NeurIPS 2026 Papers

Continuous-time models are a natural choice for irregular and asynchronous data. A central design choice is how to embed discrete observations into continuous time. Interpolation- and imputation-based embeddings reconstruct a continuous observation path, making the model sensitive to the choice of reconstruction. We show that this reconstruction step is unnecessary. On compact sets, universality for continuous functionals of paths transfers to universality for continuous functionals of discrete observation streams under any continuous and injective embedding. Guided by this result, and building on the rectilinear control path for Neural Controlled Differential Equations (NCDEs), we introduce a continuous and injective embedding for Log-NCDEs, a universal class of continuous-time models. This embedding records observations as increments and composes them over arbitrary query intervals to form log-signatures, giving interval-level summaries of a faithful embedding of the observed data. This avoids interpolation of observed variables, supports online computation, and allows prediction on output grids independent of the input sampling times. Experiments on synthetic controlled dynamics and real-world time-series datasets show that the representation is accurate, efficient, and robust to irregular, asynchronous, and sparse observations.

Large language models can now generate complex, multi-step mathematical proofs, but reliably determining their correctness and localizing early logical errors remains a critical challenge. Existing evaluation approaches largely depend on model-based natural-language judgments, which often overlook local reasoning gaps. While formal theorem provers like Lean offer a path to rigorous verification, using them to evaluate informal text requires solving locality and semantic mismatches: a prover might bypass a local flaw by proving an overly broad target, or validate an auto-formalized statement that drifts from the original mathematical intent. To address this, we introduce FaithSieve, a Lean-assisted framework for fine-grained evaluation of natural-language mathematical proofs. FaithSieve decomposes coarse proof steps into local reasoning units, extracts typed proof obligations, and verifies them through a formal evaluation agent. Formal validation is gated by semantic alignment scoring, so Lean evidence is incorporated only when the formal statement faithfully preserves the context, objects, and logical form of the original claim. We construct two expert-verified datasets, ProofLoc-Olympiad and ProofLoc-University, to benchmark first-error localization. On the 350-problem Olympiad dataset, FaithSieve using a GPT-5.4 backbone achieves 81.43\% exact first-error accuracy, outperforming the direct-judging baseline of 72.29\%. Furthermore, on the 200-problem ProofLoc-University benchmark spanning six advanced domains, FaithSieve reaches 84.5\% exact accuracy, compared to 75.0\% for the direct judge. Our work demonstrates that decomposing proofs into fine-grained units and grounding them with faithful formal evidence significantly improves reliable evaluation of natural-language reasoning.

Fairness has emerged as a central consideration in machine learning, motivating the study of fair range $k$-supplier clustering as a fundamental problem that focuses fairness on the selected centers. Given a set of suppliers and clients, where each supplier may belong to one or more demographic or functional groups, the objective is to select $k$ suppliers that minimize the maximum client-to-center distance while ensuring that the number of selected suppliers from each group satisfies prescribed lower and upper bounds. For disjoint supplier groups, we develop a polynomial-time $3$-approximation algorithm in the offline setting and a $(3+\epsilon)$-approximation algorithm in the streaming setting. We further consider overlapping supplier groups and show that this generalization admits a parameterized $3$-approximation algorithm whose runtime is exponential in the number of clusters. Finally, experiments on both synthetic and real-world datasets demonstrate that our algorithms achieve significantly better clustering quality and runtime efficiency in comparison with state-of-the-art methods.

Algorithmic ranking systems increasingly dictate high-stakes outcomes, yet most fairness interventions implicitly assume that protected attributes are categorical. When sensitive attributes are inherently continuous (e.g., age, income, or health scores), standard practices rely on arbitrary discretization, which discards crucial fine-grained information and destroys the natural ordinality of the data. In this paper, we study the problem of fair ranking with continuous protected attributes without relying on thresholding. We formalize fairness via the Kendall correlation between the ranking and the continuous attribute, and measure utility loss via the Kemeny distance from an initial score-based ranking. To solve this, we propose Fair Bubble Sort (FBS), a highly efficient adjacent-swap algorithm that minimizes utility loss subject to a strict continuous fairness constraint. We provide strong theoretical guarantees, proving that FBS is exactly optimal for the unweighted Kemeny distance. Extensive experiments on synthetic and real-world datasets show that FBS is scalable and consistently outperforms discretization-based baselines, achieving a superior fairness-accuracy Pareto front.

Confirmation bias, the tendency to seek evidence that supports rather than challenges one's belief, hinders one's reasoning ability. We examine whether large language models (LLMs) exhibit confirmation bias by adapting the rule-discovery study from human psychology: given a sequence of three numbers (a "triple"), an agent engages in an interactive feedback loop where it (1) proposes a new triple, (2) receives feedback on whether it satisfies the hidden rule, and (3) guesses the rule. Across eleven LLMs of multiple families and scales, we find that LLMs exhibit confirmation bias, often proposing triples to confirm their hypothesis rather than trying to falsify it. This leads to slower and less frequent discovery of the hidden rule. We further explore intervention strategies (e.g., encouraging the agent to consider counter examples) developed for humans. We find prompting LLMs with such instruction consistently decreases confirmation bias in LLMs, improving rule discovery rates from 42\% to 56\% on average. Lastly, we mitigate confirmation bias by distilling intervention-induced behavior into LLMs, showing promising generalization to a new task, the Blicket test. Our work shows that confirmation bias is a limitation of LLMs in hypothesis exploration, and that it can be mitigated via injecting interventions designed for humans.

Vital sign measurement using cameras presents opportunities for comfortable, ubiquitous health monitoring. Remote photoplethysmography (rPPG), a foundational technology, enables cardiac measurement through minute changes in light reflected from the skin. However, practical deployment is limited by the computational constraints of performing analysis on front-end devices and the accuracy degradation of transmitting data through compressive channels that reduce signal quality. We propose a memory efficient rPPG algorithm - FacePhys - built on temporal-spatial state space duality, which resolves the trilemma of model scalability, cross-dataset generalization, and real-time operation. Leveraging a transferable heart state, FacePhys captures subtle periodic variations across video frames while maintaining a minimal computational overhead, enabling training on extended video sequences and supporting low-latency inference. FacePhys establishes a new state-of-the-art, with a substantial 49% reduction in error. Our solution enables real-time inference with a memory footprint of 3.6 MB and per-frame latency of 9.46 ms -- surpassing existing methods by 83% to 99%. The training code, a real-time inference demo for mobile browsers, and the demonstration video can be found in the supplementary materials.

Modeling resting-state functional magnetic resonance imaging (rs-fMRI) data is crucial for understanding brain-wide neural activity. However, traditional methods struggle to capture complex temporal dynamics over long horizons, to account for the brain's anatomical spatial structure, and to model high-dimensional ambient signals that lie on a low-dimensional intrinsic subspace. We propose FAST-Brain, a unified flow-aligned spatio-temporal surrogate brain model that addresses all three challenges. At its core is a flow-aligned generative framework that directly predicts the clean blood-oxygen-level-dependent (BOLD) signal, paired with a graph convolutional network that captures spatial structural constraints and a Transformer that models long-range temporal dependencies. Theoretically, we show that under a low-dimensional subspace assumption, the approximation error of our model scales with the intrinsic dimension rather than the ambient dimension, which justifies our direct modeling of the BOLD signal. Extensive experiments on synthetic and Human Connectome Project datasets demonstrate that FAST-Brain achieves state-of-the-art performance in recovering functional connectivity, effective connectivity, and the implicit low-dimensional signal subspace.

Vision-language models (VLMs) have rapidly evolved into general-purpose multimodal reasoners with strong zero-shot generalization. In this context, VLMs could greatly benefit the analysis of human gaze and attention, a central task in human behavior understanding that requires reasoning about the physical scene as well as the activity, interactions, and social context. However, the extent to which VLMs can reliably understand human gaze and related attentional behaviors remains largely unexplored. In this work, we present EyeVLM, a systematic evaluation framework for gaze understanding in VLMs across two complementary dimensions: tasks and models. To assess gaze understanding capabilities, we focus on two core tasks. The first, gaze following, i.e., predicting the 2D location where a person is looking, has a geometric and visual processing focus, requiring a precise understanding of the human face, attention direction, 3D scene structure, and spatial grounding of attended targets. The second, social gaze prediction, requires social and relational reasoning over multi-person interactions (e.g., mutual gaze and shared attention), and may benefit more from the LLM semantic reasoning capabilities within VLMs. Regarding models, EyeVLM evaluates these tasks in two ways: a zero-shot setting with a diverse set of state-of-the-art open- and closed-source VLMs, exploring different prompting strategies; and a fine-tuning approach based on task-specific QA pairs, studying the impact of model scale and data scale. As benchmarks, we rely on existing gaze understanding datasets and perform a systematic comparison with state-of-the-art purely visual models. Overall, our results show that current VLMs lack precise gaze understanding capabilities. While standard training helps reduce the gap with visual models, significant improvements are still needed.

Air quality prediction at unmonitored locations is challenging because historical AQI observations are unavailable, while conventional spatiotemporal models largely rely on target histories to learn spatial dependencies. Meanwhile, widely available weather covariates provide useful station-specific evidence for target-absent inference. In this paper, we propose \textbf{ExtrapAir}, a lightweight weather-bridged framework for air quality inference at unmonitored locations. ExtrapAir preserves variable-specific weather patterns through per-variable weather encoding and learns adaptive weather and AQI correlations for spatial transfer. To support robust inference, we introduce \textbf{Activation Attention with Prior Inductive Biases}, which enables non-competitive spatial aggregation, incorporates geographic and semantic priors for station-pair guidance, and avoids full station-to-station attention computation for scalability. Extensive experiments on five real-world air-quality datasets against \textbf{32} baselines show that ExtrapAir reduces MAE by up to \textbf{15.24\%} overall and \textbf{16.01\%} on unmonitored stations, while cutting training time by \textbf{84.9\%} and memory usage by \textbf{76.23\%}, achieving a strong accuracy--efficiency trade-off.

We aim to design revenue-maximizing single-item auctions that are deterministic, strategy-proof, and ex post individually rational --- the quintessential fundamental model for optimal mechanism design. While Myerson's seminal work solved this model for independent bidders, straightforward extensions to correlated settings often result in non-monotonic, and therefore non-strategy-proof allocations. Critically, optimal allocation design for correlated bidders is NP-hard to approximate, rendering theoretical optimality guarantees in this domain computationally intractable. We establish a new standard of empirical rigor for this theoretically hard model by proposing an empirical pipeline. We synthesize neural interpolation of Myerson's greedy allocation based on marginal profits (the correlated variant of virtual valuation), formal neural verification to enforce exact strategy-proofness, and a constructive repair procedure. Empirically, our method is highly effective, consistently achieves near-optimal revenue across a wide range of distributions, including synthetic, adversarial, and real-world (consumer, financial, and industrial) datasets. Compared to existing manual and neural baselines, our approach shows substantial improvement, often reducing the revenue gap by an order of magnitude. Our study is also the first to introduce (unattainable) greedy revenue as a rigorous upper bound for empirical benchmarking, providing a definitive quantitative performance measure where true optima remain theoretically elusive. We demonstrate the generality of our approach by extending it to multi-unit auctions with unit demand and integrating our verification techniques into RegretNet to achieve exact strategy-proofness.

While spatiotemporal deepfake detectors have shown high AUC, our experiments reveal that they remain susceptible to evasion attacks. These models tend to overfit on fragile temporal spectrum cues, rather than learning robust semantic causality. To mitigate this vulnerability, we propose SpInShield, a temporal spectral-invariant defense framework explicitly designed to decouple semantic motion from manipulatable spectral artifacts. We propose a learnable spectral adversary that dynamically synthesizes severe spectral deformations, simulating extreme attack scenarios. By employing a shortcut suppression optimization strategy, SpInShield compels the encoder to extract reliable forensic cues while autonomously purging unstable spectral statistics from the latent space. Experiments show that SpInShield obtains competitive performance on widely used datasets and outperforms the strongest baseline by 21.30\% AUC under simulated amplitude spectral attacks.

The asymptotic behaviour of Monte Carlo Exploring Starts (MCES) is a long-standing open question in reinforcement learning, even in the tabular setting. We investigated the convergence properties of tabular MCES by constructing examples in which the algorithm converges to suboptimal solutions. This paper presents new counterexamples for both initial-visit and first-visit MCES and gives a convergence-restoring modification for the initial-visit case. We show that stable suboptimal solutions may exist for initial-visit MCES with sample-average updates even when greedy actions are updated more often than non-greedy actions on average. However, by scaling learning rates inversely to update frequencies on a state-by-state basis, convergence to optimality is guaranteed. Unlike previous uniformisation methods, this modification is applicable to large-scale problems that require approximating the estimated value function. We then extend the example to show that sample-average first-visit MCES may also converge to suboptimal solutions. This largely settles a fundamental open problem and shows that exploring starts alone do not guarantee convergence to optimality. More broadly, these results highlight that convergence depends critically on the relative size and frequency of updates applied to different actions, making the choice of learning rates and the balance between exploration and exploitation central to the analysis of MCES and the implementation of scalable Monte Carlo control methods.

SHAP explanations are widely used in high-stakes settings to justify decisions, yet they can differ substantially across repeated runs, even when the model, the input instance, and the prediction are held fixed. Prior work has documented disagreement *between* explanation methods; we show that substantial disagreement arises even *within* SHAP across reruns of the same estimator on the same trained model and instance. We call this phenomenon *explanation multiplicity* and develop an evaluation methodology for characterizing it under deployment-realistic computational budgets, combining a dual-seed protocol that disentangles model-induced from explainer-induced variability, a hierarchy of magnitude-, rank-, and set-based metrics, and randomized Dirichlet and Mallows null models that calibrate when observed disagreement exceeds chance. Across multiple datasets, model classes, and sampling strategies, we find that explanation multiplicity is pervasive and persists even for high-confidence predictions. The dominant source depends on the data regime: model-induced variability dominates in small-data settings, while explainer-induced variability dominates at scale. Commonly used $\ell_2$ distance is largely insensitive to this instability, while rank-based metrics reveal severe reordering of top-ranked features. Improved sampling methods such as CTE do not eliminate rank-level multiplicity, and deterministic alternatives such as K-Means achieve stability only by targeting a different estimand that diverges sharply from Shapley values defined against the empirical training distribution. Practitioners should treat single-run SHAP outputs as realizations of a distribution rather than as authoritative artifacts.

Physical reasoning is central to agents that step into the physical world. Models now excel at code and math, but their physical reasoning capabilities remain largely untested. Existing physical benchmarks evaluate goal-state matching rather than functional performance. This position paper argues that evaluating physical reasoning in LLM agents requires construction benchmarks, where physics verifies functional outcomes. To operationalize physical reasoning evaluation, we identify five capabilities spanning the full agentic loop from goal to verified artifact. Our audit of eleven physical benchmarks finds only two that combine realistic physics with functional verification, the minimum requirements for testing physical reasoning; both are construction benchmarks. Neither covers all five capabilities, yet frontier models already achieve near-zero success as task complexity increases. Progress depends on the breadth of benchmarks we build. We call on academia, game studios, and industry labs to expand construction benchmarks along both axes, widening capability coverage and deepening physical challenges. Their breadth determines how fully agents move from code and math to reshaping the physical world.

Current evaluation of epistemic uncertainty relies on tasks such as out-of-distribution detection and active learning. However, the Bayes-optimal decision strategies for these tasks do not coincide with the scores commonly used to quantify epistemic uncertainty. Building on the epistemic reject-option framework, we evaluate epistemic uncertainty using its ability to identify regret, the reducible error. Formulating selective prediction as a constrained optimization over coverage, expected risk, and regret, we prove the optimal selector is a thresholded convex combination of the ground-truth aleatoric and epistemic uncertainties. This theoretical unification exposes a weakness in recent uncertainty disentanglement literature: we demonstrate that standard correlation metrics between learned components do not necessarily predict their actual operational utility. We instead propose to evaluate the achievable (risk, regret, coverage) surface of the decomposition as a diagnostic for joint disentanglement and utility. Benchmarking standard methods on datasets with dense human annotations reveals that decision-theoretic rankings can disagree substantially with proxy-task rankings, including pairwise rank inversions between methods that are top-ranked on one criterion and bottom-ranked on other.

Compositional generalization is an important form of out-of-distribution generalization, defined as the ability to train on some combinations of modules (e.g., functions such as `sort`, `filter`) and then generalize to unseen combinations. Despite substantial empirical work evaluating compositional generalization in transformers, findings have been inconsistent because evaluations were often conducted on a limited set of train-test splits, defined in an ad hoc manner. Through a systematic evaluation, we identify two key aspects of the train-test distribution that strongly affect performance: **composition equivalence** and **module coverage**. We show that the apparent performance of direct models (trained only on final outputs) results primarily from exploiting composition equivalences—different sequences of modules that reduce to identical end-to-end functions. When benchmarks eliminate these equivalences, performance drops significantly, showing their inability to generalize to compositions of known modules that produce novel end-to-end functions. We further demonstrate that performance degrades monotonically as module coverage shifts increase—when modules appear in different contexts between train and test—affecting both direct and step-by-step models (trained on intermediate and final outputs). These findings have concrete implications for benchmark design: benchmarks that include compositional equivalences can lead to significant overestimation of the generalization abilities of direct models, and benchmarks that include both module coverage violations and compositional equivalences can exacerbate shortcut learning. We further demonstrate the effect of compositional equivalence on the generalization performance of the pre-trained model Llama3-8B on the code-output prediction task in the coding benchmark [LiveCodeBench](https://livecodebench.github.io/) and discuss its real-world implications.

Frontier large language models can often recognize when they are being evaluated, a capability known as evaluation awareness. If models behave differently in evaluations than in deployment, this undermines the validity of evaluation results, which are a crucial component of current AI safety frameworks. We introduce EvalAwareBench, an open pipeline and benchmark for measuring evaluation awareness that works with any Inspect-compatible evaluation, allowing practitioners to test against current and future benchmarks. EvalAwareBench ships with a newly curated transcript suite covering current frontier system-card evaluations and diverse deployment sources. The benchmark serves two purposes: measuring how reliably frontier LLMs recognize that they are being evaluated, and assessing how detectable individual benchmarks are as evaluations. We identify two methodological choices in the existing literature that introduce systematic bias: the identity of the model that generated the deployment transcripts accounts for 11.25% of measurement variance and can reorder model rankings; and elicitation prompts selected for high performance on one model can perform near chance on others. EvalAwareBench corrects for both via per-model probe calibration and a stratified generator-harmonisation procedure. We release EvalAwareBench as an open pipeline and dataset.

Membership inference attacks (MIAs) have emerged as the standard tool for evaluating the privacy risks of AI models. However, state-of-the-art attacks require training numerous, often computationally expensive, reference models, limiting their practicality. We present a novel approach for estimating model-level vulnerability to the Likelihood Ratio Attack (LiRA), the strongest available attack, directly from the train and test loss distributions of the target model and without training any reference models. We show that LiRA's per-sample signal decomposes into a variance-ratio term and a residual mean-shift term, with the relative contribution of each determined by how much training collapses model uncertainty at the trained sample. This places models on a continuum, with different regimes calling for different reference-free loss-based statistics as proxies for LiRA TPR. The shapes of the loss distributions themselves indicate which proxy applies. We instantiate the framework with two natural proxies. At the heavy-tailed end, the LOSS attack TNR predicts LiRA TPR@FPR=$10^{-3}$ with RMSE 0.03 across 9 image classification architectures and 4 datasets, outperforming low-cost reference-model attacks such as RMIA. At the symmetric end, the LOSS attack AUC predicts LiRA TPR with RMSE 0.01 across five GPT-2 sizes from 10M to 1B parameters. We also show these proxies to outperform both low-cost (few reference models) attacks such as RMIA and other measures of distribution difference.

Offline goal-conditioned reinforcement learning remains challenging in stochastic long-horizon settings, where compounding value estimation errors hinder reliable goal reaching. While prior methods have sought to address this challenge through various approaches, a key challenge remains path mirage, where agents overcommit to spuriously successful trajectories in offline datasets induced by stochasticity, often leading to failure on difficult tasks. To address this issue, we propose Branch-aware Graph Planning (BGP), which captures stochastic branching structures by identifying high-variability points as graph nodes and designing goal-conditioned edges with segmented learning to avoid unreliable branches and reduce unnecessary stochasticity along paths. As a result, BGP enables reliable goal reaching even in highly stochastic long-horizon environments, and experiments on diverse OGBench tasks show that it substantially outperforms prior state-of-the-art offline goal-conditioned RL methods.