ICML 2024 论文列表

In science we are interested in finding the governing equations, the dynamical rules, underlying empirical phenomena. While traditionally scientific models are derived through cycles of human insight and experimentation, recently deep learning (DL) techniques have been advanced to reconstruct dynamical systems (DS) directly from time series data. State-of-the-art dynamical systems reconstruction (DSR) methods show promise in capturing invariant and long-term properties of observed DS, but their ability to generalize to unobserved domains remains an open challenge. Yet, this is a crucial property we would expect from any viable scientific theory. In this work, we provide a formal framework that addresses generalization in DSR. We explain why and how out-of-domain (OOD) generalization (OODG) in DSR profoundly differs from OODG considered elsewhere in machine learning. We introduce mathematical notions based on topological concepts and ergodic theory to formalize the idea of learnability of a DSR model. We formally prove that black-box DL techniques, without adequate structural priors, generally will not be able to learn a generalizing DSR model. We also show this empirically, considering major classes of DSR algorithms proposed so far, and illustrate where and why they fail to generalize across the whole phase space. Our study provides the first comprehensive mathematical treatment of OODG in DSR, and gives a deeper conceptual understanding of where the fundamental problems in OODG lie and how they could possibly be addressed in practice.

The ability of machine learning (ML) algorithms to generalize well to unseen data has been studied through the lens of information theory, by bounding the generalization error with the input-output mutual information (MI), i.e., the MI between the training data and the learned hypothesis. Yet, these bounds have limited practicality for modern ML applications (e.g., deep learning), due to the difficulty of evaluating MI in high dimensions. Motivated by recent findings on the compressibility of neural networks, we consider algorithms that operate by *slicing* the parameter space, i.e., trained on random lower-dimensional subspaces. We introduce new, tighter information-theoretic generalization bounds tailored for such algorithms, demonstrating that slicing improves generalization. Our bounds offer significant computational and statistical advantages over standard MI bounds, as they rely on scalable alternative measures of dependence, i.e., disintegrated mutual information and $k$-sliced mutual information. Then, we extend our analysis to algorithms whose parameters do not need to exactly lie on random subspaces, by leveraging rate-distortion theory. This strategy yields generalization bounds that incorporate a distortion term measuring model compressibility under slicing, thereby tightening existing bounds without compromising performance or requiring model compression. Building on this, we propose a regularization scheme enabling practitioners to control generalization through compressibility. Finally, we empirically validate our results and achieve the computation of non-vacuous information-theoretic generalization bounds for neural networks, a task that was previously out of reach.

The last decade has seen blossoming research in deep learning theory attempting to answer, ``Why does deep learning generalize?" A powerful shift in perspective precipitated this progress: the study of overparametrized models in the interpolation regime. In this paper, we argue that another perspective shift is due, since some of the desirable qualities of LLMs are not a consequence of good statistical generalization and require a separate theoretical explanation. Our core argument relies on the observation that AR probabilistic models are inherently non-identifiable: models zero or near-zero KL divergence apart---thus, equivalent test loss---can exhibit markedly different behaviors. We support our position with mathematical examples and empirical observations, illustrating why non-identifiability has practical relevance through three case studies: (1) the non-identifiability of zero-shot rule extrapolation; (2) the approximate non-identifiability of in-context learning; and (3) the non-identifiability of fine-tunability. We review promising research directions focusing on LLM-relevant generalization measures, transferability, and inductive biases.

Training autonomous agents that can learn new tasks from only a handful of demonstrations is a long-standing problem in machine learning. Recently, transformers have been shown to learn new language or vision tasks without any weight updates from only a few examples, also referred to as in-context learning. However, the sequential decision making setting poses additional challenges having a lower tolerance for errors since the environment's stochasticity or the agent's actions can lead to unseen, and sometimes unrecoverable, states. In this paper, we use an illustrative example to show that naively applying transformers to sequential decision making problems does not enable in-context learning of new tasks. We then demonstrate how training on sequences of trajectories with certain distributional properties leads to in-context learning of new sequential decision making tasks. We investigate different design choices and find that larger model and dataset sizes, as well as more task diversity, environment stochasticity, and trajectory burstiness, all result in better in-context learning of new out-of-distribution tasks. By training on large diverse offline datasets, our model is able to learn new MiniHack and Procgen tasks without any weight updates from just a handful of demonstrations.

We investigate the generalization error of statistical learning models in a Federated Learning (FL) setting. Specifically, we study the evolution of the generalization error with the number of communication rounds $R$ between $K$ clients and a parameter server (PS), i.e. the effect on the generalization error of how often the clients' local models are aggregated at PS. In our setup, the more the clients communicate with PS the less data they use for local training in each round, such that the amount of training data per client is identical for distinct values of $R$. We establish PAC-Bayes and rate-distortion theoretic bounds on the generalization error that account explicitly for the effect of the number of rounds $R$, in addition to the number of participating devices $K$ and individual datasets size $n$. The bounds, which apply to a large class of loss functions and learning algorithms, appear to be the first of their kind for the FL setting. Furthermore, we apply our bounds to FL-type Support Vector Machines (FSVM); and derive (more) explicit bounds in this case. In particular, we show that the generalization bound of FSVM increases with $R$, suggesting that more frequent communication with PS diminishes the generalization power. This implies that the population risk decreases less fast with $R$ than does the empirical risk. Moreover, our bound suggests that the generalization error of FSVM decreases faster than that of centralized learning by a factor of $\mathcal{O}(\sqrt{\log(K)/K})$. Finally, we provide experimental results obtained using neural networks (ResNet-56) which show evidence that not only may our observations for FSVM hold more generally but also that the population risk may even start to increase beyond some value of $R$.

Ensemble of deep neural networks has achieved great success in hedging against single-model failure under distribution shift. However, existing techniques suffer from producing redundant models, limiting predictive diversity and yielding compromised generalization performance. Existing ensemble pruning methods can only guarantee predictive diversity for in-distribution data, which may not transfer well to out-of-distribution (OoD) data. To address this gap, we propose a principled optimization framework for ensemble pruning under distribution shifts. Since the annotations of test data are not available, we explore relationships between prediction distributions of the models, encapsulated in a topology graph. By incorporating this topology into a combinatorial optimization framework, complementary models with high predictive diversity are selected with theoretical guarantees. Our approach is model-agnostic and can be applied on top of a broad spectrum of off-the-shelf ensembling methods for improved generalization performance. Experiments on common benchmarks demonstrate the superiority of our approach in both multi- and single-source OoD generalization. The source codes are publicly available at: https://github.com/joffery/TEP.

Understanding the generalization properties of heavy-tailed stochastic optimization algorithms has attracted increasing attention over the past years. While illuminating interesting aspects of stochastic optimizers by using heavy-tailed stochastic differential equations as proxies, prior works either provided expected generalization bounds, or introduced non-computable information theoretic terms. Addressing these drawbacks, in this work, we prove high-probability generalization bounds for heavy-tailed SDEs which do not contain any nontrivial information theoretic terms. To achieve this goal, we develop new proof techniques based on estimating the entropy flows associated with the so-called fractional Fokker-Planck equation (a partial differential equation that governs the evolution of the distribution of the corresponding heavy-tailed SDE). In addition to obtaining high-probability bounds, we show that our bounds have a better dependence on the dimension of parameters as compared to prior art. Our results further identify a phase transition phenomenon, which suggests that heavy tails can be either beneficial or harmful depending on the problem structure. We support our theory with experiments conducted in a variety of settings.

Since machine learning technologies are being used in various practical situations, models with merely low prediction errors might not be satisfactory; prediction errors occurring with a low probability might yield dangerous results in some applications. Therefore, there are attempts to achieve an ML model whose input-output pairs are guaranteed to satisfy given constraints. Among such attempts, many previous works chose the approach of modifying the outputs of an ML model at the inference time to satisfy the constraints. Such a strategy is handy because we can control its output without expensive training or fine-tuning. However, it is unclear whether using constraints only in the inference time degrades a model's predictive performance. This paper analyses how the generalization error bounds change when we only put constraints in the inference time. Our main finding is that a class of loss functions preserves the relative generalization error, i.e., the difference in generalization error compared with the best model will not increase by imposing constraints at the inference time on multi-class classification. Some popular loss functions preserve the relative error, including the softmax cross-entropy loss. On the other hand, we also show that some loss functions do not preserve relative error when we use constraints. Our results suggest the importance of choosing a suitable loss function when we only use constraints in the inference time.

$E(n)$-Equivariant Graph Neural Networks (EGNNs) are among the most widely used and successful models for representation learning on geometric graphs (e.g., 3D molecules). However, while the expressivity of EGNNs has been explored in terms of geometric variants of the Weisfeiler-Leman isomorphism test, characterizing their generalization capability remains open. In this work, we establish the first generalization bound for EGNNs. Our bound depicts a dependence on the weighted sum of logarithms of the spectral norms of the weight matrices (EGNN parameters). In addition, our main result reveals interesting novel insights: $i$) the spectral norms of the initial layers may impact generalization more than the final ones; $ii$) $\varepsilon$-normalization is beneficial to generalization --- confirming prior empirical evidence. We leverage these insights to introduce a spectral norm regularizer tailored to EGNNs. Experiments on real-world datasets substantiate our analysis, demonstrating a high correlation between theoretical and empirical generalization gaps and the effectiveness of the proposed regularization scheme.

A common method to study deep learning systems is to use simplified model representations—for example, using singular value decomposition to visualize the model’s hidden states in a lower dimensional space. This approach assumes that the results of these simplifications are faithful to the original model. Here, we illustrate an important caveat to this assumption: even if the simplified representations can accurately approximate the full model on the training set, they may fail to accurately capture the model’s behavior out of distribution. We illustrate this by training Transformer models on controlled datasets with systematic generalization splits, including the Dyck balanced-parenthesis languages and a code completion task. We simplify these models using tools like dimensionality reduction and clustering, and then explicitly test how these simplified proxies match the behavior of the original model. We find consistent generalization gaps: cases in which the simplified proxies are more faithful to the original model on the in-distribution evaluations and less faithful on various tests of systematic generalization. This includes cases where the original model generalizes systematically but the simplified proxies fail, and cases where the simplified proxies generalize better. Together, our results raise questions about the extent to which mechanistic interpretations derived using tools like SVD can reliably predict what a model will do in novel situations.

Stochastic weight averaging (SWA) method has empirically proven its advantages compared to stochastic gradient descent (SGD). Despite it is widespread used, theoretical investigations have been limited, particularly in scenarios beyond the ideal setting of convex and sampling with replacement. However, non-convex cases and sampling without replacement are very practical in real-world applications. The main challenges under the above settings are two-folds: (i) All the historical gradient information introduced by SWA is considered, while the analysis of SGD using the tool of uniform stability requires only to bound the current gradient. (ii) The $(1+\alpha\beta)$-expansion property causes the boundary of each gradient step dependent on the previous step, making the boundary of each historical gradient in SWA nested and the theoretical analysis even harder. To address the theoretical challenges, we adopt mathematical induction to find a recursive representation that bounds the gradient at each step. Based on this, we establish stability bounds supporting sampling with and without replacement in the non-convex setting. Furthermore, the derived generalization bounds of SWA are sharper than SGD. At last, experimental results on several benchmarks verify our theoretical results.

Out-of-distribution (OOD) generalization deals with the prevalent learning scenario where test distribution shifts from training distribution. With rising application demands and inherent complexity, graph OOD problems call for specialized solutions. While data-centric methods exhibit performance enhancements on many generic machine learning tasks, there is a notable absence of data augmentation methods tailored for graph OOD generalization. In this work, we propose to achieve graph OOD generalization with the novel design of non-Euclidean-space linear extrapolation. The proposed augmentation strategy extrapolates structure spaces to generate OOD graph data. Our design tailors OOD samples for specific shifts without corrupting underlying causal mechanisms. Theoretical analysis and empirical results evidence the effectiveness of our method in solving target shifts, showing substantial and constant improvements across various graph OOD tasks.

We investigate the out-of-domain generalization of random feature (RF) models and Transformers. We first prove that in the `generalization on the unseen (GOTU)' setting, where training data is fully seen in some part of the domain but testing is made on another part, and for RF models in the small feature regime, the convergence takes place to interpolators of minimal degree as in the Boolean case (Abbe et al., 2023). We then consider the sparse target regime and explain how this regime relates to the small feature regime, but with a different regularization term that can alter the picture in the non-Boolean case. We show two different outcomes for the sparse regime with q-ary data tokens: (1) if the data is embedded with roots of unities, then a min-degree interpolator is learned like in the Boolean case for RF models, (2) if the data is not embedded as such, e.g., simply as integers, then RF models and Transformers may not learn minimal degree interpolators. This shows that the Boolean setting and its roots of unities generalization are special cases where the minimal degree interpolator offers a rare characterization of how learning takes place. For more general integer and real-valued settings, a more nuanced picture remains to be fully characterized.

Despite great advances in algorithms for multi-label learning, research on the theoretical analysis of generalization is still in the early stage. Some recent theoretical results has investigated the generalization performance of multi-label learning under several evaluation metrics, however, how to reduce the dependency on the number of labels, explicitly introduce label correlations, and quantitatively analyze the impact of various inductive biases in the generalization analysis of multi-label learning is still a crucial and open problem. In an attempt to make up for the gap in the generalization theory of multi-label learning, we develop several novel vector-contraction inequalities, which exploit the Lipschitz continuity of loss functions, and derive generalization bounds with a weaker dependency on the number of labels than the state of the art in the case of decoupling the relationship among different components, which serves as theoretical guarantees for the generalization of multi-label learning. In addition, we derive the generalization bound for Macro-Averaged AUC and analyze its relationship with class-imbalance. The mild bounds without strong assumptions explain the good generalization ability of multi-label learning with first-order label correlations and high-order label correlations induced by norm regularizers.

Time-series forecasting (TSF) finds broad applications in real-world scenarios. Due to the dynamic nature of time-series data, it is crucial for TSF models to preserve out-of-distribution (OOD) generalization abilities, as training and test sets represent historical and future data respectively. In this paper, we aim to alleviate the inherent OOD problem in TSF via invariant learning. We identify fundamental challenges of invariant learning for TSF. First, the target variables in TSF may not be sufficiently determined by the input due to unobserved core variables in TSF, breaking the fundamental assumption of invariant learning. Second, time-series datasets lack adequate environment labels, while existing environmental inference methods are not suitable for TSF. To address these challenges, we propose FOIL, a model-agnostic framework that endows time-series forecasting for out-of-distribution generalization via invariant learning. Specifically, FOIL employs a novel surrogate loss to mitigate the impact of unobserved variables. Further, FOIL implements joint optimization by alternately inferring environments effectively with a multi-head network while preserving the temporal adjacency structure and learning invariant representations across inferred environments for OOD generalized TSF. Extensive experiments demonstrate that the proposed FOIL significantly and consistently improves the performance of various TSF models, achieving gains of up to 85%.

Causal inferences from a randomized controlled trial (RCT) may not pertain to a *target* population where some effect modifiers have a different distribution. Prior work studies *generalizing* the results of a trial to a target population with no outcome but covariate data available. We show how the limited size of trials makes generalization a statistically infeasible task, as it requires estimating complex nuisance functions. We develop generalization algorithms that supplement the trial data with a prediction model learned from an additional *observational* study (OS), without making *any* assumptions on the OS. We theoretically and empirically show that our methods facilitate better generalization when the OS is "high-quality", and remain robust when it is not, and *e.g.*, have unmeasured confounding.

It is by now well-established that modern over-parameterized models seem to elude the bias-variance tradeoff and generalize well despite overfitting noise. Many recent works attempt to analyze this phenomenon in the relatively tractable setting of kernel regression. However, as we argue in detail, most past works on this topic either make unrealistic assumptions, or focus on a narrow problem setup. This work aims to provide a unified theory to upper bound the excess risk of kernel regression for nearly all common and realistic settings. When applied to common kernels, our results imply benign overfitting in high input dimensions, nearly tempered overfitting in fixed dimensions, and explicit convergence rates for regularized regression. As a by-product, we obtain time-dependent bounds for neural networks trained in the kernel regime. Our results rely on new relative perturbation bounds for the eigenvalues of kernel matrices, which may be of independent interest. These reveal a self-regularization phenomenon, whereby a heavy tail in the eigendecomposition of the kernel implicitly leads to good generalization.

Large Language Models (LLMs) have demonstrated remarkable proficiency in understanding and generating natural language. However, their capabilities wane in highly specialized domains underrepresented in the pretraining corpus, such as physical and biomedical sciences. This work explores how to repurpose general LLMs into effective task solvers for specialized domains. We introduce a novel, model-agnostic framework for learning custom input tags, which are parameterized as continuous vectors appended to the LLM’s embedding layer, to condition the LLM. We design two types of input tags: domain tags are used to delimit specialized representations (e.g., chemical formulas) and provide domain-relevant context; function tags are used to represent specific functions (e.g., predicting molecular properties) and compress function-solving instructions. We develop a three-stage protocol to learn these tags using auxiliary data and domain knowledge. By explicitly disentangling task domains from task functions, our method enables zero-shot generalization to unseen problems through diverse combinations of the input tags. It also boosts LLM’s performance in various specialized domains, such as predicting protein or chemical properties and modeling drug-target interactions, outperforming expert models tailored to these tasks.

This paper presents a new generalization error analysis for Decentralized Stochastic Gradient Descent (D-SGD) based on algorithmic stability. The obtained results overhaul a series of recent works that suggested an increased instability due to decentralization and a detrimental impact of poorly-connected communication graphs on generalization. On the contrary, we show, for convex, strongly convex and non-convex functions, that D-SGD can always recover generalization bounds analogous to those of classical SGD, suggesting that the choice of graph does not matter. We then argue that this result is coming from a worst-case analysis, and we provide a refined optimization-dependent generalization bound for general convex functions. This new bound reveals that the choice of graph can in fact improve the worst-case bound in certain regimes, and that surprisingly, a poorly-connected graph can even be beneficial for generalization.