NeurIPS 2026 Papers

The Abstraction and Reasoning Corpus (ARC) has become a prominent benchmark for evaluating skill acquisition in AI models. Yet standard ARC evaluation considers only a single capability: producing the correct output grid for a test input. We argue that this narrow format underestimates the diversity of abilities required for genuine abstract skill acquisition. We introduce PotARCin, a benchmark that extends ARC by assessing understanding of a task’s underlying abstract rule across five dimensions: Definition, Classification, Constrained Generation, Editing, and Inversion. PotARCin uses explicit generator and verifier programs, enabling dynamic generative sampling beyond fixed input-output pairs. Across four state-of-the-art models evaluated on the ARC-AGI-1 training set, we observe a 30–50 percentage-point performance gap between standard ARC evaluation and PotARCin. We further investigate effects of generative sampling, difficulty of corruption types and questions of self-consistency. We also introduce P-ARC, a hand-crafted test set with generator and verifier programs, on which models achieve 0-8% accuracy across all five dimensions, underscoring the difficulty of acquiring versatile abstract skills.

Generative models are increasingly used to solve scientific inverse problems, but existing evaluations still focus primarily on whether a method can produce a single plausible reconstruction. This is insufficient for ill-posed problems, where multiple solutions may be consistent with the same sparse or noisy observations. In these settings, a method can achieve strong pointwise accuracy while still failing to capture the true posterior through mode collapse, over-confident uncertainty, or averaging incompatible solutions. We introduce PosteriorBench, a benchmark for evaluating the distributional accuracy of generative inverse solvers. PosteriorBench evaluates four physics-based inverse problems: Darcy flow inversion, Poisson source recovery, carbon capture and storage, and light transport material inference. For each task, we construct high-fidelity reference posteriors using slow but established procedures such as rejection sampling and Markov chain Monte Carlo, enabling direct assessment of whether solvers recover the full set of solutions rather than the single best sample. The benchmark spans sparse sensing, low-resolution observations, nonlinear forward models, varying noise levels, and multimodal priors, with a unified pipeline for distribution matching, uncertainty quantification, and hyperparameter calibration. Our experiments reveal substantial distribution-matching gaps across current solvers, while showing that neural operators improve resolution robustness and that guidance weights and generation noise are key to posterior-variance calibration.

We study fixed-confidence best-arm identification in Bernoulli bandits. A learner sequentially samples from $K$ arms and aims to identify the unique best arm while keeping the error probability at most $\delta$. We ask whether the classical lower bound on expected sample complexity can be matched asymptotically without ongoing forced exploration. We propose a posterior-tracking algorithm that first samples each arm once, then repeatedly draws a bandit instance from the posterior, computes the oracle allocation for that instance, and randomly selects the next arm according to that allocation. Stopping is based on a Bernoulli generalized likelihood ratio test. Since the algorithm has no explicit forced-exploration mechanism after initialization, the main technical challenge is to show that posterior randomness alone sustains sufficient exploration. We prove that, with summable tail probabilities, every arm is sampled at least logarithmically often. This yields an integrable stabilization time after which the true best arm remains the empirical leader and the corresponding generalized likelihood ratio statistic grows linearly at the information-theoretic lower-bound rate. Consequently, the proposed procedure is $\delta$-correct and achieves asymptotically optimal expected sample complexity as $\delta \to 0$.

Learning in POMDPs is known to be significantly harder than in MDPs. In this paper, we consider the online learning problem for episodic POMDPs with unknown transition and observation models. We propose a Posterior Sampling-based reinforcement learning algorithm for POMDPs (PS4POMDP), which is much simpler and more implementable compared to state-of-the-art optimism-based online learning algorithms for POMDPs. We show that the Bayesian regret of the proposed algorithm scales as the square root of the number of episodes and is polynomial in the other parameters. In a general setting, the regret scales exponentially in the horizon length $H$, and we show that this is inevitable by providing a lower bound. However, when the POMDP is undercomplete and weakly revealing (a common assumption in the recent literature), we establish a polynomial Bayesian regret bound. We finally propose a posterior sampling algorithm for multi-agent POMDPs, and show it too has sublinear regret.

We study posterior contraction rates for sparse Bayesian Kolmogorov-Arnold networks (KANs) over anisotropic Besov spaces, providing a statistical foundation of KANs from a Bayesian point of view. We show that sparse Bayesian KANs equipped with spike-and-slab-type sparsity priors attain the near-minimax posterior contraction. In particular, the contraction rate depends on the intrinsic anisotropic smoothness of the underlying function. Moreover, by placing a hyperprior on a single model-size parameter, the resulting posterior adapts to unknown anisotropic smoothness and still achieves the corresponding near-minimax rate. A distinctive feature of our results, compared with those for standard sparse MLP-based models, is that the KAN depth can be kept fixed: owing to the flexibility of learnable spline edge functions, the required approximation complexity is controlled through the network width, spline-grid range and size, and parameter sparsity. Our analysis develops theoretical tools tailored to sparse spline-edge architectures, including approximation and complexity bounds for Bayesian KANs. We then extend to compositional Besov spaces and show that the contraction rates depend on layerwise smoothness and the effective dimension of the underlying compositional structure, thereby effectively avoiding the curse of dimensionality. Together, the developed tools and findings advance the theoretical understanding of Bayesian neural networks and provide rigorous statistical foundations for KANs.

Ambiguous inverse problems often admit multiple clean signals that are consistent with the same observation. In such settings, a sampler should not only produce plausible or measurement-consistent reconstructions, but also allocate probability mass correctly across the alternatives that remain unresolved. We formalize this requirement as \emph{posterior alternative calibration} and introduce mode coverage error (MCE), a finite-alternative diagnostic that measures calibration after pushing the posterior and sampler distributions onto a benchmark-specified alternative label space. This perspective reveals a basic failure mode of point-centered inverse solvers: measurement consistency can be preserved by averaging across alternatives, even when the resulting point lies outside the nonconvex set of valid posterior explanations. We prove that local point-denoising updates can therefore suffer barycentric collapse under weak branch identification, while calibrated local branch probabilities are sufficient to control MCE. Across controlled Gaussian, imbalanced, nullspace, and template-inpainting diagnostics, MCE exposes posterior mass-allocation failures that are missed by residual error, recall, diversity, and confidence. A semantic-label inpainting benchmark with DDIM, DPS, DDNM, RePaint, and clustering-based samplers further shows that practical samplers can recover all specified alternatives while assigning different branch probabilities. These results position MCE as a targeted evaluation axis for finite-alternative ambiguity benchmarks, complementary to reconstruction fidelity and sample quality.

As synthetic images become increasingly realistic, reliable synthetic image detection techniques are of pressing need to prevent their misuse. Despite satisfactory in-distribution performance, deep neural network-based synthetic image detectors (SIDs) lack reliability in deployment and often fail in the presence of common covariate shifts, resulting in poor detection accuracy. To avoid the risk caused by potential errors, we adopt a selective classification (SC) strategy by allowing SIDs to abstain from making low confidence predictions. For practicality, we focus on post-hoc methods which perform confidence estimation on a given SID without retraining. However, we show that conventional logit-based confidence score functions (CSFs) exhibit pathological behavior under covariate shifts, leading to SC performance close to or even worse than random guessing. To address this, we propose a simple yet effective SC framework for **Re**liable **S**ynthetic **I**mage **De**tection (ReSIDe). First, we generalize the notion of logits to an SID's intermediate layers from a centroid matching perspective, extending the use of logit-based CSFs to any layer of an SID. Then, we introduce a preference optimization algorithm that aggregates confidence scores extracted from different layers to a final confidence estimate by minimizing an upper bound of the area under the risk-coverage curve (AURC). Extensive experimental results show that ReSIDe significantly boosts the SC performance of various logit-based CSFs under common covariate shifts, achieving up to 69.55% AURC reduction.

Vision Transformers (ViTs) demonstrate strong performance, but their substantial memory footprint and computational overhead necessitate efficient compression techniques such as post-training quantization (PTQ). However, pushing ViTs to low-bit precision incurs significant accuracy degradation. Recent PTQ methods adopt block reconstruction-based optimization with curvature-aware objectives, typically implemented using Fisher-based approximations. These approaches rely on explicit curvature modeling based on diagonal or structured approximations, which still fail to capture cross-dimensional interactions. Moreover, they often involve matrix inversion, leading to numerical instability under ill-conditioned settings. To address these limitations, we propose Gradient-Projected Fisher Approximation for Quantization (GPFA-Q), a block reconstruction-based PTQ framework that avoids explicit curvature matrix construction while capturing off-diagonal interactions. First, we introduce Gradient-Projected Reconstruction (GPR), a reconstruction objective that captures cross-dimensional interactions without explicitly constructing curvature matrices. To further support GPR, we integrate Soft Grid Rounding (SGR), which reduces the mismatch between continuous reconstruction and discrete inference. Extensive experiments demonstrate that our GPFA-Q achieves the state-of-the-art performance in low-bit quantization across diverse vision tasks.

Formal model evaluation methods typically certify that a model satisfies a prescribed target key performance indicator (KPI) level. However, in many applications, the relevant target KPI level may not be known a priori, and the user may instead wish to compare candidate models by analyzing the full trade-offs between performance and reliability achievable at test time by the models. This task, requiring the reliable estimate of the test-time KPI distributions, is made more complicated by the fact that the same data must often be used both to pre-select a subset of candidate models and to estimate their KPI distributions, causing a potential post-selection bias. In this work, we introduce post-selection distributional model evaluation (PS-DME), a general framework for statistically valid distributional model assessment after arbitrary data-dependent model pre-selection. Building on e-values, PS-DME controls post-selection false coverage rate (FCR) for the distributional KPI estimates and we establish explicit conditions under which it is provably more sample efficient than a baseline method based on sample splitting. Experiments on synthetic data, text-to-SQL decoding with large language models, and telecom network performance evaluation demonstrate that PS-DME enables reliable comparison of candidate configurations across a range of reliability levels, supporting the statistically reliable exploration of performance--reliability trade-offs.

This paper studies binary classification under generalized performance metrics, going beyond standard misclassification error. We focus on linear-fractional measures—including the $F$-score and Jaccard index—which are widely used in class-imbalanced settings. We first provide a unified characterization of the optimal classifier, showing that it admits a thresholding structure on the regression function. This reduces the original infinite-dimensional, non-decomposable optimization problem to the estimation of a single scalar parameter. Building on this result, we analyze plug-in classifiers that combine a regression estimator with a data-driven estimate of the optimal threshold. We show that this threshold is characterized as the solution of a fixed-point equation depending only on the marginal distribution, enabling its estimation using unlabeled data and avoiding standard validation-based procedures. Our main contribution is a finite-sample analysis of this approach. We derive excess risk bounds that decompose the error into contributions from regression estimation, threshold estimation, and sampling effects, providing a modular understanding of learning under non-decomposable metrics. Under standard margin assumptions, we further establish fast convergence rates. Our results yield a unified theoretical framework for plug-in classification under linear-fractional metrics, extending prior analyses beyond specific measures such as the $F$-score. Empirical results on synthetic and real datasets support our theoretical findings.

The validity of statistical inference depends critically on how data are collected.When data gathered through active data collection (ADC) are reused for a post-hoc inferential task, conventional inference can fail because the sampling process is adaptively biased toward regions favored by the collection strategy. This issue is especially pronounced in black-box optimization, where sequential model-based optimization (SMBO) methods such as the tree-structured Parzen estimator (TPE) and Gaussian process upper confidence bound (GP-UCB) preferentially concentrate evaluations in promising regions. We study statistical inference on actively collected data when the inferential target is constructed in a data-dependent manner after data collection. To enable valid inference in this setting, we propose post-ADC inference, a framework that accounts for the biases arising from both the active data collection process and the subsequent data-driven target construction. Our method builds on selective inference and provides valid $p$-values and confidence intervals that correct for both sources of bias. The framework applies to a broad class of ADC processes by imposing only assumptions on the observation noise, without requiring any assumptions on the underlying black-box function or the surrogate model used by the SMBO algorithm. Empirical results also show that post-ADC inference provides valid inference for data collected by GP-UCB and TPE.

Vision-Language Models (VLMs) for radiology report generation are typically trained on retrospective clinical reports, which suffer from omission noise: clinically present findings are left unreported due to the omission of subtle findings. For example, prior studies show that cardiomegaly may be omitted from ICU chest X-ray reports when the imaging request is focused on monitoring support device placement. As a result, models trained with standard approaches inherit these omissions, learning to under-report findings themselves. We propose PU-DPO, a preference optimization framework that constructs contrastive pairs via editing model responses, producing variants that explicitly mention or omit a specific finding. To prevent omission noise from corrupting the preference signal, we reformulate the objective under a positive-unlabeled (PU) learning framework, treating absent mentions as unlabeled rather than truly negative. Across semi-synthetic experiments and preliminary analyses on real-world chest radiograph benchmarks where adjudicated labels are available, PU-DPO yields consistent gains in detection rates across multiple pathologies without compromising specificity or overall report quality, and is more robust to omission noise than prior approaches.

Positional encoding in transformers is commonly implemented through positional embeddings, attention masks, or bias terms, but formal connections between these mechanisms remain limited. We study attention with positional bias through the lens of locality-sensitive hashing (LSH), focusing on Attention with Linear Biases (ALiBi). We show that the ALiBi bias matrix is the expectation of contiguous block-diagonal binary masks induced by a ``positional LSH'' scheme. The empirical mean of masks sampled from this scheme yields spectral norm and max-norm approximation guarantees with bounded block sizes with high probability. This structural theorem implies a uniform approximation theorem for ALiBi-biased attention: with high probability over the sampled masks, the approximate attention output is accurate simultaneously for all query-key-value inputs and can be computed in near-linear time in the context length, reducing long-context ALiBi to a collection of randomized short-context regular (positionally unbiased) attention operations. Conceptually, this connects positional bias, masks, and positional embeddings in a single formal framework and suggests an approach to efficient ALiBi-biased attention. Experiments on large language models validate our theoretical findings.

Transformer models have demonstrated a remarkable ability to perform a wide range of tasks through in-context learning (ICL), where the model infers patterns from a small number of example prompts provided during inference. However, empirical studies have shown that the effectiveness of ICL can be significantly influenced by the order in which these prompts are presented. Despite its significance, this phenomenon has been largely unexplored from a theoretical perspective. In this paper, we theoretically investigate how positional encoding (PE) affects the ICL capabilities of linear attention transformer models, particularly in tasks where prompt order plays a crucial role. We examine two distinct cases: linear regression, which represents an order-invariant task, and dynamical systems, a classic time-series task that is inherently sensitive to the order of input prompts. Theoretically, we evaluated the change in the model output when two types of positional encoding (one-hot and RoPE) is incorporated and the prompt order is altered. In all cases, the leading dependence on the permutation size and context length is $k/N$, with constants determined by the positional encoding, model weights, input dimension, and task dependent parameters. These theoretical findings are experimentally validated.

This position paper argues that the research community must act to maintain research pipeline reliability despite increasing threats from GenAI. We start in the pre-GenAI era by highlighting some of the prominent critiques of the research pipeline, consisting of: (a) Authoring, (b) Reviewing, and (c) Evaluating researchers based on bibliometrics. Then, we discuss some of the effects GenAI has had on each research pipeline component based on the best available data, limited though it may be. Importantly, due to opaqueness of the submission pipeline, it is difficult to measure both the impact of GenAI and the efficacy of interventions, which leads us to call for greater transparency. Last, we conclude by offering three alternative views and ten paths forward that may mitigate some of the issues we highlight by keeping human researchers as the primary driver of science

Neuro-symbolic learning was proposed to address challenges with training neural networks for complex reasoning tasks with the added benefits of interpretability, reliability, and efficiency. Neuro-symbolic learning methods traditionally train neural models in conjunction with symbolic programs, but they face significant challenges that limit them to simplistic problems. On the other hand, purely-neural foundation models now reach state-of-the-art performance through prompting rather than training, but they are often unreliable and lack interpretability. Supplementing foundation models with symbolic programs, which we call neuro-symbolic prompting, provides a way to use these models for complex reasoning tasks. Doing so raises the question: What role does specialized model training as part of neuro-symbolic learning have in the age of foundation models? To explore this question, we highlight three pitfalls of traditional neuro-symbolic learning with respect to the compute, data, and programs leading to generalization problems. This position paper argues that foundation models enable generalizable neuro-symbolic solutions, offering a path towards achieving the original goals of neuro-symbolic learning without the downsides of training from scratch.

Large Language Models and their multi-modal variants see increasingly rapid adoption and deployment, including in settings where reliability matters. However their uncertainty remains difficult to assess as classic or early token-level approaches cannot deal with the open-ended outputs of such models. Semantic uncertainty arises as a promising solution to the limits of token-level confidence by measuring disagreement among multiple generated responses. This position paper argues that this framing is incomplete: semantic uncertainty measures semantic disagreement, not actual reliability. A model can be uncertain while producing several valid answers, or certain while repeatedly producing the same wrong answer. We introduce a semantic bias–uncertainty decomposition to show that reliability depends both on variability across meanings and systematic deviation from correct or grounded meanings. This perspective reveals that common hallucination-detection evaluations conflate uncertainty with error. We argue for reliability-centered evaluation that separates semantic disagreement, correctness, and enables a more fine-grained characterization of uncertainty beyond the level of the full answer.

Modern frontier AI has been driven by a powerful but increasingly narrow recipe: scale the model, extend the context, and rely on emergent capabilities to support more complex forms of reasoning. \textbf{This position paper argues that this recipe is approaching a structural bottleneck. Robust reasoning requires more than parameter count, stored knowledge, or longer context windows. It requires intrinsic temporal structure i.e. the capacity of a system to generate, inhabit, and reason relative to its own internal time.} We argue that current architectures lack this capacity not merely as an implementation detail, but because most are built around fixed-pass or externally clocked computation rather than self-clocked, persistent, and dynamically coordinated processing. Our position is motivated by three converging lines of evidence. First, psychometric research links intelligence to the allocation and precision of processing time. Second, Global Workspace Theory suggests that flexible cognition depends on competitive access to a limited shared present and third, neural binding theories show that integration across distributed processors requires temporal co-activation rather than spatial co-location alone. Together, these motivate a two-level architectural view in which a diverse long-term population of specialist processors develops private temporal dynamics, while a short-term workspace constructs a shared present moment through selective competition and broadcasts it back to guide subsequent processing. We argue that existing work on continuous thought machines, conscious Turing machines, adaptive computation, memory-augmented models, mixture-of-experts, and quality-diversity neuroevolution already contains many of the necessary ingredients, but has not yet coupled them around intrinsic time as the organising principle. We outline falsifiable predictions for this view, including that harder reasoning problems should require deeper internal temporal trajectories, that synchronisation patterns should track task structure, and that self-clocked architectures should exhibit stronger adaptation under equal compute than fixed-pass alternatives. We call on the AI community to treat intrinsic temporal structure as a first-class architectural objective, not as an incidental by-product of scale.

The rapid rise of AI has seen the coexistence of open-weight models and closed-source, API-based deployment, each with its own strengths and limitations. A growing share of deployment scenarios needs both local, customizable execution and owner-side accountability, yet neither extreme serves them well. Such scenarios include on-prem enterprise use with sensitive data, edge and offline robotics, and local fine-tuning or retrieval-augmented generation. This position paper argues that the middle regime between closed APIs and open-weight release deserves a principled deployment-level primitive of its own, and proposes OML—Open, Monetizable, Loyal—as a starting point for that primitive. An OML-formatted artifact aims to be simultaneously Open (open-weight and locally executable), Monetizable (usage is accountable to the owner), and Loyal (owner-declared use constraints are enforceable). Throughout, "open" refers to open-weight, locally executable artifacts rather than to fully open-source release, and "loyal" refers to owner-declared use constraints rather than to remote control over a running model. We articulate the desirable properties and threat model for OML, survey theoretical and practical constructions across software, hardware, and cryptographic primitives, and outline an end-to-end deployment protocol together with market-based and policy alternatives. We then describe OML 1.0, a low-overhead instantiation based on AI-native fingerprinting, and characterize the regime in which it provides meaningful guarantees. We close with a research agenda calling on the ML, cryptography, systems, and mechanism-design communities to refine the primitives needed to make OML deployable at scale.