NeurIPS 2026 论文列表

Kalman filtering provides a principled inference framework for linear Gaussian hidden Markov models, but it leaves open a complementary question of representation: what is the minimum amount of information about the observation history that must be retained to support accurate filtering? We show that this question leads naturally to an indirect rate-distortion problem, in which an encoder observes the history of noisy measurements while distortion is evaluated with respect to the latent state. Directly solving this problem is challenging, since the optimization ranges over arbitrary stochastic kernels from a time-varying observation history to an output representation, resulting in an infinite-dimensional formulation. We overcome this difficulty by proving that any feasible encoder can be replaced by a stochastic encoder acting only on the Kalman posterior mean, achieving the same mean-square error with no larger mutual information. The reduced problem admits a closed-form solution in the form of a linear Gaussian blurring mechanism determined by the spectral decomposition of the Riccati solution. This yields an explicit expression for the rate distortion function $R_t(\epsilon)$, showing that any representation with distortion at most $\epsilon$ must retain at least $R_t(\epsilon)$ nats of information. We further use this characterization to derive information-theoretic lower bounds on the population risk of sequential learning and on the prediction error of temporal GP. Numerical experiments corroborate the theoretical predictions.

Manifold learning is a fundamental task at the core of data analysis and visualisation. It aims to capture the simple underlying structure of complex high-dimensional data by preserving pairwise dissimilarities in low-dimensional embeddings. Traditional methods rely on symmetric Riemannian geometry, thus forcing symmetric dissimilarities and embedding spaces, e.g. Euclidean. However, this discards in practice valuable asymmetric information inherent to the non-uniformity of data samples. We suggest to harness this asymmetry by switching to Finsler geometry, an asymmetric generalisation of Riemannian geometry, and propose a Finsler manifold learning pipeline that constructs asymmetric dissimilarities and embeds in a Finsler space. This greatly broadens the applicability of existing asymmetric embedders beyond traditionally directed data to any data. We also modernise asymmetric embedders by generalising current reference methods to asymmetry, like Finsler t-SNE and Finsler UMAP. On controlled synthetic and large real datasets, we show that our asymmetric pipeline reveals valuable information lost in the traditional pipeline, e.g. density hierarchies, and consistently provides superior quality embeddings than their Euclidean counterparts.

The advancement of large language models~(LLMs) has significantly accelerated the development of search agents capable of autonomously gathering information through multi-turn web interactions. However, existing benchmarks often construct queries backward from answers, producing tasks misaligned with real-world needs. Moreover, these benchmarks tend to focus on either locating specific information or aggregating information from multiple sources, while relying on static answer sets prone to data contamination. To bridge these gaps, we introduce GISA, a benchmark for General Information-Seeking Assistants comprising 373 human-crafted queries reflecting authentic information-seeking scenarios. GISA features four structured answer formats (item, set, list, and table), enabling deterministic evaluation. It integrates both deep reasoning and broad aggregation within unified tasks, and includes a live subset with periodically updated answers to resist memorization. Notably, GISA provides complete human search trajectories for every query, serving as valuable references for analyzing and improving search agent behavior. Experiments on mainstream LLMs and commercial search products reveal that even the best model achieves only 19.30% exact match, with performance notably degrading on tasks requiring complex planning and comprehensive information gathering.

Multimodal Large Language Models (MLLMs) can listen and see, but how do audio and visual signals actually travel through the network to shape an answer? Despite their growing role in research and real-world applications, the internal pathways through which audio and visual tokens influence the final prediction remain poorly understood. In this study, we examine audio-visual information flow inside Audio-Visual Large Language Models (AVLLMs), tracing how AVLLMs route, utilize, and integrate audio and visual information across two input configurations, audio-visual video and multiple interleaved audio-visual items. We find that for audio-visual video, AVLLMs follow the sequential information flow pathway established for VLMs and VideoLLMs, with audio and visual contribution flowing along this pathway in proportion to the task's reliance on each modality. In settings with multiple interleaved audio-visual items, this routing shifts to different parallel streams. Furthermore, we demonstrate that audio-visual and other token types can be discarded once their information is transferred to LLM, with minimal impact on the model's prediction or even slight improvement, generalizing across multiple tasks and datasets, enabling more efficient inference. These findings hold across multiple models and scales, Qwen2.5-Omni and Video-SALMONN2 Plus at 3B and 7B scales, leading to hypotheses on why these flow structures emerge. Together, these results deliver the first coherent picture of how AVLLMs orchestrate sound and sight inside the network and lay the groundwork for the next wave of interpretability, design, and efficiency advances in audio-visual and broader MLLMs.

Modern models can have high average accuracy and benign loss tails while remaining fragile on rare subpopulations. We identify an information-geometric mechanism: after nuisance projection, the task direction can become locally nonidentifiable even when loss and raw Fisher look well behaved. Fisher-Glass certifies this failure by applying CVaR to inverse nuisance-projected task information. We prove a loss--information separation theorem and show that, under a boundary-mass condition, the hidden-environment tail of inverse projected Fisher controls robust classification sample complexity. We then derive stable ridge certificates and repair principles: reserves lift Fisher-null tails, portfolios increase collapse codimension, and tail-transverse influence selects counterfactual repairs by combining Fisher-Glass directionality with loss leverage. Synthetic experiments validate the theory; WILDS/Waterbirds diagnostics show that weakest identifiability need not mean lowest accuracy; and Waterbirds training plus counterfactual repair show that Fisher-Glass controls an identifiability axis complementary to loss.

A fruitful approach towards understanding generalization in machine learning involves characterizing how models separate generalizable structure from idiosyncratic or even corrupted features of training data. Fisher information has emerged as a diagnostic tool for this separation, leveraging loss geometry to distinguish generalization from memorization. Here we investigate this connection in vision models trained on CIFAR-10 with controlled label noise that can be learned only through memorization. We show that projecting model weights onto the top Fisher eigenvectors decouples general task performance from noisy sample memorization, and we identify the layer in which this decoupling emerges. We show that the same phenomena are present in small transformers trained to perform in-context learning and reproduced in closed form in a simple, analytically solvable linear model. Our results reveal that Fisher information captures aspects of the geometric structure underlying how neural networks allocate capacity between generalization and memorization.

Building on SODA 2026 work Kearns et al. (2026), we study learning in directed acyclic graphs in which each agent observes only a subset of the input coordinates and may use the predictions of its parents as additional features. In the finite-sample protocol, the message sent along each edge is the agent's prediction vector on a shared sample, so the communication cost is linear in the sample size $m$. In this paper we study this model under communication constraints. First, we revisit the finite-sample analysis of the full-message protocol. We identify a gap in the finite-sample proof of Kearns et al. (2026) and develop a different argument that establishes a finite-sample population-risk guarantee along paths satisfying deterministic $M$-coverage. Second, we introduce a shared-sketch protocol in which each agent sends a $k$-dimensional linear sketch of its prediction vector instead of the full $m$-dimensional message, where $k\ll m$. We analyze this protocol through a reduction to least squares on the compressed sample together with an oblivious subspace embedding argument. The resulting bound separates statistics from communication: the statistical term is still governed by the original sample size $m$, while the additional error due to compression is controlled by the sketch dimension $k$. For Gaussian sketches, we obtain an explicit high-probability population-risk bound, showing that row subsampling is not the only possible communication-statistics tradeoff for networked information aggregation.

Fine-tuning is often believed to reduce uncertainty and diversity in large language models, but existing analyses overlook output length, a key confounder, and therefore fail to capture how uncertainty is distributed across an entire generation rollout. To address this, we propose Canopy Entropy ($\mathrm{CE}^\star$), a measure that views language generation from a tree perspective, where "canopy" represents the space of all possible rollouts, making $\mathrm{CE}^\star$ naturally quantify the effective size of the generation space. $\mathrm{CE}^\star$ jointly captures the output length $N$ and the generated sequence $Y_{1:N}$, and we show that it equals to total Shannon entropy $H(N, Y_{1:N}\mid X)$, where $X$ denotes the prompt. This formulation yields interpretable metrics, including a length--uncertainty correlation term $\rho(N, r_N)$, where $r_N$ is the entropy rate, quantifying information conveyance efficiency by indicating whether longer outputs are more or less informative per token. Empirically, across tasks and model families, we find that fine-tuned models consistently exhibit stronger positive correlation $\rho(N, r_N)$, even when total entropy decreases. Furthermore, after controlling for model family, task, prompt, and output-length effects, we find that fine-tuning nearly triples the strength of the relationship between entropy rate and semantic diversity, suggesting that aligned models convert uncertainty into semantically meaningful variation much more efficiently. Overall, these results suggest that fine-tuning does not simply reduce uncertainty, but fundamentally reorganizes it into more informative and semantically meaningful generations.

Diffusion models generate data through a continuum of denoising problems, and are widely observed to reveal coarse structure before fine detail. Yet, this intuition is mostly empirical and qualitative. We introduce \emph{feature information dynamics}, an information-theoretic framework for localizing when a feature is generated during diffusion. Using the I-MMSE identity, we connect the rate of feature mutual information change to a gap between optimal unconditional and feature-conditional denoising losses, yielding practical estimators for feature information density. We further develop a chained decomposition that separates shared from incremental information in a feature hierarchy. We use this framework first to quantitatively confirm spectral autoregression in pixel diffusion, and then to extend the analysis beyond frequency: under a class$\to$mask$\to$Canny conditioning chain, the per-feature information densities differ across pixel, SDVAE, VAVAE, and RAE, exposing fundamental differences between these representations.

We introduce a novel Mutual Information (MI) estimator that fundamentally reframes the discriminative approach. Instead of training a classifier to discriminate between joint and marginal distributions, we learn a normalizing flow that transforms one into the other. This technique produces a computationally efficient and precise MI estimate that scales well to high dimensions and across a wide range of ground-truth MI values.

On-device machine learning exposes deep neural networks as white-box artifacts, making them vulnerable to model-stealing attacks. Trusted Execution Environments (TEEs) mitigate this risk by isolating model execution, but running entire models inside TEEs incurs prohibitive overhead. To balance security and efficiency, prior work proposes TEE-Shielded DNN Partitioning (TSDP), which executes privacy-insensitive components on GPUs while confining sensitive layers to TEEs. We demonstrate that existing TSDP schemes remain vulnerable because exposed GPU weights provide an effective warm start. This allows adversaries to exploit inevitable information leakage and reconstruct high-fidelity surrogates using only a fraction of the training data. To address this vulnerability, we propose FILOsofer, a principled defense that strategically obfuscates exposed weights using Fisher Information. By deliberately rendering leaked weights misleading, FILOsofer steers an adversary’s initialization away from the true optimum. To recover user-side accuracy, we introduce a novel cross-layer LoRA mechanism that efficiently restores performance while storing only lightweight LoRA parameters inside the TEE. Extensive evaluation in real-world settings shows that FILOsofer achieves black-box–equivalent security in the worst case, while reducing computational overhead by more than $50\times$ compared to prior approaches.

Memorization in large language models has been studied almost exclusively through prefix-conditioned extraction, a natural choice for autoregressive models. However, diffusion language models (DLMs) can denoise masked tokens at arbitrary positions. Thus, prefix-only probing reveals only one facet of memorization in DLMs and significantly underestimates the risk of training-data extraction. In order to realistically model extractability of training data in DLMs, we introduce infilling extraction, a data-extraction protocol parameterized by an arbitrary binary mask that subsumes prefix-only probing and accounts for the bidirectional inductive bias of DLMs. Instantiating it on LLaDA-8B and Dream-7B across five extraction modes, three training pipelines, and three corpora covering verbatim and partial leakage, we find that mask geometry governs extractability: edge-conditioned masks extract up to three times more verbatim sequences than prefix-conditioned ones, and bidirectional access opens channels inaccessible in autoregressive models. In particular, we show that a realistic adversary with access to training data where personally identifiable information has been redacted, can even achieve higher recall on extracting redacted email addresses from DLMs than from scale-matched autoregressive models. Tunable parameters for decoding measurably affect extraction performance, while a follow-up supervised finetuning stage does not eliminate the prior memorization.

Multimodal learning has advanced visual understanding through powerful multimodal LLMs (MLLMs). In visual generation, however, these models are often used only as global text or context encoders for diffusion generators, limiting their ability to provide structured spatial and temporal guidance. This creates an interface gap: MLLMs can parse complex layouts, attributes, and knowledge-intensive scenes, yet current generation pipelines often struggle to transfer such understanding into images and videos with precise, controllable structure. We propose MetaCanvas, a lightweight framework that organizes MLLM representations into spatially indexed canvas tokens and interfaces them with diffusion generators through patch-wise residual fusion. This provides structured spatial and spatiotemporal conditioning rather than relying only on a single global embedding or 1D query sequence. We implement MetaCanvas on three diffusion backbones and evaluate it across six generation and editing tasks requiring precise layouts, robust attribute binding, and fine-grained multimodal control. Under matched settings, MetaCanvas consistently improves over global-conditioning baselines, narrows the gap to specialized closed-source visual generation and editing systems, and unlocks new editing and in-context capabilities for video diffusion backbones. These results suggest that spatially aligned MLLM-derived canvas tokens provide a promising latent interface for transferring multimodal understanding into diffusion-based generation.

Large language models (LLMs) are often ensembled together to improve overall reliability and robustness, but in practice models are strongly correlated. This raises a fundamental question: which models should be selected when forming an LLM ensemble? We formulate budgeted ensemble selection as maximizing the mutual information between the true label and predictions of the selected models. Furthermore, to explain why performance can saturate even with many models, we model the correlated errors of the models using a Gaussian-copula and show an information-theoretic error floor for the performance of the ensemble. Motivated by these, we propose a simple greedy mutual-information selection algorithm that estimates the required information terms directly from data and iteratively builds an ensemble under a query budget. We test our approach on four datasets spanning binary and multi-class classification and sentiment analysis: MEDMCQA, MMLU, AG News, and IMDB. Across all datasets, we observe that our method consistently outperforms strong baselines under the same query budget.

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.

Benchmarks for large language models typically evaluate the accuracy of answers against fixed reference labels. But a central step in many complex real-world tasks is identifying which questions are worth asking in the first place: decomposing a difficult problem into subquestions whose answers provide key steps on the path toward solving the larger problem. To evaluate this capability of information discovery, we introduce CruxBench, a benchmark that grades LLM-generated questions by their Value of Information (VOI): how much a model-proposed subquestion updates beliefs about a target outcome. To automate this measurement at scale, we target as outcomes the prices in continuously updating forward-looking prediction markets. Our benchmark has three rare properties: it is contamination-resistant by construction, since ground truth is generated by future world events; it is open-ended, admitting unbounded and complex text-based submissions rather than one correct numeric answer; and it is grounded, with informativeness measured against quantified changes in real-world beliefs (prices). We evaluate eight frontier and open-weight models on 336 target outcomes and find that VOI correlates highly with independent measures of model quality ($r=0.87$) and predicts downstream usefulness when the generated questions are passed to a separate forecasting agent.

We study finite-horizon two-player zero-sum perfect-recall partial-information games and ask for the minimal finite-dimensional state sufficient to answer all rooted observation-measurable unilateral continuation queries. For each player $i$ and information set $I$, we consider the span $\mathcal L_i(I)$ of feasible counterfactual beliefs and the effective local query space $\mathcal E_i(I)$ generated by rooted continuation queries restricted to $\mathcal L_i(I)$. We prove that its dimension $d_i(I)$ is simultaneously the rank of the local counterfactual query operator, the minimum core-query basis size, the minimum exact local realization dimension, and the dimension of the canonical quotient $\mathcal L_i(I)/\mathcal N_i(I)$, yielding reduced counterfactual predictive-state representations, unique up to similarity, with exact first-return update operators. Aggregating the local ranks defines the deviation-conditioned predictive-state dimensions $d_t^i$, $d_t$, $d_\star$, and $D_\star$. We then prove that local rooted payoff-query control transfers to global exploitability, and under local design richness and bounded one-step parameter norms obtain a rollout-based upper bound in these minimal coordinates. We complement this with a minimax lower bound showing that $\Omega(d/\gamma^2)$ local rollouts are necessary even when the peak DCPSD equals $d$, and with an exponential separation theorem exhibiting games with $d_\star=m$ but observable continuation-trace complexity $2^m$. Finally, we show that DCPSD recovers finite-rank predictive-state, observable-equivalence, and linearly parameterized continuation-law models as special cases.

Circuit extraction identifies model components that preserve a target behavior under ablation, yet it remains unclear which parts of the reported circuit—components, edges, or coarser summaries—remain stable across reasonable extraction choices. We study this question in a Lean-style, rule-generated tactic-prediction benchmark spanning atomic and compositional proof tasks. The proof-state rules and task structure are fixed by construction, and dense and weight-sparse variants of one transformer architecture are compared. In this controlled setting, we compare three ways to describe a circuit: a compact prediction-preserving circuit, a broader graph that keeps read, write, and routing components around that circuit, and a pruning graph whose size is set by a target post-ablation loss budget. We vary model sparsity, whether the query and key sides of attention are represented together or separately, the post-ablation loss budget for the pruning graph, and which supervised checkpoint initializes reinforcement learning (RL). When the same extraction method is used, dense and weight-sparse checkpoints overlap far more in the set of attention heads identified than in exact component-to-component edge lists. This head-level overlap is well above a random top-$k$ baseline; the exact-edge overlap is not consistently so. Tracking query and key sides separately, and varying the loss budget across the tested range, preserves the ordering of the RL initialization conditions when each graph is summarized by how many components it selects. Among these RL conditions, the largest gains on compositional tasks are accompanied by the largest fraction of compositional-task circuit nodes that lie outside the matched atomic-task circuits. These findings show that, even in this controlled setting, behavior preservation under ablation does not determine a unique circuit-level conclusion: the conclusion depends on which graph is reported, how it is extracted, and at which level of description the comparison is made.

Autoregressive language models (ARMs) have been shown to memorize and occasionally reproduce training data verbatim, raising concerns about privacy and copyright liability. Diffusion language models (DLMs) have recently emerged as a competitive alternative, yet their memorization behavior remains largely unexplored due to fundamental differences in generation dynamics. To address this gap, we present a systematic theoretical and empirical characterization of memorization in DLMs. We propose a generalized probabilistic extraction framework that unifies prefix-conditioned decoding and diffusion-based generation under arbitrary masking patterns and stochastic sampling trajectories. Theorem 4.3 establishes a monotonic relationship between sampling resolution and memorization: increasing resolution strictly increases the probability of exact training data extraction, implying that autoregressive decoding corresponds to a limiting case of diffusion-based generation by setting the sampling resolution maximal. Extensive experiments across model scales and sampling strategies validate our theoretical predictions. Under aligned prefix-conditioned evaluations, we further demonstrate that DLMs exhibit substantially lower memorization-based leakage of personally identifiable information (PII) compared to ARMs.