NeurIPS 2026 Papers

LLM chain-of-thought reasoning improves with additional compute, but standard 2 inference scaling [Wei et al., 2022, Wang et al., 2022, Snell et al., 2024, Brown 3 et al., 2024] treats all steps equally. We ask: which step in a reasoning chain benefits 4 most from extra computation? We make three layered contributions, each scoped 5 explicitly. (I) Measurement. We define expansion utility Uk as the marginal 6 gain in correctness probability from resampling from step k onward, measured via 7 a step-oracle sweep. Across nine model families (8B–123B), seven benchmarks 8 (math, science, code), and 6,500 chains, every one of the 41 healthy (model, bench) 9 cells shows positive oracle gap at 10% step budget (95% Wilson CI [0.914, 1.000]; 10 mean +22.0 pp, range +1 to +48 pp). (II) Structure. Per-step utility is sparse 11 (97.6% of cells: Gini ≥ 0.80); Gini and mean oracle gap are tightly anti-correlated (Pearson r = −0.913, p = 9.5 × 10−17 12 ). A resample-stability simulation and 13 a segmentation-rule sensitivity check (Appendix J) bound the headline against 14 noise and rule-choice confounders. (III) Routing proof-of-concept. A cross15 model router trained with a within-example listwise loss [Cao et al., 2007] and a 16 learned depth prior, combined at inference with a bench-conditional depth mask 17 and a confidence gate, recovers 5-seed-averaged gated GR@10% = +0.149 (95% 18 bootstrap CI [+0.085, +0.217]) of the cross-model oracle gap at matched step19 budget, with no architectural change to the underlying model. We frame this as 20 proof the framework is actionable cross-model, not as deployment-ready scaling; 21 matched-token comparison to self-consistency / best-of-N requires a separate 22 generation campaign and is left to follow-up (§7). Methodological observation. 23 Within-example pointwise top-k BCE under cross-model pooling produces a high24 AUC discriminator (AUC@10 = 0.70) that selects the wrong steps (gated GR 25 = −0.15); the listwise loss is shift-invariant to per-(model, bench) utility scale and 26 removes this inversion.

Multiplicative motor and observation noise, along with internal noise corrupting computation, are central features of the sensorimotor system in biological and robotic agents. Yet, analytical solutions for stochastic optimal control are largely restricted to additive noise models and neglect internal noise. Here, we consider the problem of finding optimal control and filter laws for partially observable stochastic linear systems under quadratic costs with multiplicative control and observation noise, as well as internal noise. We provide an efficient, analytically derived coordinate-descent algorithm that computes mutually optimal linear control and filter laws by reformulating the problem as a constrained optimization. Our method provably guarantees monotonic decrease of the expected cost and convergence to a critical point, and overcomes the suboptimality and incompleteness of prior analytical approaches. Compared to state-of-the-art numerical methods, it achieves orders-of-magnitude computational speedups. Our solution also proves instrumental in revealing novel internal-noise-dependent, task-structured control strategies in a redundant arm control task.

We study Slowly Annealed Langevin Dynamics (SALD), a sampler for tracking a path of moving target distributions and approximating the terminal target through time slowdown. We establish non-asymptotic convergence guarantees via a KL differential inequality, showing that slowdown improves tracking through contraction of intermediate targets and the complexity of the path. Motivated by training-free guided generation with pretrained score-based generative models, we further introduce Velocity-Aware SALD (VA-SALD), which explicitly incorporates the underlying marginal distributions of the pretrained model and uses slowdown to correct the additional deviation induced by guidance. This yields a principled framework for training-free guided generation for diffusion-based and related generative model families, together with convergence guarantees that clarify the roles of intermediate functional inequalities and guidance bias.

The Gromov--Wasserstein (GW) problem provides a framework for aligning heterogeneous datasets by matching their intrinsic geometry, but its statistical and computational scaling remains an issue for high-dimensional problems. Slicing techniques offer an appealing route to scalability, but, unlike Wasserstein distances, GW problems do not generally admit closed-form solutions in one-dimension. We resolve this problem for the GW problem with inner product cost (IGW), propose a sliced IGW distance that enjoys a natural rotational invariance property, and comprehensively study its structural and computational properties. Numerical experiments validating our theory are presented, followed by applications to heterogeneous clustering of text data and language model representation comparison.

Covering problems are fundamental combinatorial optimization problems with broad connections to clustering, facility location, and various applications such as machine learning and controlling disease outbreaks. In this work we study a variant of the set cover problem that generalizes the partition set cover problem~\citep{bera2014approximation}. In partition set cover, given an instance $(P, S)$ with a universe $P = \cup_{c \in [\ell]} P_c$ (where $[\ell]$ denotes $\{1, 2, \ldots, \ell\}$), a collection of subsets \(S\) (each with associated costs), and coverage requirements $k_1,k_2,\dots,k_\ell$, the objective is to find a subcollection with minimum cost that covers at least $k_c$ elements from each group $c \in [\ell]$. We generalize this problem by allowing for the groups $P = \cup_{c \in [\ell]} P_c$ to be overlapping thus capturing both \emph{group fairness} and \emph{multigroup fairness}. We further allow for probabilistic coverage requirements for each element in the ground set thus capturing the notion of \emph{individual fairness}. Our main result is a randomized iterated-rounding-based algorithm with provable guarantees. Our main result is a randomized iterated rounding based algorithm with provable guarantees. We supplement our theoretical results by showing that algorithm has significantly running times and outperforms the best known algorithm of \citep{inamdar18PartitionSetCover}.

Current virtual staining approaches offer the potential for time- and cost-efficient biomarker quantification in cancer diagnostics and prognostics. However, patch-wise inference for gigapixel whole slide images (WSIs) fails to maintain spatial continuity, yielding artifacts that cause catastrophic mismatches with ground-truth images. Although pathology Vision Foundation Models (VFMs) offer rich representations, their self-attention causes varying global contexts to produce inconsistent embeddings for the same physical region. We formalize and validate this ``context contamination'' as a sheaf-theoretic problem where these embeddings form a presheaf that violates the gluing axiom. To address this, we propose SheafStain, a new approach that reinterprets VFM features as sheaf-like sections for spatially and biologically coherent virtual staining. Specifically, SheafStain integrates class and patch tokens into a Schr\"odinger Bridge framework as sheaf-like sections. While the class token anchors biological consistency, patch tokens form a per-position spatial map. A backbone co-pretrained on Hematoxylin \& Eosin (H\&E) and Immunohistochemistry (IHC) yields non-degenerate cross-stain stalks, so a single VFM feature space supervises both input conditioning and output stain alignment. Departing from prior work that evaluates on isolated $256 \times 256$ patches and either random-crops or resizes the $1024 \times 1024$ ground truth, we translate at $256 \times 256$ and evaluate on the stitched $1024 \times 1024$ outputs across HER2, ER, PR, and Ki-67. SheafStain demonstrates promising results against six prior methods while mitigating patch-boundary stitching artifacts. Code will soon be released upon acceptance.

Policy mirror descent (PMD) has a mature finite-time theory in discounted Markov decision processes (MDPs), but less is known in the average-reward setting, a more natural objective for many control applications. We give a finite-time, finite-sample analysis of PMD in ergodic average-reward MDPs built around a single master recursion that governs convergence under any gradient proxy, without external regularization. Its specializations yield linear rates (with a superlinear regime in the well-conditioned case) for exact, inexact-tabular, and linear function approximation (LFA) updates. We complement these convergence results with end-to-end sample complexities of order $t_{\mathrm{mix}}^3/\varepsilon^2$ in both tabular ($|\mathcal S||\mathcal A|$-dependent) and LFA ($d$-dependent) settings. The LFA rate sharpens the prior best $t_{\mathrm{mix}}^5$ mixing dependence to $t_{\mathrm{mix}}^3$, and matching information-theoretic lower bounds establish that the $t_{\mathrm{mix}}^3/\varepsilon^2$ critic core is unimprovable in both settings.

Robust deployment of clinical electroencephalography (EEG) models requires source-trained models to generalize to unseen hospitals without target-domain calibration, hospital identifiers, or clinical reports at inference. This is challenging because acquisition protocols, hardware, montages, and patient populations perturb low-level EEG statistics, while clinical interpretation is organized around higher-level semantic concepts. We argue that this abstraction mismatch limits conventional signal-level invariant learning: aligning feature distributions alone cannot distinguish clinically irrelevant variation from diagnostic content. We propose Text-Guided Invariant Learning (TG-IL), a deployment-oriented framework that uses clinician-authored reports only during training as semantic anchors for EEG representation learning. TG-IL combines stochastic recording-level aggregation, a variational semantic information bottleneck, and prototype-guided EEG--report alignment to preserve report-derived clinical semantics while mitigating site-specific nuisance variation. At inference, all text-side modules are discarded and the model operates solely on EEG. On a three-hospital clinical EEG benchmark, TG-IL improves zero-shot cross-hospital generalization and worst-case robustness while reducing hospital-specific information in learned representations.

AI agents deployed on the open web are becoming more capable of performing actions that may breach contracts and violate computer security laws. In this work, we introduce $\text{ScrapeBench}$, the first agentic benchmark for evaluating the legal compliance of frontier AI agents with website scraping policies, including terms of service (ToS) and $\texttt{robots.txt}$ directives. Across widely used closed-weight and open-weight AI agents, we find that most agents exhibit low compliance rates (< 5\%) when instructed to scrape websites in our sample of 1,626 popular websites that explicitly prohibit scraping. In addition, we observe that even where AI agents actively check the applicable ToS and $\texttt{robots.txt}$, they continue to exhibit low compliance rates. Conversely, in our sample of 269 websites that do not prohibit scraping, we observe that agents regularly refuse to scrape despite it being lawful, such as Claude Opus 4.6 exhibiting an over-refusal rate of 98.8%. Lastly, our human baseline experiments ($n$ = 180 participants) suggest that humans exhibit compliance rates comparable to AI agents but over-refuse at much higher rates. We release our anonymized code and data in this repository: https://anonymous.4open.science/r/scrapebench-75D6

Recent neural decoding approaches achieve strong performance by training on large collections of paired neural-behavioral recordings, but such datasets are expensive, invasive, and difficult to scale. In contrast, behavioral data is abundant and easy to collect, raising the question of whether neural decoding can benefit from decoupling behavioral and neural representation learning. We introduce BeeMO, a flexible multi-session framework that enables training with arbitrary mixtures of paired neural-behavioral recordings and unpaired behavioral data. A behavior decoder learns movement dynamics directly from behavioral trajectories, while neural activity is incorporated through cross-attention layers when available, allowing behavioral and neural supervision to scale independently. By decoupling neural and behavioral data, we unlock a new dimension for scaling: unpaired behavioral data, which is substantially cheaper and easier to collect than paired neural recordings, can be used directly to improve decoding performance. Across multiple intracortical motor datasets and tasks in nonhuman primates, we show that incorporating unpaired behavioral data consistently improves decoding performance, particularly, and that incorporating task-aligned behavioral trajectories can further improve transfer. We further show that behavior-only pretraining, without any neural pretraining, outperforms single-session supervised baselines and is comparable to models pretrained on substantially larger neural datasets. Together, our results suggest that scaling behavioral data offers a practical and cost-effective path toward neural decoding models that generalizes across subjects and tasks.

Cortical neurons are complex, multi-timescale processors wired into recurrent circuits, shaped by long evolutionary pressure under stringent biological constraints. Mainstream machine learning, by contrast, predominantly builds models from extremely simple units, a default inherited from early neural-network theory. We treat this as a normative architectural question. How should one split a fixed parameter budget $P$ between the number of units $N$, per-unit effective complexity $k_e$, and per-unit connectivity $k_c$? What controls the optimal allocation? This calls for a model in which per-unit complexity can be tuned independently of width and connectivity. Accordingly, we introduce the ELM Network, whose recurrent layer is built from Expressive Leaky Memory (ELM) neurons, chosen to mirror functional components of cortical neurons: multi-timescale memory, structured synaptic integration, and nonlinear internal computation. The architecture allows for individually adjusting $N$, $k_e$, and $k_c$ and trains stably across orders of magnitude in scale. We evaluate the model on two qualitatively different sequence benchmarks: the neuromorphic SHD-Adding task and Enwik8 character-level language modeling. Performance improves monotonically along each of the three axes individually. Under a fixed budget, a clear non-trivial optimum emerges in their tradeoff, and larger budgets favor both more *and* more complex neurons. A closed-form information-theoretic model captures these tradeoffs and attributes the diminishing returns at two ends to: per-neuron signal-to-noise saturation and across-neuron redundancy. Connectivity enters as a related mechanism that helps neurons learn distinct signals. A hyperparameter sweep spanning three orders of magnitude in trainable parameters traces a near-Pareto-frontier scaling law consistent with the framework, mapping the budget-constrained tradeoff surface between unit count, unit complexity, and connectivity. This suggests that the simple-unit default in ML is not obviously optimal once this surface is probed, and offers a normative lens on cortex's reliance on complex spatio-temporal integrators.

Large language model agents increasingly act through tools, browsers, code interpreters, and external APIs, turning safety from a single-output problem into a trace-level problem. We identify \emph{compositional emergent risk} (CER), a failure mode where individually safe actions interact across time to produce unsafe outcomes. We show that bounded-window safety filters can miss CER whenever the risky dependency lies outside their visible context. To study this failure systematically, we introduce \textsc{CER-Bench}, a controlled long-horizon benchmark with 440 tasks and 19,525 actions across 5--500 steps, spanning five risk domains and two compositional mechanisms. At the largest tier, each trace induces a 79M+ candidate risk-composition search space. Across 15 frontier and open-source LLM agents, every model exhibits a non-zero compositionality gap (CG), ranging from 44.4\% to 100.0\% with a mean of 82.2\%. Moreover, 86.1\% of compliant executions contain caution language yet still proceed, showing that verbal risk awareness does not reliably prevent unsafe composition. We introduce \textsc{RiskShield}, a conformal-calibrated runtime shield that learns trace-risk boundaries, evaluates planned continuations before commitment, and substitutes risky suffixes while preserving safe prefixes. On 7 held-out \textsc{CER-Bench} models, \textsc{RiskShield} reduces mean \textsc{CER-5} CG from 69.9\% to 0.0\%, with no shielded pass observed in 763 evaluations and a 95\% upper confidence bound of 1.6\%, while preserving 78.4\% step-level task completion. It outperforms cumulative-threshold, sliding-window, full-trace, and published safety baselines, with 63.3\% of tasks requiring no extra API call and additional robustness across longer traces, risk domains, and external agent-safety benchmarks. Code and benchmark are available at \url{https://anonymous.4open.science/r/RiskShield-2284}.

Image segmentation into superpixels is a widely used technique in computer vision, with a large body of work developed over the years. Yet, its evaluation remains poorly standardized, as methods are compared under heterogeneous protocols, across inconsistent scale ranges, and with redundant or misaligned metric subsets. In this work, we introduce $\textbf{SUPERVISE}$ (SUperpixel PERformance VISualization and Evaluation), a unified and reproducible benchmark that addresses these longstanding inconsistencies. Built on a scale-normalized protocol based on interpolation over the actual number of generated superpixels, SUPERVISE enables fair and consistent cross-method comparisons. We leverage this standardized framework to conduct the first large-scale statistical analysis of 20 evaluation metrics across 7 datasets and 31 methods — revealing strong inter-metric correlations and significant redundancy that challenge common evaluation practices. These findings provide empirical grounding for a compact, representative metric subset. SUPERVISE is released as a lightweight, modular framework built on precomputed shared label maps, making large-scale reproducible evaluation accessible to the community. All code, label maps, and evaluation results are publicly available at: https://anonymous.4open.science/r/evaluation_superpixel-08B1/

Infrared (IR) spectral unmixing recovers individual component spectra from a measured mixture, enabling chemical identification. Existing methods either assume linear superposition of components, which fails for liquid-phase mixtures where molecular interactions alter spectral shapes, or use deep networks that entangle all components in a shared representation. We introduce SLOT-IR, a slot-based architecture that decomposes mixture spectra into separate per-component embeddings and decodes each independently into a predicted spectrum. A two-stage training procedure first learns to map a single molecule from gas-phase spectra to liquid-phase, then trains the full unmixing model on mixtures. On the benchmark of annotated infrared spectra, SLOT-IR outperforms all baselines on both binary and ternary mixture identification. To verify that the model captures genuine chemical structure rather than statistical shortcuts, we apply a post-hoc BatchTopK Sparse Autoencoder (SAE) to frozen slot embeddings and test whether recovered features correspond to known functional groups. Statistical and causal analyses confirm model alignment with established chemistry.

Systematic reviews -- which requires comprehensive evidence collection and synthesis from large document corpora in response to targeted research questions -- are foundational in finance, social sciences, and other technical fields. Manual construction of evidence tables is labor-intensive, and recent LLM-based assistants relying on embedding or keyword based search often fail to meet the coverage standards of systematic reviews. We introduce SLIDERS, a novel LLM-based methodology for systematic reviews, by automatically assembling evidence tables tailored to research questions. In addition to extracting structured data from documents, SLIDERS can extract full-text excerpts that serve as direct evidence or as provenance for structured data. Core to SLIDERS is an automated evidence reconciliation agent that writes code to analyze and reconcile extracted evidence, bringing together information fragmented across documents, resolving inconsistencies across excerpts, and synthesizing overlapping findings into a coherent evidence table. In addition, SLIDERS allows users to ask follow-up questions in natural language to further explore the assembled evidence. We evaluate SLIDERS on three systematic-review-style tasks over large document collections. SLIDERS outperforms the best-performing baseline across benchmarks, remains near 90\% accuracy across 6M-11M-token corpora. On two new follow-up analysis benchmarks \system{} can answer 77.9% and 58.3% followup questions accurately.

Cognitive neuroscience research indicates that human spatial navigation relies not merely on abstract global map representations, but rather on anchoring local observations to spatially stable, decision-relevant landmarks to effectively align the current scene with the cognitive map. Inspired by this mechanism, we propose SFPR, a structural fingerprint-based LiDAR-to-OpenStreetMap (OSM) place recognition framework. This framework goes beyond the traditional coarse retrieval paradigm that relies exclusively on global descriptor similarity and further introduces fine-grained discrimination based on structural fingerprints to achieve more accurate place recognition. Specifically, we propose a structural fingerprint-aware attention mechanism that utilizes sparse but spatially stable anchors as saliency prompts, directing the network's attention toward potential fingerprint regions while dynamically generating global descriptors. Subsequently, we formulate the extraction and matching of structural fingerprints as an alternating optimization problem guided by this fingerprint-aware attention. Through iterative optimization, we extract structural fingerprints with high fingerprint-aware attention and geometric consistency from anchors. These structural fingerprints are further fed back into the training stage as geometric priors, effectively suppressing false matches characterized by similar global features but contradictory local structures. Experiments demonstrate that SFPR effectively overcomes the retrieval bottleneck in macroscopically homogeneous scenes, achieving a relative improvement of 30.20\% in Top-1 Recall@1m compared to the current state-of-the-art method. Code are publicly available at https://anonymous.4open.science/r/SFPR.

Reconstructing speech from non-invasive brain signals offers a promising pathway for restoring communication in individuals who are cognitively intact but unable to speak. Existing EEG-to-speech approaches formulate this task as \emph{acoustic reconstruction}, optimizing waveform fidelity while ignoring whether the generated speech preserves high-level semantic content. In this work, we revisit this formulation and argue that EEG signals carry not only acoustic but also semantic information. We identify two key limitations of prior methods: (1) the neglect of spatial relationships between EEG electrodes, and (2) the failure to exploit the semantic structure of the N400 paradigm, where congruent and incongruent trials reflect distinct semantic processing. We propose \textbf{SENSE} (\textbf{S}emantic-\textbf{E}EG \textbf{N}eural \textbf{S}peech Synth\textbf{E}sis), which combines a graph-based EEG encoder over electrode geometry with EEG Semantic Conditioning (ESC), aligning EEG to a pretrained semantic space using only congruent trials. On the N400 dataset, SENSE consistently outperforms prior methods on both acoustic and semantic metrics, and model-internal channel attribution suggests distributed reliance on auditory, sensorimotor, and centro-parietal regions, consistent with known speech-perception neuroscience. In the unseen-subject setting, SENSE trained on only two subjects already surpasses the strongest baseline trained on all eighteen subjects in word error rate, and matches it on acoustic metrics with as few as eight subjects.

Solubility prediction is a standard benchmark in computational chemistry, yet multi-solvent models which reportedly approach the experimental-noise ceiling (i.e. the aleatoric limit) are not yet reliable enough to be deployed. We argue that this gap is partly artefactual: published benchmarks differ in curation policies, evaluate on count-weighted RMSE that hides failure on tail-heavy solvent distributions, and treat the widely cited 0.6–0.8 log S inter-laboratory figure as the aleatoric ceiling even though it reflects worst-case, not expected, disagreement. We introduce SC3, a multi-solvent solubility benchmark built on BIGSOLDB v2.1 with three contributions: (i) a reproducible curation pipeline yielding 101,535 measurements over 1,327 solutes and 206 solvents, with a recalibrated aleatoric floor of 0.106 log S—roughly 6× tighter than the conventional figure; (ii) nested Gold/Silver/Bronze consensus tiers with per-point σ\sigma σ, three leakage-checked splits, and a multi-solvent metric suite (PS-RMSE, Z-RMSE); and (iii) a 31-model benchmark across six families, whose best Bronze PS-RMSE sits at ≈5×εaleatoric\approx 5 \times \varepsilon_{\text{aleatoric}} ≈5×εaleatoric, and we observe this is a gap unclosed by any deep alternative tested. We perform three follow-on analyses: data scaling, transfer from quantum-chemistry solvation energies, and feature-level attribution, which demonstrates that calibrated per-point uncertainty is a reusable infrastructure for diagnosis beyond point prediction.

Graph Neural Networks (GNNs) face a fundamental dichotomy between expressiveness and scalability. Recent spectral and transformer-based models approach universal approximation capabilities but rely on computationally intensive global operators that scale poorly to large graphs. Conversely, scalable approaches often compromise structural fidelity through sampling or decoupling, resulting in incomplete structural acquisition. We identify that this trade-off stems from a homogeneous treatment of graph topology, where uniform computational complexity is applied to heterogeneous structures. We propose a paradigm shift towards Hierarchical Structural Acquisition and introduce S\&P (Scalable \& Powerful), a framework grounded in Fusion Frame Theory that aligns the operator with the intrinsic hierarchy of the data. S\&P decomposes the global operator into intra-component and inter-component, and we prove that this design preserves universal spectral filtering capacity for non-degenerate inputs while remaining numerically stable and linear in complexity. Experiments on 14 datasets show that S\&P achieves state-of-the-art accuracy, bridging the gap between scalability and expressiveness. Our code is available at https://anonymous.4open.science/r/HierarchicalSP.