NeurIPS 2026 Papers

Partitioned routed distillation is hard to interpret when route count, supervision grouping, and search or filtering budget change together. We study that attribution problem inside one fixed routed family using two matched nulls: a routing-only control (Latent-Routing MoA) and a structure-matched shuffled-partition control (Matched-Partition-Shuffle), with teacher tokens, trainable parameters, and router depth matched exactly. The decisive result is Table tab:main: the zero-manual deployable row ModeDistill-Auto-v4-Open, whose partition source is induced by GPT-OSS-120B-Instruct pairwise same-strategy judgments (Apache- 2.0 , distinct from the trace-generating teacher), beats MoA by +2.46 pp and Matched-Partition-Shuffle by +2.04 pp on the five-domain primary-shift average (A1), with positive OOD gaps on all five primary domains. Table tab:external_breadth_transfer is intentionally weaker evidence: for that exact same headline row it reports only four external benchmark aggregate means, where Auto-v4-Open beats MoA by +4.91 / +3.99 / +3.70 / +2.87 pp, and it does not support slice-wise breadth or cross-family generality. The open pipeline remains within 0.05 pp of the manual upper-bound reference on A1 and within the pre-specified 0.50 pp tie band on every external mean, so we keep it as the deployable row and retain the manual row only as calibration. The claim is therefore narrow: within this routed family, once routed budget is matched, the residual OOD gain is attributable to the externally induced partition source rather than to routing alone or to structure-matched shuffled partitions. Figure fig:identification and the appendix are corroborative only. The weakest primary shift remains ALFWorld tool reconfiguration ( +1.15 pp vs.\ MoA, paired CI [-0.12,+2.41] ), and discovery-time verifier calls and teacher generation are disclosed separately from the matched comparison.

Large language models are increasingly deployed for open-ended question answering, yet their answers rarely come with calibrated uncertainty. We propose CAELUM, a framework that builds semantic prediction sets and separates aleatoric from epistemic uncertainty in their construction. CAELUM samples answers under prompt-ensembled clarifications, clusters them by semantic equivalence, estimates aleatoric and epistemic components via kernel Von Neumann entropy, and calibrates cluster-APS nonconformity scores with split conformal prediction. A per-instance weight $w_\lambda(x)=1+U_{\mathrm{ale}}(x)+\lambda\,U_{\mathrm{epi}}(x)$ controls how epistemic uncertainty enters the set, and a per-cell coefficient $\lambda^\star$ is fit on a held-out split to minimise prediction-set size. Our central observation is that, in open-ended generation, coverage on cluster-APS scores is silently capped by \emph{matchability}: the fraction of items whose reference answer appears in any sampled cluster. We make this dependence verifiable with a Mondrian split-conformal bound on a learned stratum, where matchability is predicted from pre-generation question features by a lightweight classifier. Across $18$ (model, dataset) cells and four split seeds on three open-weight 4--9B LLMs, the learned classifier lifts predicted-matchable coverage from $0.61$ overall to $0.71$ on non-fallback rows ($0.82$ vs $0.63$ when oracle-fallback rows are included as upper bounds), and the classifier transfers across LLMs at AUC $0.78$ (in-sample $0.80$). The cell-level $\lambda^\star$ doubles as a regime diagnostic: large values flag epistemic dominance (retrieve, abstain) and $\lambda^\star\to 0$ flags aleatoric dominance (clarify), with a per-instance log-ratio $R(x)$ extending the read-out to individual queries.

Low-budget molecular optimization is often framed as Bayesian optimization in a learned latent space, but standard benchmarks typically allow hundreds or thousands of evaluations, whereas a realistic wet-lab round may allow only a few dozen. We revisit this regime using a SELFIES molecular variational autoencoder and GuacaMol objectives at $N=30$ oracle calls. The main finding is not a new surrogate model, but a geometric mismatch in candidate generation. The training latents of the VAE concentrate near a narrow spherical shell, while many high-dimensional optimizers propose candidates from boxes or box-shaped trust regions. Such candidates can leave the decoder's training distribution even when their coordinates look individually plausible. We study a simple geometric constraint, the on-sphere scaffold, that restricts candidate generation to the empirical shell occupied by the VAE training latents. Uniform random search on this shell already outperforms most of the classical box-supported Bayesian optimization baselines. We then introduce two minimal optimizers to probe what remains useful once the support is fixed. GeoWalk performs geodesic local search on the empirical sphere and outperforms every published Bayesian optimization baseline tested. GeoCMA keeps the scaffold but adds covariance learning in a random subspace, becoming preferable when the search representation contains learnable directional or semantic structure, as in LassoBench, NAS-Bench-101 graph-VAE optimization, and GSM8K text-latent prompt optimization. A controlled ablation of three recent Gaussian-process recipes, changing only whether candidates are proposed on the empirical sphere or on the published box-supported domain, shows that the scaffold rather than the surrogate is the load-bearing component. The practical lesson is simple: first match the empirical search support; add a surrogate or covariance learner only when the remaining search space contains directional structure that can be learned from the available budget.

In materials-science papers, quantitative evidence—XRD peak shifts, Raman ID/IG ratios, high-frequency Z′ intercepts in EIS—lives in line plots. Hosted vision–language models describe these plots fluently but cannot recover the (x, y) values an agent needs to query, compare, or integrate. We release three coupled artifacts. MatCurvs is a real-coordinate chart benchmark for materials-science spectra, organized in three tiers spanning XRD, Raman, XPS, XAFS, EIS, GCD, and CV: 1,375,165 classified subfigures from 55,763 articles (L0); 204 panels with manual per-curve pixel polylines (L1); and 8,026 verified real-coordinate curves over 3,817 panels (L2). MatDeplot is a local extractor that recovers 45.8% of curves within a 5-pixel IoU tolerance against L1 ground truth, versus ≤1.2% for the strongest hosted VLM—a 38× pixel-anchoring gap, closed in roughly 1.5 seconds per image. MatCurvs-Reasoning is a 14,740-question deterministic numerical evaluation: feeding MatDeplot’s extracted (x, y) data to an LLM cuts median relative error from 54% for an image-only VLM to about 4%, and a text LLM with the data alone matches the same VLM prompted with both image and data. By turning each published chart into a numerically queryable curve, the released artifacts let a deployer compute derived materials parameters—Raman ID/IG disorder ratios, XRD Scherrer crystallite sizes, and phase-purity audits—directly from a literature-scale chart corpus, where most papers under-report these numbers and the chart is the only available record.

Video models absorb rich priors over how the visual world moves, interacts, and responds to contact, making them promising substrates for robotic world modeling. The central challenge is how to communicate action to such models in a form aligned with the visual space in which they learned these interaction priors, yet still grounded in physical manipulation. We introduce Masked Visual Actions, a pixel-space control interface that expresses action as a partially revealed trajectory of an arbitrary entity in a video. Revealing robot motion makes the model act as a forward dynamics model that predicts the scene's response to low-level robot actions, while revealing desired object motion makes the same model recover robot behavior consistent with that outcome. Finetuned with only 15 hours of masked examples from real videos and simulation, a single checkpoint achieves strong visual fidelity and controllability across diverse scenes and multiple embodiments. In downstream manipulation settings, the model produces imagined rollouts whose outcomes correlate with real-world execution for policy evaluation, improves decision making by ranking candidate futures in model-based planning, and supports inverse modeling by synthesizing robot motion from desired object motion.

Optimization proxies amortize parametric constrained optimization by learning fast approximations of solution maps. Because these maps are smooth only within active-set regimes, the parameter space may split into combinatorially many critical regions, making finite-sample generalization and reliable constraint behavior central challenges. To address this challenge, this paper develops sparse stochastic masked Sobolev training for optimization proxies, augmenting value supervision with randomly selected solver-sensitivity targets rather than dense Jacobian matching. The mask acts as an algorithmic control: it exposes the proxy to local derivative information while avoiding overconstraint from conflicting active constraint set signals. We provide approximation bounds showing that, under coverage and regularity, joint value-and-Jacobian matching improves finite-sample generalization. Experiments characterize when and how this benefit appears. In smooth optimal-control distillation, where feasibility is guaranteed by construction, and only a few active-set regimes arise, Sobolev supervision reaches 95\% of teacher performance about $2.5\times$ faster than value-only training. In AC optimal power flow, masked Sobolev training keeps optimality gaps below 0.22\% across three PGLib networks while reducing the median worst-case constraint violation by up to $4\times$. A mean--variance portfolio study identifies the complementary limitation: when sensitivities are highly local or vanish across active-set regimes, derivative supervision can be less useful than value-only training.

Pixel-space diffusion models have recently seen a revival in image generation, yet their training remains less efficient than that of their latent-space counterparts. Existing methods reduce this cost by equipping diffusion models with external representations from clean images. In contrast, representation consistency training, a new generative pretraining paradigm, stands out as it eliminates the need of any off-the-shelf semantic encoders. It proposes pre-training the diffusion model to simultaneously capture meaningful visual semantics from clean images while aligning them with data points across various noise levels. Nevertheless, its training depends on contrastive learning with hand-crafted augmentations. This introduces strong semantic prior into the pretraining, limiting model performance when transferred to downstream target distributions that substantially deviate from the pretraining manifold. To address this, we propose Masked Pixel-space Generative Pretraining (MPG), an augmentation-free framework based on masked image modeling. MPG trains the encoder to recover masked image area and aligns those predictions with samples of different noise levels. To measure the performance of pretrained model, we further introduce NC-CKNNA, a metric that quantifies the semantic structure consistency across different noise levels. Under the same architectures and fine-tuning settings, MPG consistently produces better generation performance across seven downstream datasets, while retaining competitive generation quality on ImageNet-256. These results suggest masked generative pretraining as a practical alternative for training pixel diffusion models.

Temporal action localization (TAL) requires recognizing the target event and localizing its start and end times precisely in untrimmed videos. Recent vision-language formulations improve semantic reasoning and support language-conditioned outputs, but their autoregressive decoders still generate tokens from left to right, preventing later semantic evidence from revising earlier timestamp predictions. We adapt masked diffusion vision-language models (MDVLMs) to TAL so that semantic tokens and boundary tokens remain editable throughout iterative denoising with bidirectional attention, allowing temporal boundaries and semantic content to be refined jointly. Direct adaptation, however, creates two TAL-specific mismatches: standard masked diffusion training corrupts all positions uniformly at random, but the time tokens are more reliable when enough semantic context is available; and token-level cross-entropy does not reflect temporal IoU. To address these mismatches, we introduce a Planned Training Objective that uses boundary-aware masking and step-weighted reconstruction to rehearse the late recovery of time tokens, together with a Step-Level IoU Reward that provides overlap-aware supervision during denoising. A standard sequence-level cross-entropy term provides the base reconstruction signal. Experiments on ActivityNet-RTL, ActivityNet-1.3, and THUMOS-14 show that MDVLM-TAL improves both temporal reasoning and boundary localization over autoregressive vision-language baselines, with especially strong gains under stricter temporal IoU criteria.

Designing tool-integrated reasoning agent systems for complex chemical tasks remains a fundamental challenge. Although recent chemical agents have demonstrated promising performance through the integration of external tools, they are still built on the autoregressive paradigm, which is inherently constrained by causal attention and left-to-right generation. As a result, they often struggle with bidirectional molecular understanding, global coordinated tool planning and multi-source evidence integration. To address this challenge, we introduce ChemDiffAgent, the first masked diffusion language agent for tool-integrated chemical reasoning. It reformulates chemical reasoning as iterative denoising over interleaved reasoning and tool-use trajectories, enabling tool-use decisions to be jointly determined under full-trajectory context and thereby better aligning the agent's decision boundary with its knowledge boundary. We further analyze how this paradigm benefits agentic reasoning through harder infilling subproblems during training and flexible arbitrary-order decoding during inference. Then we develop a two-stage post-training framework, comprising agentic supervised fine-tuning and variance-reduced preference optimization, to enhance tool-use and reasoning capabilities. We also construct a comprehensive benchmark covering six chemistry tasks across both single-turn and multi-turn tool-use scenarios. Under matched budgets and evaluation, ChemDiffAgent consistently outperforms autoregressive agents, achieving an overall improvement of approximately 20\%. Notably, our 8B model achieves performance comparable to, in some cases surpassing, significantly larger frontier models, such as GPT 5.5 and Claude Opus 4.7.

While autoregressive models dominate the LLM landscape, Discrete Diffusion Language Models have emerged as a compelling alternative due to their advantages in parallel decoding and bidirectional contextual modeling. To enhance scalability and efficiency, recent works have integrated the Mixture-of-Experts architecture into the DLM framework. However, MoE-DLMs remain underexplored. In this work, we present an empirical study revealing that MoE-DLMs exhibit not only task-level expert specialization, but also exhibit specialization across different mask-rate diffusion regimes. We further show that during fine-tuning, gradients induced by mismatched mask rates can interfere with the updates of regime-specialized experts, leading to suboptimal adaptation. Motivated by this, we propose MaGM, an adaptive mask-conditioned gradient masking method for MoE-DLM fine-tuning, which dynamically masks expert parameter updates based on the mask rate of training instance. Experiments demonstrate that MaGM consistently outperforms standard full-parameter fine-tuning for diffusion language models, validating the benefits of regime-aware expert adaptation. Our code will be publicly released.

Existing unified 4D reconstruction and point tracking approaches typically rely on heuristic interpolations or just predict at integer timestamps, lacking kinematic coherence and failing to model dynamics at any arbitrary timestamp. In this paper, we propose Uni4R, a framework that unifies these tasks by learning continuous velocity fields through the synergy of Optimal Transport (OT) and Ordinary Differential Equation (ODE). Importantly, this continuous velocity field acts as a kinematic prior that mutually benefits both 4D reconstruction and point tracking. Specifically, we propose the Flow Matching Guided Decoder (FMGD). A global velocity branch first extracts anchor features that capture the global dynamic state of the sequence. Then, FMGD leverages Flow Matching (FM) theory to formulate a probability path defined by OT on the anchor feature manifold, instantiating it as FM-guided velocity features for velocity prediction. This establishes a robust kinematic inductive bias. Meanwhile, a point reconstruction branch provides geometric features. The local velocity prediction module then joint above features and time embeddings, to decode velocities at arbitrary timestamps. To overcome the absence of high-quality ground-truth velocities in fractional frames, we propose an integral-consistency training strategy. This strategy uses an ODE solver to integrate velocities to recover target pointmaps, enabling the model to be supervised end-to-end directly from integer timestamps. Experimental results demonstrate that Uni4R achieves SOTA performance in both 4D reconstruction and point tracking, and achieves SOTA in our new kinematics-aware benchmark at continuous time.

Neural trajectory predictors are increasingly used in physical-system pipelines for reconstruction, simulation, forecasting, and downstream analysis. In these settings, low prediction error alone is insufficient. A trajectory may remain statistically plausible while violating dynamics, actuator limits, or state constraints, making it unreliable for physical interpretation or control-aware reasoning. This problem is especially difficult when controls are unobserved and the available dynamics model is only partially specified. We introduce the Markovian Dynamics Enforcer (MaDE), a framework for post-hoc feasibility enforcement under learned controlled dynamics. MaDE acts as a time-invariant correction operator that maps state-transition proposals onto a learned feasible dynamics manifold. For each transition, it infers latent controls through inverse dynamics, recomputes state evolution using a known-physics model augmented with a learned residual, and corrects controls through gradient-based inequality reduction while re-integrating the dynamics after each correction step. MaDE is trained from feasible state observations without ground-truth controls and is designed to operate as a frozen downstream layer for arbitrary trajectory predictors. We evaluate MaDE on simulated controlled systems spanning fully specified and underspecified dynamics, with deterministic bound-violation and Gaussian observation-noise stress tests. MaDE is the only method that drives known-, learned-, and true-dynamics residuals to essentially zero across the fully specified systems. In the underspecified dynamic-bicycle setting, it reduces true-dynamics residual from 1.40--2.90 for the baselines to 0.33, while reducing trajectory fidelity error by more than 60% relative to the next-best method. These results show that MaDE enforces model-relative physical feasibility while preserving proximity to the original trajectory.

We study Metrical Task Systems, a broad class of problems in online algorithms, under a model where input requests are generated by a stochastic process. We first consider the case of requests drawn IID from an unknown distribution, and then extend the model to requests generated by a finite-state Markov chain, where the algorithm observes both the current request and the current state of the chain before making its next move. This formulation captures practical settings in which requests are generated by an evolving environment. In both settings, we show how to find in polynomial time an algorithm whose expected cost per step is arbitrarily close to the cost of the best possible online algorithm. Our theoretical results are complemented by a brief empirical evaluation of our algorithms.

LLM multi-agent systems rely on division of labor to solve complex tasks, but their execution can be blocked by contention for shared resources such as GPU test environments, CPU execution slots, and exclusive tool sessions. Existing workflows, task allocation methods, and runtime schedulers usually arbitrate such access indirectly through workflow position, dependency structure, queue state, or resource metrics. These criteria do not fully capture the value of satisfying a specific request, because request value is distributed across agents' local execution states and changes with tests, retries, and downstream results. We propose a market-based protocol for access arbitration in LLM multi-agent systems. Each agent converts its current plan and local execution state into a structured, budget-constrained bid that signals relative urgency. For asynchronous requests, an online clearing method based on optimal stopping decides when to close the clearing window, allocate access rights, settle payments, and track resource occupation until release. Across three contention scenarios, Market reduces makespan by 5.2\%, 2.5\%, and 4.9\% relative to the strongest primary baselines, while improving task score by about two percentage points.

Multi-agent LLM decision systems for portfolio management still lack a principled way to assign credit across specialist agents, remain vulnerable to cold-start dominance under regime shifts, and offer limited transparency into how final allocations are formed. We propose Market Regime Council (MRC), a cooperative multi-agent decision system that computes exact Shapley credits across all single, pairwise, and Grand-coalition outputs for online agent weighting. Instantiated with $N{=}3$ specialist agents, at each trading period, MRC recomputes coalition-based Shapley weights from exponentially weighted performance histories, uses a Bayesian adaptive mixture to stabilize early periods, applies regime-dependent multipliers to adjust agent authority, and records each rebalance through a five-layer causal trace. Over 1,037 trading days across 13 crypto assets and five seeds, MRC achieves a Sharpe ratio of 1.51 and a cumulative return of 440.1\%, ranking first on CR, SR, and IR among active baselines and attaining the lowest MDD among active methods. Ablation results show that the gains come from Shapley-weighted integration across coalition outputs rather than from any single stage in isolation. Code and demo data are included in the supplementary material.

Language model watermarking schemes fall into two broad categories: inference-time methods, which modify the decoding process at generation time, and model-embedded methods, which encode a secret signal directly into the model weights. Inference-time watermarking methods incur additional inference overhead and are not applicable in the increasingly prevalent open-weight model settings. In contrast, model-embedded watermarks introduce no additional inference latency---generation uses the standard sampling pipeline---and are particularly well-suited to open-weight settings. However, existing model-embedded approaches such as GaussMark face a fundamental quality-detectability trade-off: achieving strong detection power typically requires weight perturbations that noticeably degrade generation quality. We introduce MarkTune, a theoretically grounded on-policy fine-tuning framework that treats the GaussMark detection statistic as a reward while explicitly regularizing for text quality. Empirically, MarkTune substantially improves the quality-detectability frontier of GaussMark, approaching the detectability of strong inference-time schemes while preserving generation quality and downstream task performance. MarkTune is also extremely robust to paraphrasing and fine-tuning attacks, and generalizes across datasets: models fine-tuned on one corpus retain substantial detection power on unseen data.

We study the problem of multiclass classification within the framework of *marginal-nonuniform* learning, where the constants in the learning rate may depend on the unknown marginal distribution generating the unlabeled data, but not on the target concept. This notion naturally lies between classical PAC learning, where the constants are independent of both the marginal distribution and the target concept, and more recent universal learning, where the constants may depend on both. We give a complete characterization of the optimal marginal-nonuniform learning rates, establishing a fundamental trichotomy: exponential, linear, and arbitrarily slow rates. This characterization is witnessed by a new combinatorial dimension, termed the *uncentered DS-eluder dimension*. Technically, a key ingredient in the upper-bound proofs is a set of new *distributional exhaustion* lemmas that exploit the sequential nature of this dimension and may be of independent interest.

Practitioners choose among LLM alignment methods largely by trial and error. We provide a theoretical foundation: each pairwise method defines a vector field on the probability simplex that governs how the model redistributes mass between preferred and dispreferred completions. Projecting onto a single preferred/dispreferred pair reduces this to a one-dimensional margin ODE with a closed-form solution. These solutions reveal that DPO margins grow as $O(\log t)$ while IPO margins converge exponentially to $1/(2\tau)$; that label noise induces a qualitative phase transition in DPO (unbounded $\to$ bounded) but affects IPO only quantitatively; and that gradient concentration under asymmetric weighting governs trainability at scale. We confirm all three predictions across five model families spanning four benchmarks. The closed-form solutions also enable principled method design: we prove that adding \emph{any} label smoothing $\varepsilon > 0$ to SimPO creates a finite margin attractor at $\Delta^* = \beta^{-1}\log((1{-}\varepsilon)/\varepsilon)$, while $\varepsilon{=}0$ (standard SimPO) has no attractor. We test this across three model scales (3.8B--9B) and confirm it: the theory-derived configuration (TPO-S, $\varepsilon{=}0.05$) achieves the highest mean IFEval score on all three models.

Inspired by long-standing open problems in algebraic combinatorics, we show that modern machine learning can meaningfully contribute to verifiable mathematical discoveries. In particular, we focus on the construction of simple mathematical functions under exact distributional constraints, a setting we formalize as Simple Learning Under Rigid Proportions (SLURP). We tackle this problem by introducing two methods: MapSeek-Functional, which models the desired function alternating pseudo-labeling and supervised training steps; and MapSeek-Symbolic, designed to directly produce symbolic formulas. We successfully apply both methods to a research problem in algebraic combinatorics, discovering a new combinatorial interpretation of the $q,t$-Narayana polynomials arising from representation theory. To our knowledge, this is the first such interpretation based on noncrossing partitions. Using one discovered statistic, we find a combinatorial proof of the symmetry of these polynomials in a previously unsolved case. To streamline verification and reproducibility, we release all code, including a formalization of the mathematical discoveries of this paper in Lean 4.