and a hierarchical graph kernel network branch, which explore graph topology in implicit and explicit manners. Besides, we incorporate coupled branches into a holistic multi-view contrastive learning framework, which not only incorporates graph representations learned from complementary views for enhanced understanding, but also encourages the similarity between cross-domain example pairs with the same semantics for domain alignment. Extensive experiments on popular datasets show that our CoCo outperforms these competing baselines in different settings generally.

A large-scale deep model pre-trained on massive labeled or unlabeled data transfers well to downstream tasks. Linear evaluation freezes parameters in the pre-trained model and trains a linear classifier separately, which is efficient and attractive for transfer. However, little work has investigated the classifier in linear evaluation except for the default logistic regression. Inspired by the statistical efficiency of naive Bayes, the paper revisits the classical topic on discriminative vs. generative classifiers. Theoretically, the paper considers the surrogate loss instead of the zero-one loss in analyses and generalizes the classical results from binary cases to multiclass ones. We show that, under mild assumptions, multiclass naive Bayes requires $O(\log n)$ samples to approach its asymptotic error while the corresponding multiclass logistic regression requires $O(n)$ samples, where $n$ is the feature dimension. To establish it, we present a multiclass $\mathcal{H}$-consistency bound framework and an explicit bound for logistic loss, which are of independent interests. Simulation results on a mixture of Gaussian validate our theoretical findings. Experiments on various pre-trained deep vision models show that naive Bayes consistently converges faster as the number of data increases. Besides, naive Bayes shows promise in few-shot cases and we observe the "two regimes'' phenomenon in pre-trained supervised models. Our code is available at https://github.com/ML-GSAI/Revisiting-Dis-vs-Gen-Classifiers.

Compared with full client participation, partial client participation is a more practical scenario in federated learning, but it may amplify some challenges in federated learning, such as data heterogeneity. The lack of inactive clients' updates in partial client participation makes it more likely for the model aggregation to deviate from the aggregation based on full client participation. Training with large batches on individual clients is proposed to address data heterogeneity in general, but their effectiveness under partial client participation is not clear. Motivated by these challenges, we propose to develop a novel federated learning framework, referred to as FedAMD, for partial client participation. The core idea is anchor sampling, which separates partial participants into anchor and miner groups. Each client in the anchor group aims at the local bullseye with the gradient computation using a large batch. Guided by the bullseyes, clients in the miner group steer multiple near-optimal local updates using small batches and update the global model. By integrating the results of the two groups, FedAMD is able to accelerate the training process and improve the model performance. Measured by $\epsilon$-approximation and compared to the state-of-the-art methods, FedAMD achieves the convergence by up to $O(1/\epsilon)$ fewer communication rounds under non-convex objectives. Empirical studies on real-world datasets validate the effectiveness of FedAMD and demonstrate the superiority of the proposed algorithm: Not only does it considerably save computation and communication costs, but also the test accuracy significantly improves.

Unsupervised out-of-distribution detection (OOD) seeks to identify out-of-domain data by learning only from unlabeled in-domain data. We present a novel approach for this task -- Lift, Map, Detect (LMD) -- that leverages recent advancement in diffusion models. Diffusion models are one type of generative models. At their core, they learn an iterative denoising process that gradually maps a noisy image closer to their training manifolds. LMD leverages this intuition for OOD detection. Specifically, LMD lifts an image off its original manifold by corrupting it, and maps it towards the in-domain manifold with a diffusion model. For an OOD image, the mapped image would have a large distance away from its original manifold, and LMD would identify it as OOD accordingly. We show through extensive experiments that LMD achieves competitive performance across a broad variety of datasets. Code can be found at https://github.com/zhenzhel/lift_map_detect.

Machine learning force fields (MLFF) have been proposed to accelerate molecular dynamics (MD) simulation, which finds widespread applications in chemistry and biomedical research. Even for the most data-efficient MLFFs, reaching chemical accuracy can require hundreds of frames of force and energy labels generated by expensive quantum mechanical algorithms, which may scale as $O(n^3)$ to $O(n^7)$, with $n$ proportional to the number of basis functions. To address this issue, we propose a multi-stage computational framework -- ASTEROID, which lowers the data cost of MLFFs by leveraging a combination of cheap inaccurate data and expensive accurate data. The motivation behind ASTEROID is that inaccurate data, though incurring large bias, can help capture the sophisticated structures of the underlying force field. Therefore, we first train a MLFF model on a large amount of inaccurate training data, employing a bias-aware loss function to prevent the model from overfitting the potential bias of this data. We then fine-tune the obtained model using a small amount of accurate training data, which preserves the knowledge learned from the inaccurate training data while significantly improving the model's accuracy. Moreover, we propose a variant of ASTEROID based on score matching for the setting where the inaccurate training data are unlabeled. Extensive experiments on MD datasets and downstream tasks validate the efficacy of ASTEROID. Our code and data are available at https://github.com/abukharin3/asteroid.