NeurIPS 2026 Papers

Do language models make decisions under uncertainty like humans do? And if so, what role does extended reasoning play in the underlying decision process? We answer this question by introducing an active probabilistic reasoning task that cleanly separates sampling (actively acquiring evidence) from inference (integrating evidence towards a decision). Benchmarking humans and a broad set of contemporary LLMs against optimal reference policies reveals a consistent pattern: extended reasoning is the key determinant of strong performance, driving large gains in inference, while yielding only modest improvements in active sampling. To explain these differences, we fit a behavioral model that captures systematic deviations from optimal Bayesian behavior through interpretable parameter families, placing humans and models in a shared low-dimensional cognitive space. The resulting fits show how reasoning shifts models toward human-like regimes of evidence accumulation and belief-to-choice mapping, and yield testable predictions about the latent dynamics that might drive each decision. Probing residual-stream activations of an open-weight reasoning model, we find that the geometry of internal representations tracks these predicted dynamics, linking behavior to representational correlates of the fitted latent dynamics.

Many high-throughput scientific experiments produce distributional outputs, requiring conditional generative models to interpret the data, and to predict outcomes at new inputs. Acquiring experimental data at new conditions (e.g., for a new antigen or a new cell type) is often expensive, motivating the need for automated experimental design methods. However, existing active learning frameworks are limited as they assume scalar or vector-valued outputs. We first show that the Wasserstein test risk of a conditional generative task decomposes into a mean term and a shape term, demonstrating why mean-based active learning is blind to distributional shape. To capture both, we propose the transport Neural Tangent Kernel (tNTK), a tractable kernel that measures how sensitive a generative model's predicted distribution is with respect to its parameters. The tNTK recovers the standard NTK in the deterministic limit and upper-bounds the posterior Fréchet variance of the prediction under small parameter perturbations. It admits a closed form for affine Gaussian transport and tractable Monte Carlo estimators otherwise. Treating the tNTK as a Gaussian process covariance function, we greedily select inputs that minimize the total GP posterior variance across the pool, yielding a distribution-aware active learning strategy. We evaluate this strategy across four classes of conditional generative models, including conditional flow matching and conditional Monge gap, on synthetic distributions, intent-labeled sentences, and single-cell perturbation responses. In these experiments, the tNTK outperforms the baseline NTK computed from the conditional mean, demonstrating the value of distribution-aware active learning for generative-modeling tasks.

We consider the active learning problem where the goal is to learn an unknown function with low error under a Boltzmann distribution induced by the function itself. This self-induced weighting arises naturally in problems such as molecular energy modeling and free energy estimation, yet poses unique challenges as the target distribution is unknown and its partition function is intractable. We propose an acquisition function, AB-SID-iVAR, based on Gaussian Process surrogates that approximates the intractable Bayesian target distribution in closed form while avoiding partition function estimation, applicable to both discrete and continuous input domains. We also analyze a Thompson sampling alternative (TS-SID-iVAR) as a higher variance Monte Carlo variant. Despite the unknown target, under mild conditions, we establish that the terminal prediction error vanishes with high probability, and provide a tighter average-case guarantee. We demonstrate superior performance over existing active learning approaches on synthetic benchmarks and real-world modeling tasks.

Generative compressed sensing uses the range of a pretrained generator as a nonlinear model for recovering structured signals from limited measurements. We study a conditional version of this problem for image recovery from subsampled Fourier measurements using prompt-conditioned generative models. Our framework separates two roles of conditioning: the prompt used to design the sampling distribution and the prompt used to define the recovery model. For ReLU and Lipschitz conditional generators, we prove stable recovery bounds showing that prompt-matched Christoffel sampling retains the same Christoffel complexity constant as existing near-optimal generative compressed sensing theory, while prompt mismatch incurs an explicit compatibility penalty. Experiments with Stable Diffusion show that prompts meaningfully reshape Christoffel sampling distributions and influence image recovery. Overall, our results suggest that prompts should be treated as design variables with distinct effects on sensing, approximation, and recovery.

Most active learning (AL) methods estimate sample value through empirical criteria such as prediction ambiguity, diversity, or distributional coverage. We revisit AL from a spectral-geometric perspective by regarding the feature span of the current labeled set as the modeled subspace and its orthogonal complement as an operational residual subspace. The projected residual component of an unlabeled sample then reflects its relation to representation components weakly expressed by the labeled-feature spectrum. Based on this formulation, we propose a spectrally driven nullspace regulation framework that unifies spectrum-induced subspace decomposition, cross-cycle residual persistence estimation, and coverage-aware acquisition in the residual-coordinate space. This yields an acquisition criterion that favors samples whose residual components are both persistent across cycles and complementary to already selected samples. Experiments on visual benchmarks show competitive or improved sample efficiency over strong baselines. Further analyses support the proposed view by showing that residual components shrink anisotropically and that acquisition rankings vary substantially across backbones, indicating that sample value is conditioned on the current representation state rather than being purely data-intrinsic.

Standard flow and diffusion pre-training matches the distribution of available data (e.g., molecules), which often covers only a small fraction of the valid design space. In generative discovery, however, one aims to sample valid new-to-nature designs, assigned negligible probability under, and thus inaccessible to, standard models fitted to the observed data. To overcome this limitation, we depart from data distribution matching and view a generative model through its generable set: the region it covers with non-negligible probability. This allows to introduce a new learning principle for out-of-distribution flow modeling: enlarging a model’s generable set to increase coverage of the valid design space. We propose Active Flow Expansion (ActFlow), a continued pre-training method that employs verifier feedback to expand a pre-trained model over new valid regions by iteratively adapting to synthetic data generated through active exploration in the learned flow representation. Theoretically, we establish to our knowledge first-of-their-kind statistical learning guarantees for out-of-distribution flow modeling, analyzing generable set expansion as a local-to-global reachability process over a learned representation. Empirically, we assess ActFlow with suitable out-of-distribution generative modeling metrics across small organic molecules, mid-sized drug-like molecules, therapeutic peptides, and protein sequence design tasks. Results show that ActFlow expands valid coverage far beyond the region modeled by the initial pre-trained model, significantly outperforming widely adopted synthetic flow pre-training methods.

Neural subgraph retrieval (NSR) models degrade under query distribution shifts, and retraining for each new distribution requires collecting fresh ground-truth labels, each of which entails an NP-hard subgraph-matching instance across a large corpus—making repeated label collection computationally prohibitive. We introduce ACROSS, an active corpus selection framework that, under a fixed solver budget, selects a small corpus subset per out-of-distribution query whose labels suffice for effective NSR training. We prove that allocating the entire budget to retrieving positives is optimal given extreme class imbalance. To enable efficient positive retrieval across arbitrary query distributions, we linearize corpus embeddings around a base model, apply randomized projections to eliminate hinge nonlinearities, and train distribution-shift-tolerant representations via adversarial parameter perturbation. The resulting corpus index is built once and reused across all distributions. Experiments on four molecular graph datasets show ACROSS consistently outperforms six baselines in downstream retrieval accuracy.

We study how the MLP activation function shapes the long-time geometry of token representations in a deep transformer. We work in the stochastic transformer dynamics of [Agazzi et.al. 2026], in which tokens evolve as interacting particles on the sphere under deterministic attention and a common MLP noise whose covariance is the activation's NNGP kernel. For each of ReLU, ReLU², ReLU³, GELU, SiLU, and tanh, we identify the dimensions at which common noise stops driving tokens to full synchronization and sustains non-degenerate spread. We further prove that, even in the presence of attention, ReLU noise admits dispersion ceilings close to consensus, while ReLU$^2$ noise prevents complete token collapse under an explicit attention strength condition.

Large Language Models (LLMs) deployed as AI agents frequently exhibit a task-completion bias, executing hallucinated, undesired actions to force a resolution rather than expressing uncertainty. Existing detection methods fail to provide actionable, real-time correction as they either do not localize the hallucinations or incur prohibitive inference latency. We introduce the Latent Critic, a lightweight low-rank adapter (LoRA) that operates concurrently with a frozen base LLM's generation to actively restructure the transformer's residual stream---amplifying epistemic uncertainty signals and translating them into localized, natural language feedback within a single sequence. By refining the base model's native uncertainty signals, this manipulation of the latent space enables highly reliable, granular detection without the overhead of secondary inference loops. Mechanistic analysis via activation patching and layer-wise probing shows that this rank-invariant behavior restructures pre-existing uncertainty geometry into a linearly separable representation. Using tool-calling as an instantiation of granular hallucinations, we validate the detection and downstream improvements enabled by the Latent Critic architecture across Qwen and Llama-based models. Demonstrating superior real-time efficacy, our approach significantly outperforms equivalent-scale external detectors and internal probes in isolating hallucinations (0.870 vs. 0.695 F1), achieving >80% accuracy in localization (e.g., ungrounded: date). When deployed in a closed-loop ReAct environment, the Critic acts as a zero-latency guardrail, intercepting hallucinations before execution to prevent undesired actions while simultaneously enabling efficient agent self-correction.

Vision-Language-Action (VLA) models have shown great promise for robotic manipulation by mapping multi-modal semantics to physical actions. However, this mapping inherently struggles to align these coarse-grained semantics with fine-grained temporal execution. It leaves VLA models with limited generalization and insufficient robustness in cluttered environments. To overcome this issue, we propose ActionUNet, an efficient multi-scale fine-tuning framework that enhances pre-trained VLA models with minimal computational cost. ActionUNet first constructs a lightweight temporal U-Net within the temporal-aligned action feature space to fuse hierarchical structural priors, effectively bridging the scale gap between semantics and temporal executions. Recognizing that multi-scale modeling can disrupt microscopic temporal continuity and cause mechanical oscillations, ActionUNet then employs a conditional SIREN as a continuous action decoder. Equipped with explicit second-order smoothness constraints, this decoder guarantees temporal continuity and reduces high-frequency motion jitter. By smoothing temporal discontinuities from multi-scale fusion, this continuous formulation reduces mechanical execution failures while preserving the base VLA model's generalization and manipulation robustness. Extensive experiments on RoboTwin 2.0 and LIBERO-Plus benchmarks, together with real-world hard evaluations, demonstrate that ActionUNet significantly improves $\pi_{0.5}$ success rates by absolute 9.8\%, 6.1\%, and 11.4\%, respectively, while also generalizing to the regression-based OpenVLA-OFT backbone, highlighting its effectiveness and efficiency as a fine-tuning strategy. Code will be made publicly available upon acceptance.

Personalization histories vary across domains because surface actions and objectives differ: users watch or skip movies, click or ignore news, or request recommendation, summarization, question answering, or response generation. Rather than build a separate history encoder for each action space, we rewrite native interactions into a shared *action-on-item event schema*: a specific action on a specific item becomes positive, negative, or command-like evidence over a target-locus embedding whose geometry induces item-kind abstraction. Task requests become generalized commands over the active item-side abstraction. The modeling problem is how this evidence enters a user-specific state, persists, and is read out by the active command. We formulate the Multi-Timescale State Hypothesis (MTSH), where signed and command-like evidence flows through long-term stable interests, recency-sensitive short-term interests, and bursty episodic traces. We instantiate MTSH with $\texttt{PerTIDE}$, an action-conditioned multi-timescale encoder that learns a user-specific preference-history state and uses command-conditioned readout to produce a task-ready state. We evaluate $\texttt{PerTIDE}$ on MovieLens, MIND, and PENS for prediction, and PENS/OpenAI-Reddit for generation. $\texttt{PerTIDE}$ improves over the strongest baselines without explicit trace factorization by +2.36/+3.47, +10.05/+9.01, and +0.90/+1.42 MRR/nDCG on MovieLens, MIND, and PENS; and over the strongest two-shot large language model by +0.10/+0.18 and +0.04/+0.19 PerSEval-JSD/PerSEval-METEOR on PENS and OpenAI-Reddit. Removing action conditioning and command-conditioned readout degrades MIND by 6.52 MRR / 9.13 HR@10 and 4.14 MRR / 4.42 HR@10. Trace diagnostics show L/S/E specialization, while the full $L+S+E$ model is strongest under mixed stable, recency-sensitive, and episodic command evidence. These results support action-conditioned multi-timescale preference flow as a reusable user-history encoding principle.

Vision-Language-Action (VLA) models exhibit remarkable action generation for embodied intelligence, but their heavy compute and memory demands strain deployment on edge robotic platforms. Aggressive weight quantization (e.g., sub-4-bit) is the natural lever, yet existing post-training quantization (PTQ) methods suffer severe performance degradation in this regime. To address this, we introduce \textbf{ActQuant}, an action-guided mixed-precision PTQ framework that operates in two stages: (1) an inter-tensor allocator that assigns each weight matrix a single bit-width based on how much it contributes to predicting the agent's actions; (2) an intra-tensor scale optimizer tunes per-block quantization scales using action-aware curvature, so that dynamic range is concentrated on the weights most influential for control. We evaluate ActQuant both in simulation and on a real-world 6-DoF UR3 arm. On the LIBERO benchmark, ActQuant achieves state-of-the-art success rates across the sub-4-bit regime, retaining 94.95\% on OpenVLA-OFT and 94.8\% on $\pi_{0.5}$ at 3.0 bits-per-weight (vs. 96.9\% and 97.0\% for the half-precision baselines, respectively), while reducing backbone memory by up to $5.3\times$; on the physical robot, ActQuant successfully maintains the baseline's success rate. To our knowledge, ActQuant is the first PTQ approach that can quantize VLA models below four bits while retaining practical task success with very limited calibration data.

Video world models promise general-purpose interactive simulators, but their training is limited by action supervision: action labels are scarce, fragmented across incompatible specifications, and do not scale with the unlabeled video pretraining corpus. A common workaround jointly trains an action encoder to compress consecutive frames into a latent action and a decoder to reconstruct the next frame from the previous frame and that latent, forcing the latent to capture only new information. This has two limitations: learning the action space from scratch can limit generalization to unseen domains, and the bottleneck trades expressiveness for separation, with tighter settings losing nuance and looser ones risking scene leakage under domain shifts. We argue for a different starting point: rather than learning an action representation from scratch, we adapt a pretrained Multimodal Large Language Model (MLLM), which was trained on large-scale, diverse video-language data and whose embeddings already carry partial action information. This provides a more generalizable foundation for action representation. The remaining challenge is to disentangle action from scene. To this end, we propose a contrastive adaptation framework that reshapes the geometry of the pretrained space without imposing a low-dimensional bottleneck, preserving the expressiveness of the original embeddings. We introduce a unified evaluation protocol that probes action representations along three axes - action expressiveness, scene invariance, and action-conditioned video generation quality - across several robot and game benchmarks in both in-domain and out-of-domain settings. Our representations outperform prior annotation-free latent-action methods on all three axes.

Every control action on a physical system is already a do-operator intervention, yet causal discovery and control are typically treated as separate stages. This separation leaves deployed controllers unable to test whether the causal graph they rely on remains valid under changing operating conditions. We present \textsc{PolicyGRID}, a closed-loop framework that uses actuator interventions to validate candidate causal edges, fits a structural causal model over the validated graph, and reuses that graph for both policy optimization and latent-regime monitoring. In a multi-actuator physical simulation with latent operating regimes (building energy management), interventional graph validation reduces closed-loop energy use by 21\% at a standard comfort target relative to an otherwise identical observation-only graph, while improving four-way latent-context identification from 61.2\% to 80.8\%. A targeted ablation shows that the gains originate in graph pruning. Validation removes 16 of 47 candidate edges; with coefficient training held fixed, the validated graph reduces closed-loop energy relative to the unvalidated candidate set, while refitting coefficients on the same graph does not. On a live physical testbed, the same pipeline runs without code changes, performs 21 physical interventions, discovers 16 edges, and produces a target-responsive control policy where the observation-only baseline is insensitive to the comfort-energy target. These results show that physical controllers can use their own actions to validate causal structure and improve downstream control under latent regime shifts.

In adversarial multi-armed bandits, two performance measures are commonly used: static regret, which compares the learner to the best fixed arm, and dynamic regret, which compares it to the best sequence of arms. While optimal algorithms are known for each measure individually, there is no known algorithm achieving optimal bounds for both simultaneously. \cite{marinov2021pareto} first showed that such simultaneous optimality is impossible against an \emph{adaptive} adversary. Our work takes a first step to demonstrate its possibility against an \emph{oblivious} adversary when losses are \emph{deterministic}. First, we extend the impossibility result of \cite{marinov2021pareto} to the case of deterministic losses. Then, we present an algorithm achieving optimal static and dynamic regret simultaneously against an oblivious adversary. Together, they reveal a fundamental separation between adaptive and oblivious adversaries when multiple regret benchmarks are considered simultaneously. It also provides new insight into the long open problem of simultaneously achieving optimal regret against switching benchmarks of different numbers of switches. Our algorithm uses negative static regret to compensate for the exploration overhead incurred when controlling dynamic regret, and leverages Blackwell approachability to jointly control both regrets. This yields a new model selection procedure for bandits that may be of independent interest.

This paper addresses the challenge of obtaining strong optimality guarantees in constrained nonsmooth nonconvex optimization under mild regularity conditions, namely local Lipschitz continuity and existence and continuity of directional derivatives. While standard methods typically ensure weak stationarity notions, achieving directional (d-)stationarity remains nontrivial. We show that a random direction exploration step is sufficient to attain d-stationarity. The proposed approach augments any base optimization method with a single exploration step that samples a direction and step size and accepts the candidate based on a function value comparison. The resulting scheme guarantees that all accumulation points are d-stationary almost surely, independently of the behavior of the underlying method. Moreover, it preserves convergence rates of the base method, as established for DCA and prox-linear-type schemes. The theoretical results are complemented by numerical experiments illustrating the effect and guarantees of the exploration step.

Online bilevel optimization (OBO) has emerged as a powerful framework for many machine learning problems. Prior works have developed several algorithms that minimize the standard bilevel local regret or the window-averaged bilevel local regret of the OBO problem, but the optimality of existing regret bounds remains unclear. In this work, we establish optimal regret bounds for both settings. For standard bilevel local regret, we propose an algorithm with adaptive iteration strategy that achieves the optimal regret $\Omega(1+V_T)$ with at most $O(T\log T)$ total inner-level gradient evaluations. We further develop a fully single-loop algorithm whose regret bound includes an additional gradient-variation terms. For the window-averaged bilevel local regret, we design an algorithm that captures linear environmental variation through a novel window-based analysis and achieves the optimal regret $\Omega(T/W^2)$. The algorithm also supports an efficient single-loop structure, achieving an $O(T/W)$ regret bound with $O(WT)$ total gradient evaluations. Experiments validate our theoretical findings and demonstrate the practical effectiveness of the proposed methods.

Large language models (LLMs) have achieved remarkable success while introducing critical energy bottlenecks that challenge sustainable deployment. Spiking neural networks (SNNs) provide a promising approach for energy-efficient spiking LLMs via ANN-to-SNN (A2S) conversion. Among various spike coding methods, time-to-first-spike (TTFS) coding is particularly appealing as it conveys information with a single spike, further reducing energy consumption. However, existing TTFS-based A2S conversion relies on continuous-time assumptions, requiring prohibitively large latencies (e.g., 4096 time steps) to approximate ANN's continuous values. This dependency leads to unacceptable inference delays in LLMs, posing significant challenges for developing practical temporal-coding spiking LLMs. In this paper, we propose a discrete analysis framework for TTFS-based LLMs, reformulating TTFS-based A2S conversion from continuous lossless conversion into discrete error-aware representation. Building on this analysis, we establish an equivalence between discrete TTFS-based SNNs and static quantized ANNs, allowing TTFS conversion to be handled through quantization techniques. Motivated by this equivalence, we introduce Quantization-Consistent ANN-to-SNN (QC-A2S) conversion, which combines static quantization with discretization-compatible TTFS neurons to achieve latency-efficient and high-performance temporal-coding spiking LLMs. Extensive evaluations on representative LLMs across multiple benchmarks demonstrate competitive performance with substantially reduced inference latency.

The internal activations of modern machine learning models align surprisingly well with the activities recorded in real brains. In the last five years, the alignment between encoding models and brain activities, often called brain scores, has steadily increased. Because brain recordings are noisy, there exists an upper bound to the brain scores that any model can achieve. This bound, called the noise ceiling, is crucial for two reasons: it determines whether further improvements in model performance are possible, and it enables meaningful comparisons of brain scores across benchmarks. The field has developed multiple approaches to estimate noise ceilings, but the statistical properties of existing estimators remain poorly understood, leaving it unclear in which experimental settings they provide reliable estimates. Here, we introduce a unified mathematical framework for brain recordings, use it to derive closed-form expressions for four commonly used noise ceiling estimators, and provide theoretical predictions for the behavior of each estimator. We validate the theoretical predictions with simulations that we compare to noise ceiling estimates in existing fMRI datasets. We find that the existing methods underestimate the true noise ceiling in many settings. We conclude with recommendations for best practice in different situations.