NeurIPS 2026 论文列表

This position paper argues that understanding generalization in diffusion models requires fundamentally new theoretical frameworks that go beyond both classical statistical learning theory and the benign overfitting paradigm developed for supervised learning. In diffusion models, unlike in supervised learning, memorization of training data and generalization to novel samples are incompatible: a model that has fully memorized its training set generates copies rather than novel data. Several theoretical explanations for why practical diffusion models nevertheless generalize have been proposed, based on capacity limitations, implicit regularization from optimization, or architectural inductive biases, but their interactions remain unclear. We argue that the field should pivot from explaining why the diffusion models do not memorize to investigating what the models actually learn during pre-memorization phase. To highligh our stance, we conduct empirical study of diffusion models trained on CIFAR-10, and we distill the findings into concrete open questions that we believe are key to improve understanding of generalization in diffusion models.

Recent advances in Time Series Foundation Models (TSFMs) increasingly rely on axial attention mechanisms, but despite their empirical success, the theoretical properties of axial attention remain largely unexplored. To bridge this gap, we extend the Single Location Regression framework introduced in Marion et al. [2025] to 2D structured data, in order to study sparse information settings where a target depends on a small number of tokens. We formulate an analytically tractable axial attention-type predictor and rigorously analyze its statistical properties and training dynamics. We prove that under a specific asymptotic regime and with knowledge of the underlying oracle parameters, our predictor achieves Bayes optimality, whereas a class of semi-linear simplifications strictly fails to do so, underlining the role of the inner non-linearity. We prove that for a specific temperature scaling, Projected Gradient Descent converges globally to the optimal oracle parameters. Extensive numerical experiments validate our theoretical findings and highlight the critical role of inverse temperature scheduling in empirical convergence.

Graph Neural Networks (GNNs) have demonstrated remarkable effectiveness on graph-based tasks. However, their predictive confidence is often miscalibrated, typically exhibiting under-confidence, which harms the reliability of their decisions. Existing calibration methods for GNNs normally introduce additional calibration components, which fail to capture the intrinsic relationship between the model and the prediction confidence, resulting in limited theoretical guarantees and increased computational overhead. To address this issue, we propose a simple yet efficient graph calibration method. We establish a unified theoretical framework revealing that model confidence is jointly governed by class-centroid-level and node-level calibration at the final layer. Based on this insight, we theoretically show that reducing the weight decay of the final-layer parameters alleviates GNN under-confidence by acting on the class-centroid level, while node-level calibration acts as a finer-grained complement to class-centroid level calibration, which encourages each test node to be closer to its predicted class centroid at the final-layer representations. Extensive experiments validate the superiority of our method.

Large vision-language models (VLMs) often exhibit degraded safety alignment when visual inputs are integrated. Even when a text prompt is explicitly harmful, adding an image can substantially increase the jailbreak success rate. In this paper, we observe that VLMs can clearly distinguish benign, refusal, and jailbreak samples in their representation space, and that jailbreak responses often contain safety warnings. These observations lead to the \textit{recognize-but-fail-to-refuse} hypothesis: VLM jailbreaks do not arise from a failure to recognize harmful intent, but instead occur because adding an image induces a representation shift that steers the sample into a distinct jailbreak state where refusal is not triggered. To quantify how this image-induced representation shift contributes to jailbreak behavior, we define a jailbreak direction and characterize the jailbreak-related representation shift as the projection of the total image-induced shift onto this direction. Our analysis shows that the jailbreak-related shift reliably characterizes jailbreak behavior, providing a unified explanation for diverse jailbreak scenarios. Finally, we propose JRS-Rem, a defense method that enhances VLM safety by removing the jailbreak-related shift at inference time. Experiments show that JRS-Rem significantly improves VLM safety across multiple scenarios while preserving utility on benign tasks.

We study feature subsampling in greedy model search, a randomization mechanism motivated by random forests and other ensemble methods. While recent theory suggests that this randomization acts solely as a variance reduction mechanism analogous to ridge regularization, these results largely rely on base learners optimized via ordinary least squares (OLS). We investigate the effects of feature subsampling on greedy forward selection, a tractable abstraction of the adaptive split search used by decision trees. Assuming an orthogonal design, we prove that ensembling with feature subsampling can reduce both bias and variance, contrasting with the pure variance reduction of convex base learners. Specifically, we show that both the training error and degrees of freedom need not be monotone in the subsampling rate, breaking the analogy with standard shrinkage methods like the lasso or ridge regression. Furthermore, we characterize the exact asymptotic behavior of the estimator, showing that it adaptively reweights OLS coefficients based on their rank, with weights that are well approximated by a logistic function. These are mechanism level results for a tractable analogue of greedy selection that depends on the response, not performance guarantees for full random forests.

Private Evolution (PE) is a differentially private algorithm for synthetic data generation. While it can be viewed as a Wasserstein learning algorithm, it performs much better in practice than worst‑case Wasserstein analyses would predict. We recast PE as a generative model‑augmented Wasserstein learning. We show theoretically that when we take into account the use of a generative model that is able to capture something about the true distribution, then PE provably obtains much better performance bounds. For example, if the generator gives samples in the same low-dimensional space as the distribution, then the sample complexity depends on the intrinsic, not the ambient, dimension. We also show that standard variants of PE can fail to converge on simple well-clustered instances, and propose a new geometry-aware version of PE with provable convergence on such instances. Experimentally, we show that our new algorithm has consistent empirical gains over standard baselines.

Multi-view transformers solve 3D vision tasks in a single feed-forward pass, yet their internal mechanisms remain poorly understood. We view their residual layers as progressively updating a latent state, and study how this state evolves during 3D reconstruction. To make the state geometrically interpretable, we train layer-wise probes that decode intermediate tokens into 3D pointmaps, yielding intermediate 3D reconstructions throughout the network. This view recasts feed-forward 3D reconstruction as progressive refinement rather than a single reconstruction step, with most layers improving reconstruction. Convergence speed varies across models and sample difficulty, with slower convergence on difficult samples. We further analyze these updates and find consistent, complementary roles for single-view and cross-view attention. Cross-view attention improves multi-view alignment, while single-view attention refines intra-view geometry and compensates for points visible in only one view. Finally, we identify cross-view attention heads that specialize in correspondence matching. We show that their correspondences are jointly refined with the reconstructed geometry, and that selected heads can be partially replaced by analytical correspondences. Our analysis provides a direct view of the reconstruction process inside multi-view transformers, and suggests a first step toward replacing emergent mechanisms with analytical operations. The code used for the analysis will be made available.

Zero-shot model size interpolation aims to create new models of intermediate target sizes by combining existing models without additional training. Recent work on boomerang distillation [Kangaslahti et al., 2026] shows that a student language model distilled from a larger teacher can be expanded by iteratively patching its layers, replacing student layers with contiguous blocks of teacher layers to obtain models whose size and performance interpolate between the student and the teacher. In this work, we provide the first systematic study of student-layer selection for model size interpolation. We cast finding the optimal layer subset for each model size as an optimization problem and prove it can be viewed as a shortest-path problem in a certain acyclic graph. In experiments, we show that patching strongly shapes interpolation behavior, with effects that vary substantially across model families. We find that simple sequential strategies---patching either from the first layer to the last or from the last to the first---often achieve surprisingly strong performance in practice. We further introduce KLPatch, a greedy patching algorithm based on KL divergence, which often improves over last-to-first patching and approximately solves the optimization problem. Together, our results provide a principled understanding of how layer patching affects model size interpolation and offer practical guidance for constructing near-optimal interpolated models.

Classical statistical theory is insufficient to explain the successes of general-purpose AI models, because it depends on handcrafted inductive biases that it cannot justify. No Free Lunch theorems force any learner that beats chance on some environments to underperform on others, and meta-learning which environments are more likely only pushes the problem up a level. The inductive bias must therefore be grounded in something other than data. By deriving its bias from Turing universality, Solomonoff induction (SI) competes with all computable learners. However, its regret bounds include large ``constants,'' such as the size of a learner's (losslessly compressed) full codebase. We relativize SI to an information vantage point, which includes all pre-existing code and data. This reframes the inductive bias: instead of favoring some absolute notion of simplicity, we favor accessibility with respect to our vantage point. The relativized SI is sample-optimal on finite data: any learner that outperforms it necessarily contains inaccessible information about the data. While SI is incomputable and hence not a practical algorithm, it provides a formal optimum for inference in the limit of infinite compute. We argue that algorithmic information theory, which underlies SI, is necessary to explain the generalization behavior of modern (and future) AI systems.

Many deep learning models exhibit a double-descent phenomenon, where test loss exhibits a sharp peak near the interpolation threshold and then descends a second time as model size grows further, contrary to the U-shape predicted by the classical bias–variance tradeoff. The double-descent phenomenon has been found and explained in toy classical models, but is not well-understood in modern deep learning despite extensive empirical study. We interpret double descent through the novel lens of universal compression. Specifically, we upper bound the maximum-likelihood test loss as a sum of three terms: an approximation error, a minimax batch regret, and an MLE-vs-Bayes gap. We show that the minimax Bayes predictor, unlike the MLE, does not exhibit the double-descent peak. Furthermore, we isolate each term through experiments with uniform random labels, and show that double descent is primarily caused by the MLE-vs-Bayes gap in this setting; here, the MLE cross-entropy grows to be roughly five times larger at the double-descent peak, while the minimax Bayes predictor cross-entropy remains flat. Additionally, we show the possibility of a second ascent in test loss at very large model sizes, and motivate this theoretically through the minimax batch regret term of our decomposition.

CMinHash promises a new direction for designing MinHash algorithms with reduced variance and storage space via circulant permutations. However, the original variance analysis is difficult to extend to other MinHash estimators. We present a new approach that gives explicit and easily comparable approximate variance expressions, and use it to analyze the Minner estimator. Numerical experiments show that our variance expression matches the empirical mean square error (MSE) of estimates. Our work thereby demonstrates how to apply circulant permutation to other MinHash estimators and compute their approximate variance.

Advances in deep reinforcement learning have enabled the development of policies capable of solving complex, high-dimensional problems, allowing AI agents to strategize and reason purely through interaction without supervision. Despite these successes, our knowledge on the functional properties and the underlying structure of the deep neural policy manifold remains limited. In this paper, we uncover a fundamental functional property in reinforcement learning: the intrinsic alignment between the advantage function and the gradient of the loss targeting directions of incoherence. We provide a rigorous theoretical foundation for this relationship, demonstrating that this intrinsic alignment characterizes how policies learn and internalize the underlying value function and how this process governs policy decisions. By leveraging this fundamental functional property, we propose a novel algorithm that can diagnose and identify deep neural policy decision volatilities. We conduct extensive empirical analysis in high-dimensional MDPs. From algorithmic and architectural changes to natural distributional shifts and worst-case perturbations, our proposed method can identify and audit the differences by leveraging the underlying structure of the deep neural policy manifold and the intrinsic correlation. Our analysis reveals foundational properties of policies trained in high-dimensional MDPs, and our paper provides a principled step toward constructing scalable, stable, and generalizable deep reinforcement learning agents.

Population analysis methods have become standard for navigating the complexity of neural data. However, these methods often assume a rate code, neglecting information encoded in the precise timing of spikes. Critically, additional information encoded in bursts of action potentials may be missed. Here, we develop a factor analysis method that disentangles the factors associated with bursts and individual spikes. This enables burst codes to be investigated directly from the structure of the data, without requiring external covariates. We demonstrate that analyzing firing rates alone obscures the latent structure and factors underlying bursts. Applying our method to simulated and experimental data, we show that it can infer the correct latent structure and be used to test for the presence of burst coding. By merging the population and burst coding perspectives, we provide a framework for linking changes in bursting to internal variables involved in attention, perception, and learning.

While hierarchical structures are intrinsic to organizing human knowledge, current representation learning on text-attributed graphs predominantly operates on flat semantic spaces, overlooking the rich coarse-to-fine granularity inherent in real-world data. To bridge this gap, we propose SHiFT, which synergizes the reasoning power of LLMs with the structural representation capability of GNNs within an Expectation-Maximization (EM) paradigm. In the E-step, we harness LLMs as expert taxonomists to induce an explicit semantic tree, introducing a lightweight Mapping \& Diagnosis strategy that reduces inference costs by surgically updating the hierarchy only when anomalies are detected. In the M-step, we align the GNN encoder with this induced hierarchy from complementary perspectives, including clustering partition, topological skeleton, and semantic concepts. Theoretical analysis interprets SHiFT as a generalized Variational EM algorithm. Extensive experiments demonstrate that SHiFT not only achieves state-of-the-art performance but also uncovers high-quality, human-readable taxonomies.

Large language models can have hidden propensities: behaviours that arise only in rare contexts. These hidden propensities pose a challenge to alignment audits, which seek to uncover problematic model behaviour but are limited in scope to scenarios anticipated by the auditor. To address this challenge, we explore _limited-parameter finetuning_ (LPF) on examples of a target behaviour. While training 3–15\% of model parameters, LPF reveals whether the model has a hidden propensity, even when standard behavioural evaluations cannot. LPF succeeds on a suite of model organisms with hidden propensities (8B-14B parameters), and also surfaces naturally occurring hidden propensities in open-weight models (27-32B parameters). LPF can thus distinguish between behaviourally equivalent models, even without knowing the context in which the propensity surfaces. LPF provides a novel affordance that may be useful for auditing frontier AI models.

In reinforcement learning from limited feedback (RLLF), only a small fraction of an offline dataset can be labeled with rewards, and the central question is *which* samples should be labeled to learn a strong policy from the resulting partially labeled dataset. Prior work formalized this as a reward-selection problem by focusing on the selection stage while treating downstream policy learning as a black box, in a regime where queried rewards are not retained for reward-model training. We instead study the retained-label setting, where queried rewards can be stored and used to fit a reward model before policy learning. We bound the suboptimality of the learned policy by two sources of error: one from offline RL on an offline dataset, and one from reward-model uncertainty. Since reward selection cannot change the offline dataset, the limited labeling budget must be used to strategically reduce reward uncertainty. Motivated by RLLF's observation that useful rewards tend to keep the agent on high-return trajectories, we propose successor-guided uncertainty reduction (SURE), which uses successor features to select rewards that are both reachable to high-valued states and uncertainty-reducing. Theoretically, we derive SURE from a bound-induced design objective and characterize its exact one-step marginal gain. Empirically, SURE reaches near full-feedback performance with few reward labels across a variety of domains, yielding a strong method for feedback-efficient reinforcement learning.

Fine-grained visual classification (FGVC) with Multimodal Large Language Models (MLLMs) remains challenging, as visually similar subordinate categories inherently induce classification uncertainty due to subtle inter-class differences. Existing reinforcement learning methods typically require the model to generate a single class name and optimize it with sparse correctness rewards. However, a seemingly incorrect prediction can still provide highly informative signals if it falls within the same local confusion set as the ground-truth class. By treating all non-exact matches as equally wrong, the rigid single-answer paradigm overlooks these valuable near-misses. Consequently, it fails to capture the model's intrinsic uncertainty and provides limited learning signals. To address these limitations, we propose List-GRPO, an uncertainty-aware listwise Group Relative Policy Optimization framework. Rather than enforcing a single prediction, our method prompts the model to adaptively generate a ranked candidate list, explicitly capturing its predictive uncertainty. Furthermore, to mitigate the advantage vanishing when online exploration completely misses the target, we introduce a dynamic ground-truth anchored response strategy. We synthesize an off-policy anchor by prepending the ground truth to the most frequent hard negatives mined from online samples. To prevent the anchored response from dominating learning, we isolate the advantage estimation of online samples from the anchored response and use a gating coefficient to modulate its contribution. Extensive experiments on multiple fine-grained benchmarks demonstrate that List-GRPO significantly improves Top-1 accuracy while maintaining high ground-truth coverage with only about three candidate predictions on average.

Graph Contrastive Learning (GCL) is an effective approach for learning node representations. However, the intrinsic uncertainty of real-world graph data introduces significant challenges, as GCL relies on crisp deterministic representations that struggle to capture such ambiguity. To model graph uncertainty, fuzzy logic has attracted increasing attention due to its mathematical rigor. Existing methods, however, simply inject fuzzy modeling into the contrastive framework without tailoring data augmentation to the needs of fuzzy representations, resulting in limited discriminability and suboptimal downstream performance. To address these limitations, we propose a novel Fuzzy Graph Contrastive Learning (FGCL) framework for uncertainty-aware node representation learning. It adopts a vertex entanglement-based augmentation strategy to generate tailored multi-views with controlled perturbations while preserving core graph topology and semantics, mitigating semantic corruption. We also design a Deep Weighted Fuzzy Graph Convolutional Neural Network (DWFGCNN) encoder, which maps crisp features to fuzzy representations via learnable membership functions, explicitly models uncertainty, and resolves the core contradiction that traditional encoders cannot balance discriminability and robustness simultaneously. Extensive experiments on multiple datasets demonstrate that FGCL consistently outperforms baselines in node classification, community detection, and link prediction tasks, validating its effectiveness in handling uncertainty in graph representation learning.

The generalized orthogonal Procrustes problem (GOPP) aims to recover rigid transformations that best align multiple point clouds and has broad applications in 3D geometry, computer vision, and biomedicine. Despite its importance, the problem is challenging due to the nonconvex orthogonality constraints. Fortunately, the generalized power method (GPM) has proven highly effective, theoretically guaranteed to converge to the global least squares (LS) estimator under reasonable conditions. Yet, the statistical inference of this global LS estimator remains largely an open problem. Specifically, the absence of an exact second-order analytic expansion prevents rigorous uncertainty quantification (UQ), which is vital for constructing confidence regions and evaluating estimator reliability. While recent UQ frameworks developed for orthogonal group synchronization offer a potential paradigm, they severely lack universality, often failing to accommodate the complex anisotropic distortions inherent in GOPP shape matrices. To bridge this gap, we propose a more general theoretical framework with which we successfully derive the exact second-order analytic expansion of the GOPP global LS estimator under additive Gaussian noise. Leveraging this theoretical foundation, we further construct confidence regions. Finally, extensive numerical experiments empirically validate the exactness of our theoretical expansion and demonstrate the robust coverage of the proposed confidence regions across varying conditions.