NeurIPS 2026 论文列表

We derive a tight generalization bound for deterministic neural networks based on their last hidden layer representations. By evaluating representation quality with a parameter-free $k$-nearest-neighbor ($k$-NN) classifier, our certificate avoids traditional parameter-space complexity measures, KL divergences to a posterior, weight norms, and compression. The bound is tight: trained from scratch, it reaches an 8.0 percentage point gap to test error on CIFAR-10 (ResNet-18) and yields the first non-vacuous certificates we are aware of on CIFAR-100; with frozen DINOv2 representations, it certifies at 1.4\% on CIFAR-10 and 23.1\% on 1,000-class ImageNet. It decomposes additively into three empirical, independently measurable quantities: local class geometry ($k$-NN decoder error), decoder-network agreement, and training stability. This allows the bound to act as a diagnostic tool: we demonstrate that actively destroying local class geometry eliminates generalization while leaving dataset memorization intact, identifying class geometry as a causally relevant mechanism for generalization. Finally, we show that learned representations are significantly less sensitive to weight noise than linear readouts, suggesting why parameter-space certificates often struggle to remain tight.

Gradient descent on overparameterized neural networks typically operates at the Edge of Stability (EoS), where the largest Hessian eigenvalue hovers around a step-size-dependent threshold. We study how sparse connectivity changes generalization below this threshold in two layer ReLU networks. Prior results have shown that for fully-connected networks (FCNs), generalization guarantees in this regime degrade and become vacuous on high-dimensional spherical inputs. Our analysis reveals that sparse connectivity fundamentally alters this picture. Under sparse connectivity, the network processes a collection of low-dimensional patches rather than the full input vector, so the effective constraint imposed by the stability condition is governed by the geometry of the training patch collection. We prove that when the receptive fields are small relative to the ambient dimension, the effective constraint yields non-vacuous generalization bounds in precisely the spherical regime where FCNs provably fail. The same framework also reveals a contrasting failure mode: if the patch collection lacks geometric structure, the constraint becomes unable to prevent overfitting. We corroborate this theory by analyzing the patch geometry of natural images, showing that standard convolutional designs produce patch multiset with low-dimensional structure that facilitates generalization. This provides a principled explanation for the generalization advantage of convolutional networks. Thus, our analysis yields a unified framework that identifies how architecture, data geometry, and gradient descent jointly govern generalization performance.

A central question in modern learning theory is what notion of compression, if any, explains why over-parameterized neural networks generalize. Existing answers measure complexity at different levels, ranging from weights to representations, and estimating the associated quantities either requires held-out data in principle or relies on mutual-information estimation in ultra-high dimensions. We approach the question through the minimum description length (MDL) principle and propose the prequential regret as a complementary signal that is computable from the training trajectory alone. We establish that, in the (nearly) interpolating regime, the expected prequential regret upper-bounds the description length of the trained parameter under the algorithm-induced distribution, and that this description length translates into a high-probability generalization bound in the PAC-MDL setting. Along the way, we show that the encoder-complexity correction recently added to the algorithm-level information bottleneck is upper-bounded by an MDL parameter description length, bringing the two views of compression onto a shared footing. Empirically, the prequential regret tracks the generalization error on CIFAR-10 and CIFAR-100, with Pearson correlations exceeding 0.9.

We study a data-dependent notion of diffusion-model generalization: when a model does not memorize the training set, where do its generated samples go relative to the geometry induced by the data? To answer this, we introduce a time-dependent family of log-density ridge manifolds constructed from the smoothed empirical distribution, and use it to characterize reverse-time inference. Our main result shows that generated samples evolve by a **reach-align-slide** mechanism: they first enter a neighborhood of the ridge, then their distance to the ridge is controlled by the normal component of training error, and finally their motion along the ridge is controlled by the tangential component. We further connect this geometric picture to training dynamics through directional decompositions of the learned error, and make this link explicit for random feature models, where architectural bias and optimization error can be separated quantitatively. Experiments on synthetic multimodal data and MNIST latent diffusion support the predicted geometric behavior in both low and high dimensions.

Cross-distribution generalization in longitudinal behavioral data remains a persistent obstacle. Models trained on one cohort degrade on new populations, and prior approaches operating through feature-distribution alignment or model-capacity scaling have not substantially improved cross-distribution performance. We diagnose the limitation as insufficient representational constraints during training. We propose holding the language model frozen, so that the coherence criterion is defined by its pre-trained language prior and cannot shift during training. We introduce PRISM, a frozen-backbone framework that decomposes each behavioral trajectory into temporal, spectral, and semantic streams and integrates them through directed cross-attention with instance-specific gating. Training uses a dual-path objective combining discriminative and coherence constraints on a shared representation. On GLOBEM, a widely used cross-cohort benchmark for behavioral health prediction, PRISM achieves 79.93\% out-of-distribution accuracy, 27.13 points above the previous best, with an in-distribution to out-of-distribution accuracy gap of 1.24 points. PRISM also achieves the highest OOD accuracy on three additional datasets (LifeSnaps anxiety, MFAFY engagement, CrossCheck schizophrenia symptoms), with consistently smaller ID-to-OOD gaps than fine-tuned VLM baselines. Ablations identify the frozen coherence constraint as the component responsible for the distribution-invariance pattern.

A neural network trained on the multiplication table of the quaternion group Q₈ can achieve perfect accuracy within each cyclic subgroup ⟨i⟩ and ⟨j⟩, predict every cross-region product wrong, and stay there indefinitely. This is the grokking plateau, and we prove its height is exactly 4 in dimension d=2, determined by the topology of the overlap before any training. The mechanism is a homotopy pullback: for G = A ∗_C B with finite overlap, the representation space of G is a homotopy pullback of those of A and B over that of C, so locally accurate modules need only agree up to a basis change. From this we derive a stratified generalization certificate whose strata are the connected components of Hom(C, U(d)): in the correct stratum, with locally accurate modules, the cross-region prediction is O(ε)-close to the target; in the wrong stratum it is provably far regardless of local accuracy, with exact gap c = 2(d − rₘₐₓ) for central cyclic overlap. The plateau is therefore the time the network spends in the wrong stratum, the grokking transition is the discrete jump between strata, and the framework predicts which task families exhibit such plateaus—those whose overlap representation space is disconnected—and which do not.

Domain Generalization (DG) aims to leverage multiple source domains to train models that can generalize to unseen target domains, thereby mitigating the performance degradation caused by domain shifts. Most existing approaches impose unified alignment or suppression constraints in the global feature space, overlooking the heterogeneity of feature channels in terms of class discriminativeness and domain stability. Such coarse-grained constraints may lead to the loss of discriminative information or the retention of domain-sensitive features. To address this issue, we propose a novel DG framework consisting of two core modules: Channel Sensitivity Decomposition (CSD), which employs channel-wise response variances along the class and domain dimensions as empirical proxy signals to partition feature channels into four functional subspaces via a continuous and differentiable soft decomposition mechanism; and Subspace-Specific Feature Augmentation (SSA), which implements tailored augmentation and regularization strategies for different subspaces to suppress environment-related spurious correlations while preserving cross-domain stable discriminative features. Additionally, a KL-divergence-based prediction consistency constraint is introduced to stabilize the training process and enhance model robustness. Extensive experiments on multiple standard DG benchmarks demonstrate that our framework consistently outperforms state-of-the-art methods.

This paper aims at analyzing the regularization effect that data augmentation induces on supervised regression methods in the proportional regime, where the number of covariates grows proportionally to the number of samples. We provide a tight characterization of the test error, measured in mean squared error, in terms only of the population quantities of the true data, as well as first and second order statistics of the augmentation scheme. Our results are valid under misspecified feature maps, and for any network architecture where only the last readout layer is trained, and the rest of the network is either frozen or randomly initialized. We specify our results in the case of Gaussian data, and show that our asymptotic characterization is tight in this setting.

We investigate the use of formal methods to provide tight and sound generalization bounds for learning algorithms. By casting the traditional notion of algorithmic stability as a specification to be verified, we demonstrate that recent advances in reachability analysis can yield provable bounds on the generalization of a given model and algorithm on a sample dataset. As sample-specific algorithmic stability is insufficient to bound the usual distributional notion of generalization, we develop a novel concentration inequality to connect the sample-specific results of formal certification algorithms to the required distributional analysis.The resulting framework enables the theoretical analysis of prior generalization bounds to extend far beyond their original restrictive analytical assumptions while achieving a provably sound bound on the generalization gap. In practice, we demonstrate that our framework provide formal generalization guarantees that are orders of magnitude tighter than alternative computational approaches at scales ranging from toy datasets to fine-tuning of modern large language models. While we implement certification-enhanced versions of several well-known stability results, future extensions of our approach will enable tighter bounds and enhanced practical adoption across the spectrum of modern generalization bounds.

Many studies argue that the success of sharpness-aware minimization (SAM) is due to the implicit regularization of the gradient norm or the eigenvalues of the Hessian. However, they cannot fully explain why the flatness-based measures do not always correlate well with generalization. For instance, we can easily construct a counterexample by only optimizing with hard examples. In this paper, we propose to resolve such a contradiction from the perspective of anti-overfitting. First, we show that the sharpness at the mini-batch level approximately equals the sum of the gradient norm and the Kullback–Leibler (KL) divergence between the predictive distributions evaluated at the current point and its adversary. Second, we show that the \emph{gradient consistency}, which approximately quantifies the inner product between the mini-batch gradient and the per-example gradient, decreases consistently during training. This result explains why SAM is less likely to suffer from overfitting. At last, building on these insights, we further introduce CASAM, an algorithm that reweights each example according to gradient consistency to enhance the generalization performance. Extensive experiments on popular benchmarks such as ImageNet-1K and Clothing1M corroborate its efficacy.

Recently, deep neural networks on manifold-valued representations have garnered significant attention across various machine learning applications. One recent focus is the generalization of Euclidean fully connected (FC) and convolutional layers to non-Euclidean geometries. However, previous approaches typically focus on a few selected manifolds and rely on specific properties of the target manifold. In contrast, this work proposes a framework for constructing FC and convolutional layers over computationally tractable Riemannian spaces. This framework incorporates several previous FC layers across different geometries as special cases and is instantiated on ten representative manifolds, including three hyperbolic models, five geometries of the symmetric positive definite (SPD) manifold, and two Grassmannian perspectives. Experiments on different manifolds demonstrate the effectiveness and applicability of our approach.

Sharpness-Aware Minimization (SAM) is widely used in domain generalization to promote flat minima that generalize to unseen distributions. Existing SAM-based methods typically penalize the sharpness of the *average* loss across domains. We show that this prevailing formulation—termed AvSAM—has a fundamental geometric limitation: it can favor solutions with misaligned domain-wise dominant Hessian eigenvectors. As a result, such solutions may appear flat on average while remaining sharp within individual domains. To address this limitation, we propose an alternative objective that penalizes the average *domain-wise* sharpness. We show that this objective decomposes into the AvSAM objective plus a non-negative residual term, which we call the *Cancellation Gap*. This gap is minimized if and only if the domain-wise dominant eigenvectors are aligned up to sign, indicating that it mitigates AvSAM's tendency to favor misaligned solutions. However, we further uncover a degeneracy: the Cancellation Gap can become small without improving alignment when sharpness is highly imbalanced across domains. To mitigate this failure mode, we propose Cancellation Gap Minimization (CGM), which augments the objective with a squared coefficient-of-variation ($\mathrm{CV}^2$) regularizer to discourage sharpness imbalance. Experiments show that CGM achieves the best average performance across standard domain generalization benchmarks among strong baselines. Diagnostic analyses further confirm reduced domain-wise sharpness and improved alignment of dominant Hessian eigenvectors.

Deep click-through rate (CTR) models commonly consist of sparse embedding blocks and feature-interaction blocks, which jointly learn predictive signals from high-dimensional categorical features. This naturally raises the question of whether different blocks in an end-to-end trained CTR model play the same role in generalization. To address this question, we investigate the generalization behavior of deep CTR models from a block-wise diagnostic perspective. Specifically, we formulate deep CTR models as two-block systems comprising an embedding block and a feature-interaction block, and introduce a retuning-based diagnostic protocol to separately assess the transferability of different blocks. Experiments across multiple datasets and architectures reveal a consistent asymmetric generalization pattern: the embedding block exhibits stronger training-set specificity, whereas the feature-interaction block preserves comparatively more transferable structure. Motivated by this diagnosis, we further develop a component-selective embedding aggregation method that averages multiple independently retuned embedding tables while keeping the feature-interaction block fixed. The resulting model retains the original single-path inference architecture and incurs no additional online inference cost. Experiments on Avazu, Criteo, and Taobao show that the proposed method improves representative deep CTR models over standard training and retuning baselines.

Despite the growing popularity of Multimodal Domain Generalization (MMDG) for enhancing model robustness, it remains unclear whether reported performance gains reflect genuine algorithmic progress or are artifacts of inconsistent evaluation protocols. Current research is fragmented, with studies varying significantly across datasets, modality configurations, and experimental settings. Furthermore, existing benchmarks focus predominantly on action recognition, often neglecting critical real-world challenges such as input corruptions, missing modalities, and model trustworthiness. This lack of standardization obscures a reliable assessment of the field's advancement. To address this issue, we introduce MMDG-Bench, the first unified and comprehensive benchmark for MMDG, which standardizes evaluation across six datasets spanning three diverse tasks: action recognition, mechanical fault diagnosis, and sentiment analysis. MMDG-Bench encompasses six modality combinations, nine representative methods, and multiple evaluation settings. Beyond standard accuracy, it systematically assesses corruption robustness, missing-modality generalization, misclassification detection, and out-of-distribution detection. With $7, 402$ neural networks trained in total across $95$ unique cross-domain tasks, MMDG-Bench yields five key findings: (1) under fair comparisons, recent specialized MMDG methods offer only marginal improvements over ERM baseline; (2) no single method consistently outperforms others across datasets or modality combinations; (3) a substantial gap to upper-bound performance persists, indicating that MMDG remains far from solved; (4) trimodal fusion does not consistently outperform the strongest bimodal configurations; and (5) all evaluated methods exhibit significant degradation under corruption and missing-modality scenarios, with some methods further compromising model trustworthiness. We release MMDG-Bench to enable more rigorous, reproducible, and directly comparable evaluation, addressing current limitations in evaluation practices and providing a stronger foundation for future progress in multimodal domain generalization.

Humans, animals, and modern machine learning models exhibit impressive abilities to learn complex behaviors and generalize these behaviors to unseen situations. This ability requires us to learn rules and regularities that allow for such generalizations. At the same time, in most complex environments, any rule will have its exceptions. How do learning systems balance between learning general regularities and memorizing exceptions? We argue that a lack of task paradigms has hindered the study of this essential ability. To address this gap, we introduce a novel task, transitive inference with exceptions, that tests for relational generalization and memorization of an exception to the relational rule. We then analytically characterize the behavior of a simple, theoretically tractable model of neural network learning (kernel ridge regression) across a broad family of representations and task parameters. We find that these models can balance between relational generalization and memorization, but unlike for transitive inference without an exception, successful generalization is sensitive to the specific representational geometry. We explain why this task is more challenging mechanistically by drawing on our analytical theory. Finally, we validate our theoretical insights in pretrained language models that are finetuned on ordered relations, finding that these models successfully generalize according to the transitive rule, but also make the kinds of systematic mistakes predicted by our theory. Overall, our theory shows how learning systems can balance between relational generalization and memorization, explains how this can go wrong, and emphasizes the need for new task paradigms designed to probe this ability.

Vision-language models are designed to capture the compositional structure of the world through multi-modal alignment; however, it remains unclear whether their representations truly align with the way a human would naturally describe the same visual input. Prior works attempt to decompose visual embeddings into their concept-level contributions, but their instance-level optimization is inherently local and does not capture the model’s global semantic structure, which is essential for compositional generalization across different inputs, tasks and domains. We introduce GRACE, a method that learns this concept-based structure at the feature space level, producing semantic and general concept decompositions. To achieve this, we propose a novel training objective that preserves the geometric relations of different samples in the concept space, enabling a better understanding of how concepts compose and relate to each other. We validate GRACE on several image and video benchmarks, showing that its concept decomposition is aligned with human perception and achieves faithful decompositions across different tasks and domains. With minimal overhead, GRACE makes existing Vision-Language Models more interpretable, while preserving most of their original performance.

Helpful-only models—that is, models that are trained to always follow user intent—are valuable for dangerous capability evaluations and other areas of AI R&D where refusals would be an obstacle. Little is known about the generalization properties of helpful-only training: they refuse less than their harmless counterparts, but previous work has not studied other dimensions of their alignment. We find that existing helpful-only models have serious shortcomings. Some show emergent misalignment, others have residual refusal behaviors, and most show poor steerability, sycophancy, and an incoherent character. We show that simple anti-refusal training can cause many of these issues. None of these problems are necessary consequences of helpful-only training, though: we show that synthetic document fine-tuning and adding character-related questions to SFT and RL can mitigate them.