NeurIPS 2024 论文列表

Bounding and predicting the generalization gap of overparameterized neural networks remains a central open problem in theoretical machine learning. There is a recent and growing body of literature that proposes the framework of fractals to model optimization trajectories of neural networks, motivating generalization bounds and measures based on the fractal dimension of the trajectory. Notably, the persistent homology dimension has been proposed to correlate with the generalization gap. This paper performs an empirical evaluation of these persistent homology-based generalization measures, with an in-depth statistical analysis. Our study reveals confounding effects in the observed correlation between generalization and topological measures due to the variation of hyperparameters. We also observe that fractal dimension fails to predict generalization of models trained from poor initializations. We lastly reveal the intriguing manifestation of model-wise double descent in these topological generalization measures. Our work forms a basis for a deeper investigation of the causal relationships between fractal geometry, topological data analysis, and neural network optimization.

Domain generalization methods aim to learn transferable knowledge from source domains that can generalize well to unseen target domains. Recent studies show that neural networks frequently suffer from a simplicity-biased learning behavior which leads to over-reliance on specific frequency sets, namely as frequency shortcuts, instead of semantic information, resulting in poor generalization performance. Despite previous data augmentation techniques successfully enhancing generalization performances, they intend to apply more frequency shortcuts, thereby causing hallucinations of generalization improvement. In this paper, we aim to prevent such learning behavior of applying frequency shortcuts from a data-driven perspective. Given the theoretical justification of models' biased learning behavior on different spatial frequency components, which is based on the dataset frequency properties, we argue that the learning behavior on various frequency components could be manipulated by changing the dataset statistical structure in the Fourier domain. Intuitively, as frequency shortcuts are hidden in the dominant and highly dependent frequencies of dataset structure, dynamically perturbating the over-reliance frequency components could prevent the application of frequency shortcuts. To this end, we propose two effective data augmentation modules designed to collaboratively and adaptively adjust the frequency characteristic of the dataset, aiming to dynamically influence the learning behavior of the model and ultimately serving as a strategy to mitigate shortcut learning. Our code will be made publicly available.

Domain generalization (DG) methods aim to maintain good performance in an unseen target domain by using training data from multiple source domains. While success on certain occasions are observed, enhancing the baseline across most scenarios remains challenging. This work introduces a simple yet effective framework, dubbed learning from multiple experts (LFME), that aims to make the target model an expert in all source domains to improve DG. Specifically, besides learning the target model used in inference, LFME will also train multiple experts specialized in different domains, whose output probabilities provide professional guidance by simply regularizing the logit of the target model. Delving deep into the framework, we reveal that the introduced logit regularization term implicitly provides effects of enabling the target model to harness more information, and mining hard samples from the experts during training. Extensive experiments on benchmarks from different DG tasks demonstrate that LFME is consistently beneficial to the baseline and can achieve comparable performance to existing arts. Code is available at https://github.com/liangchen527/LFME.

Many of the recent advances in computer vision and language models can be attributed to the success of transfer learning via the pre-training of large foundation models. However, a theoretical framework which explains this empirical success is incomplete and remains an active area of research. Flatness of the loss surface and neural collapse have recently emerged as useful pre-training metrics which shed light on the implicit biases underlying pre-training. In this paper, we explore the geometric complexity of a model's learned representations as a fundamental mechanism that relates these two concepts. We show through experiments and theory that mechanisms which affect the geometric complexity of the pre-trained network also influence the neural collapse. Furthermore, we show how this effect of the geometric complexity generalizes to the neural collapse of new classes as well, thus encouraging better performance on downstream tasks, particularly in the few-shot setting.

Recent advances in large language models have shown capabilities that are extraordinary and near-superhuman. These models operate with such complexity that reliably evaluating and aligning them proves challenging for humans. This leads to the natural question: can guidance from weak models (like humans) adequately direct the capabilities of strong models? In a recent and somewhat surprising work, Burns et al. (2023) empirically demonstrated that when strong models (like GPT-4) are finetuned using labels generated by weak supervisors (like GPT-2), the strong models outperform their weaker counterparts---a phenomenon they term *weak-to-strong generalization*. In this work, we present a theoretical framework for understanding weak-to-strong generalization. Specifically, we show that the improvement in performance achieved by strong models over their weaker counterparts is quantified by the *misfit error* incurred by the strong model on labels generated by the weaker model. Our theory reveals several curious algorithmic insights. For instance, we can predict the amount by which the strong model will improve over the weak model, and also choose among different weak models to train the strong model, based on its misfit error. We validate our theoretical findings through various empirical assessments.

Over the past decade, there is a growing interest in collaborative learning that can enhance AI models of multiple parties. However, it is still challenging to enhance performance them without sharing private data and models from individual parties. One recent promising approach is to develop distillation-based algorithms that exploit unlabeled public data but the results are still unsatisfactory in both theory and practice. To tackle this problem, we rigorously analyze a representative distillation-based algorithm in the view of kernel regression. This work provides the first theoretical results to prove the (nearly) minimax optimality of the nonparametric collaborative learning algorithm that does not directly share local data or models in massively distributed statistically heterogeneous environments. Inspired by our theoretical results, we also propose a practical distillation-based collaborative learning algorithm based on neural network architecture. Our algorithm successfully bridges the gap between our theoretical assumptions and practical settings with neural networks through feature kernel matching. We simulate various regression tasks to verify our theory and demonstrate the practical feasibility of our proposed algorithm.

Warm-starting neural network training by initializing networks with previously learned weights is appealing, as practical neural networks are often deployed under a continuous influx of new data. However, it often leads to *loss of plasticity*, where the network loses its ability to learn new information, resulting in worse generalization than training from scratch. This occurs even under stationary data distributions, and its underlying mechanism is poorly understood. We develop a framework emulating real-world neural network training and identify noise memorization as the primary cause of plasticity loss when warm-starting on stationary data. Motivated by this, we propose **Direction-Aware SHrinking (DASH)**, a method aiming to mitigate plasticity loss by selectively forgetting memorized noise while preserving learned features. We validate our approach on vision tasks, demonstrating improvements in test accuracy and training efficiency.

Solving parametric partial differential equations (PDEs) presents significant challenges for data-driven methods due to the sensitivity of spatio-temporal dynamics to variations in PDE parameters. Machine learning approaches often struggle to capture this variability. To address this, data-driven approaches learn parametric PDEs by sampling a very large variety of trajectories with varying PDE parameters. We first show that incorporating conditioning mechanisms for learning parametric PDEs is essential and that among them, \textit{adaptive conditioning}, allows stronger generalization. As existing adaptive conditioning methods do not scale well with respect to the number of parameters to adapt in the neural solver, we propose GEPS, a simple adaptation mechanism to boost GEneralization in Pde Solvers via a first-order optimization and low-rank rapid adaptation of a small set of context parameters. We demonstrate the versatility of our approach for both fully data-driven and for physics-aware neural solvers. Validation performed on a whole range of spatio-temporal forecasting problems demonstrates excellent performance for generalizing to unseen conditions including initial conditions, PDE coefficients, forcing terms and solution domain. *Project page*: https://geps-project.github.io

With the emergence of various molecular tasks and massive datasets, how to perform efficient training has become an urgent yet under-explored issue in the area. Data pruning (DP), as an oft-stated approach to saving training burdens, filters out less influential samples to form a coreset for training. However, the increasing reliance on pretrained models for molecular tasks renders traditional in-domain DP methods incompatible. Therefore, we propose a **Mol**ecular data **P**runing framework for **e**nhanced **G**eneralization (**MolPeg**), which focuses on the source-free data pruning scenario, where data pruning is applied with pretrained models. By maintaining two models with different updating paces during training, we introduce a novel scoring function to measure the informativeness of samples based on the loss discrepancy. As a plug-and-play framework, MolPeg realizes the perception of both source and target domain and consistently outperforms existing DP methods across four downstream tasks. Remarkably, it can surpass the performance obtained from full-dataset training, even when pruning up to 60-70% of the data on HIV and PCBA dataset. Our work suggests that the discovery of effective data-pruning metrics could provide a viable path to both enhanced efficiency and superior generalization in transfer learning.

It is generally accepted that starting neural networks training with large learning rates (LRs) improves generalization. Following a line of research devoted to understanding this effect, we conduct an empirical study in a controlled setting focusing on two questions: 1) how large an initial LR is required for obtaining optimal quality, and 2) what are the key differences between models trained with different LRs? We discover that only a narrow range of initial LRs slightly above the convergence threshold lead to optimal results after fine-tuning with a small LR or weight averaging. By studying the local geometry of reached minima, we observe that using LRs from this optimal range allows for the optimization to locate a basin that only contains high-quality minima. Additionally, we show that these initial LRs result in a sparse set of learned features, with a clear focus on those most relevant for the task. In contrast, starting training with too small LRs leads to unstable minima and attempts to learn all features simultaneously, resulting in poor generalization. Conversely, using initial LRs that are too large fails to detect a basin with good solutions and extract meaningful patterns from the data.

In safety-critical applications, machine learning models should generalize well under worst-case distribution shifts, that is, have a small robust risk. Invariance-based algorithms can provably take advantage of structural assumptions on the shifts when the training distributions are heterogeneous enough to identify the robust risk. However, in practice, such identifiability conditions are rarely satisfied – a scenario so far underexplored in the theoretical literature. In this paper, we aim to fill the gap and propose to study the more general setting of partially identifiable robustness. In particular, we define a new risk measure, the identifiable robust risk, and its corresponding (population) minimax quantity that is an algorithm-independent measure for the best achievable robustness under partial identifiability. We introduce these concepts broadly, and then study them within the framework of linear structural causal models for concreteness of the presentation. We use the introduced minimax quantity to show how previous approaches provably achieve suboptimal robustness in the partially identifiable case. We confirm our findings through empirical simulations and real-world experiments and demonstrate how the test error of existing robustness methods grows increasingly suboptimal as the proportion of previously unseen test directions increases.

Temporal Domain Generalization (TDG) addresses the challenge of training predictive models under temporally varying data distributions. Traditional TDG approaches typically focus on domain data collected at fixed, discrete time intervals, which limits their capability to capture the inherent dynamics within continuous-evolving and irregularly-observed temporal domains. To overcome this, this work formalizes the concept of Continuous Temporal Domain Generalization (CTDG), where domain data are derived from continuous times and are collected at arbitrary times. CTDG tackles critical challenges including: 1) Characterizing the continuous dynamics of both data and models, 2) Learning complex high-dimensional nonlinear dynamics, and 3) Optimizing and controlling the generalization across continuous temporal domains. To address them, we propose a Koopman operator-driven continuous temporal domain generalization (Koodos) framework. We formulate the problem within a continuous dynamic system and leverage the Koopman theory to learn the underlying dynamics; the framework is further enhanced with a comprehensive optimization strategy equipped with analysis and control driven by prior knowledge of the dynamics patterns. Extensive experiments demonstrate the effectiveness and efficiency of our approach. The code can be found at: https://github.com/Zekun-Cai/Koodos.

Deep neural networks have long been criticized for being black-box. To unveil the inner workings of modern neural architectures, a recent work proposed an information-theoretic objective function called Sparse Rate Reduction (SRR) and interpreted its unrolled optimization as a Transformer-like model called Coding Rate Reduction Transformer (CRATE). However, the focus of the study was primarily on the basic implementation, and whether this objective is optimized in practice and its causal relationship to generalization remain elusive. Going beyond this study, we derive different implementations by analyzing layer-wise behaviors of CRATE, both theoretically and empirically. To reveal the predictive power of SRR on generalization, we collect a set of model variants induced by varied implementations and hyperparameters and evaluate SRR as a complexity measure based on its correlation with generalization. Surprisingly, we find out that SRR has a positive correlation coefficient and outperforms other baseline measures, such as path-norm and sharpness-based ones. Furthermore, we show that generalization can be improved using SRR as regularization on benchmark image classification datasets. We hope this paper can shed light on leveraging SRR to design principled models and study their generalization ability.

In Open-Set Domain Generalization (OSDG), the model is exposed to both new variations of data appearance (domains) and open-set conditions, where both known and novel categories are present at test time. The challenges of this task arise from the dual need to generalize across diverse domains and accurately quantify category novelty, which is critical for applications in dynamic environments. Recently, meta-learning techniques have demonstrated superior results in OSDG, effectively orchestrating the meta-train and -test tasks by employing varied random categories and predefined domain partition strategies. These approaches prioritize a well-designed training schedule over traditional methods that focus primarily on data augmentation and the enhancement of discriminative feature learning. The prevailing meta-learning models in OSDG typically utilize a predefined sequential domain scheduler to structure data partitions. However, a crucial aspect that remains inadequately explored is the influence brought by strategies of domain schedulers during training. In this paper, we observe that an adaptive domain scheduler benefits more in OSDG compared with prefixed sequential and random domain schedulers. We propose the Evidential Bi-Level Hardest Domain Scheduler (EBiL-HaDS) to achieve an adaptive domain scheduler. This method strategically sequences domains by assessing their reliabilities in utilizing a follower network, trained with confidence scores learned in an evidential manner, regularized by max rebiasing discrepancy, and optimized in a bilevel manner. We verify our approach on three OSDG benchmarks, i.e., PACS, DigitsDG, and OfficeHome. The results show that our method substantially improves OSDG performance and achieves more discriminative embeddings for both the seen and unseen categories, underscoring the advantage of a judicious domain scheduler for the generalizability to unseen domains and unseen categories. The source code is publicly available at https://github.com/KPeng9510/EBiL-HaDS.

Generalization remains a central challenge in machine learning. In this work, we propose *Learning from Teaching* (**LoT**), a novel regularization technique for deep neural networks to enhance generalization. Inspired by the human ability to capture concise and abstract patterns, we hypothesize that generalizable correlations are expected to be easier to imitate. LoT operationalizes this concept to improve the generalization of the main model with auxiliary student learners. The student learners are trained by the main model and, in turn, provide feedback to help the main model capture more generalizable and imitable correlations. Our experimental results across several domains, including Computer Vision, Natural Language Processing, and methodologies like Reinforcement Learning, demonstrate that the introduction of LoT brings significant benefits compared to training models on the original dataset. The results suggest the effectiveness and efficiency of LoT in identifying generalizable information at the right scales while discarding spurious data correlations, thus making LoT a valuable addition to current machine learning. Code is available at https://github.com/jincan333/LoT.

Enhancing node-level Out-Of-Distribution (OOD) generalization on graphs remains a crucial area. In this paper, we develop a Structural Causal Model (SCM) to theoretically dissect the performance of two prominent invariant learning methods--Invariant Risk Minimization (IRM) and Variance-Risk Extrapolation (VREx)--in node-level OOD settings. Our analysis reveals a critical limitation: these methods may struggle to identify invariant features due to the complexities introduced by the message-passing mechanism, which can obscure causal features within a range of neighboring samples. To address this, we propose Cross-environment Intra-class Alignment (CIA), which explicitly eliminates spurious features by aligning representations within the same class, bypassing the need for explicit knowledge of underlying causal patterns. To adapt CIA to node-level OOD scenarios where environment labels are hard to obtain, we further propose CIA-LRA (Localized Reweighting Alignment) that leverages the distribution of neighboring labels to selectively align node representations, effectively distinguishing and preserving invariant features while removing spurious ones, all without relying on environment labels. We theoretically prove CIA-LRA's effectiveness by deriving an OOD generalization error bound based on PAC-Bayesian analysis. Experiments on graph OOD benchmarks validate the superiority of CIA and CIA-LRA, marking a significant advancement in node-level OOD generalization.

We study the generalization of two-layer ReLU neural networks in a univariate nonparametric regression problem with noisy labels. This is a problem where kernels (\emph{e.g.} NTK) are provably sub-optimal and benign overfitting does not happen, thus disqualifying existing theory for interpolating (0-loss, global optimal) solutions. We present a new theory of generalization for local minima that gradient descent with a constant learning rate can \emph{stably} converge to. We show that gradient descent with a fixed learning rate $\eta$ can only find local minima that represent smooth functions with a certain weighted \emph{first order total variation} bounded by $1/\eta - 1/2 + \widetilde{O}(\sigma + \sqrt{\mathrm{MSE}})$ where $\sigma$ is the label noise level, $\mathrm{MSE}$ is short for mean squared error against the ground truth, and $\widetilde{O}(\cdot)$ hides a logarithmic factor. Under mild assumptions, we also prove a nearly-optimal MSE bound of $\widetilde{O}(n^{-4/5})$ within the strict interior of the support of the $n$ data points. Our theoretical results are validated by extensive simulation that demonstrates large learning rate training induces sparse linear spline fits. To the best of our knowledge, we are the first to obtain generalization bound via minima stability in the non-interpolation case and the first to show ReLU NNs without regularization can achieve near-optimal rates in nonparametric regression.

Offline Reinforcement Learning (RL) suffers from the extrapolation error and value overestimation. From a generalization perspective, this issue can be attributed to the over-generalization of value functions or policies towards out-of-distribution (OOD) actions. Significant efforts have been devoted to mitigating such generalization, and recent in-sample learning approaches have further succeeded in entirely eschewing it. Nevertheless, we show that mild generalization beyond the dataset can be trusted and leveraged to improve performance under certain conditions. To appropriately exploit generalization in offline RL, we propose Doubly Mild Generalization (DMG), comprising (i) mild action generalization and (ii) mild generalization propagation. The former refers to selecting actions in a close neighborhood of the dataset to maximize the Q values. Even so, the potential erroneous generalization can still be propagated, accumulated, and exacerbated by bootstrapping. In light of this, the latter concept is introduced to mitigate the generalization propagation without impeding the propagation of RL learning signals. Theoretically, DMG guarantees better performance than the in-sample optimal policy in the oracle generalization scenario. Even under worst-case generalization, DMG can still control value overestimation at a certain level and lower bound the performance. Empirically, DMG achieves state-of-the-art performance across Gym-MuJoCo locomotion tasks and challenging AntMaze tasks. Moreover, benefiting from its flexibility in both generalization aspects, DMG enjoys a seamless transition from offline to online learning and attains strong online fine-tuning performance.