NeurIPS 2026 Papers

Mathematical autoformalization can fail before proof generation, when an informal concept is grounded to the wrong Lean/Mathlib object. Multilingual terminology makes this step non-monotonic: aliases can recover missing concepts, but under collision stress they can also pull retrieval toward nearby, non-interchangeable anchors. We introduce FACBench, a targeted dependency-light benchmark and audit protocol for multilingual formal-anchor grounding before proof generation. FACBench combines a five-language concept inventory with controlled collision queries, Mathlib-graph stress tests, no-label ablations, theorem-like probes, and Lean-facing anchor checks. In controlled collision settings, naive multilingual alias union can place the expected anchor in the candidate list while ranking a nearby distractor first. A simple rule-based source/context guard improves top-1 anchor accuracy over naive multilingual retrieval by about 11 percentage points on controlled collisions and 28 percentage points on a Mathlib-graph-mined controlled holdout. Less scaffolded and theorem-like probes show where this guard stops helping and point to the need for role-aware grounding. FACBench provides reusable collision-focused evaluation and regression-test scenarios for retrieval-augmented autoformalization systems.

Cognitive Load Theory (CLT) shows that human problem-solving is affected by both intrinsic load, arising from task difficulty, and extraneous load, arising from how task information is presented. LLMs show analogous effects, where presentation alone can affect model performance, but these effects have not yet been systematically isolated from task difficulty. To address this gap, we introduce CogLoadBench, a controlled benchmark that varies five CLT-inspired presentation factors across three reasoning task families. Across models, we find that higher extraneous load conditions often reduce accuracy by either adding competition or complicating the reasoning path. To support diagnosis and mitigation of load-related effects, we propose the Extraneous Load Score (ELS), a prompt-time metric computed from activations that estimates a model's extraneous load, and show that it generalizes across reasoning task types and load levels. We further show that shifting model representations toward lower-ELS directions at inference time can significantly improve model performance without changing prompt content.

Diffusion and flow-based models learn powerful data priors by training a denoiser to reverse Gaussian corruption. To use this prior to solve a linear inverse problem, one needs to sample from the posterior, but the score that the prior provides is the unconditional score, not the posterior score. Existing methods either steer a fixed pretrained denoiser with approximate measurement-matching corrections, or train a conditional restoration model that abandons the denoising structure of the prior. We derive the exact posterior score in closed form for linear Gaussian inverse problems under general Gaussian interpolants, and show that posterior sampling reduces to a denoising problem at an operator-dependent shifted pivot under an anisotropic noise covariance. We turn this identity into **Exact Posterior Score (EPS)**, a denoising training objective that preserves the input/output structure of standard pretraining and can therefore be trained from scratch or fine-tuned from a pretrained denoiser. At inference, EPS uses the same sampler as the underlying backbone, with no likelihood gradients or projections. We evaluate EPS on five linear inverse problems across FFHQ and ImageNet, where it outperforms training-free and training-based baselines on fidelity, perceptual, and distributional metrics, while using roughly an order of magnitude fewer denoiser evaluations than gradient-based posterior samplers.

In the past year, custom and unreleased math reasoning models reached gold medal performance on the International Mathematical Olympiad (IMO). Similar performance was then reported using large-scale inference on publicly available models but at prohibitive costs (e.g., 3000 per problem). In this work, we present an inference pipeline that attains best-in-class performance on IMO-style math problems at an average inference cost orders of magnitude below competing methods while using only general-purpose off-the-shelf models. Our method relies on insights about grader failure in solver-grader pipelines, which we call the Cognitive Well (iterative refinement converging to a wrong solution that the solver as well as the pipeline's internal grader consider to be basically correct). Our pipeline addresses these failure modes through conjecture extraction, wherein candidate lemmas are isolated from generated solutions and independently verified alongside their negations in a fresh environment (context detachment). On IMO-ProofBench Advanced (PB-Adv), our pipeline achieves 67.1\% performance using Gemini 3.0 Pro with an average cost per question of $\sim$ \$31. This surpasses the performance of the DeepThink IMO gold-winning model, and more than doubles the success rate of the next best publicly accessible pipeline, all at a fraction of the cost.

Large Reasoning Models (LRMs) have shown remarkable reasoning capabilities, yet they still suffer from overthinking, generating redundant reasoning steps which incur substantial token consumption. Existing methods, such as suppressing reflective keywords or forcing shorter reasoning lengths, attempt to mitigate this issue but inevitably truncate necessary steps and induce underthinking, thereby compromising performance. To address this dilemma, we investigate the latent representations and observe that efficient reasoning steps naturally cluster into a concentrated region in latent space, while those deviating from this region tend to produce verbose sequences. To leverage this, we keep reasoning focused within this region via a quadratic program which projects deviating hidden states back into the region. Then we propose a novel training-free framework to achieve efficient reasoning that reduces token generation costs without sacrificing performance. Extensive experiments conducted on four models ranging from 1.5B to 14B, and across six benchmarks in math reasoning, coding, and scientific QA, validate the effectiveness of our method, up to a 13.4\% improvement in accuracy while reducing generated tokens by 11.8\% to 52.8\%. Code and models will be publicly available.

Existing graph neural network-based methods for Boolean satisfiability (SAT) solving are generally constrained by limited local receptive fields, making it difficult to adequately capture the long-range dependencies between variables and clauses in SAT instances. Moreover, these methods overlook the multi-solution nature of SAT instances. Consequently, their expressive power and generalization performance remain limited. To address these issues, we propose DualSAT, a novel neural framework for the SAT problem, designed to enhance the phase selection heuristic of SAT solvers. Specifically, DualSAT adopts a novel dual-branch graph neural network that separately encodes local structural information and global structural information in the graph, and then fuses them through an attention-based cross-branch feature fusion module. An assignment decision head is further introduced to generate the initial assignment prediction of variables. This prediction process requires only a single forward pass, achieving a favorable balance between expressive power and inference efficiency. Furthermore, to account for the multiple solutions nature of SAT instances, we design a two-stage training strategy that combines supervised and unsupervised learning to improve the generalization performance of the model. Experimental results on multiple datasets show that, as an end-to-end assignment prediction model, DualSAT significantly outperforms NeuroSAT and NeuroBack. In addition, we integrate DualSAT into the classical SAT solver CaDiCaL, where it increases the number of solved instances by up to 11.6% and reduces the number of conflicts by up to 9.21% on SAT competition problem sets.

Difficulty perception is essential for adaptive reasoning in large language models (LLMs). Previous studies rely on training auxiliary models or using extra reasoning rollouts to estimate difficulty, which incurs high computational costs. In this paper, we identify an intrinsic property of LLMs: their internal representations, even before explicit reasoning, encode an informative and useful signal that correlates with problem difficulty. Inspired by this property, we propose Referential Latent Difficulty Perception (RLDP), a training-free and rollout-free method that estimates difficulty directly from hidden activations in a single forward pass, and requires only minimal reference problems. Additionally, we introduce RLDP-AdaSwitch, a lightweight controller that dynamically allocates reasoning effort based on the difficulty signals provided by RLDP, enabling efficient trade-offs between accuracy and compute. Our experimental results across multiple LLMs and diverse datasets, including math reasoning, code generation, and QA, demonstrate that RLDP provides stable and effective difficulty discrimination. This further powers RLDP-AdaSwitch to achieve 1.34×–2.00× efficiency compared to rollout-based methods, while matching the performance of training-based methods.

Evaluating whether Multimodal Large Language Models can produce trustworthy, verifiable reasoning over long, visually rich documents requires evaluation beyond end-to-end answer accuracy. We introduce DocScope, a benchmark that formulates long-document QA as a structured reasoning trajectory prediction problem: given a complete PDF document and a question, the model outputs evidence pages, supporting evidence regions, relevant factual statements, and a final answer. We design a four-stage evaluation protocol—Page Localization, Region Grounding, Fact Extraction, and Answer Verification—that audits each level of the trajectory independently through inter-stage decoupling, with all judges selected and calibrated via human alignment studies. DocScope comprises 1,124 questions derived from 273 documents, with all hierarchical evidence annotations completed by human annotators. We benchmark 6 proprietary models, 12 open-weight models, and several domain-specific systems. Our experiments reveal that answer accuracy cannot substitute for trajectory-level evaluation: even among correct answers, the highest observed rate of complete evidence chains is only 29\%. Across all models, region grounding remains the weakest trajectory stage. Furthermore, the primary difficulty stems from aggregating evidence dispersed across long distances and multiple document clusters, while an oracle study identifies faithful perception and fact extraction as the dominant capability bottleneck. Cross-architecture comparisons further suggest that activated parameter count matters more than total scale. The benchmark and code will be publicly released.

Depth-recurrence promises improved latent reasoning by sharing parameters across depths. However, prior work still relies on partially fixed layer stacks and overlooks the bottleneck of constant hidden-size; moreover, it largely lacks rigorously resource-matched ablations. To address this, we introduce depth-recurrent attention mixtures (Dreamer), a modular architecture with a single recurring layer. Concretely, we mix sequence attention, depth attention, and sparse expert attention. This alleviates the hidden-size bottleneck, decouples scaling dimensions, and achieves effective yet efficient depth-recurrence. Across natural language reasoning benchmarks at up to ~2B parameters, Dreamer requires on average ~3x fewer training tokens for the same accuracy as FLOP-, parameter-, and memory-matched modern Transformers, and outperforms ~2x larger Transformers given same training tokens. Analysis further reveals 2-11x greater expert selection diversity than conventional MoEs, highlighting the flexible knowledge sharing across depths.

Humans solve complex problems by flexibly shifting among reasoning modes, often without explicit deliberation: they plan, execute, revise intermediate goals, resolve ambiguity through associative judgment, and apply formal procedures to well-specified subproblems. Current LLM agents lack this flexibility, as their scaffolds hard-code such reasoning decisions in advance through fixed inference patterns. These scaffolds are effective when their prescribed structure matches the task, but brittle when solving the task requires adapting the structure of reasoning itself. We introduce Deep Reasoning -- an inference-time approach for constructing task-specific scaffolds through structured meta-reasoning. Deep Reasoning uses a formal language that represents meta-reasoning as executable decompositions over associative inference, formal computation, and recursive subproblem solving, enabling decomposition principles to be encoded as in-context examples that guide test-time scaffold construction. We instantiate this approach in a general-purpose agent (DOLORES) that distributes complex tasks across smaller, more controlled reasoning threads while preserving dependencies among subproblems. We evaluate DOLORES against state-of-the-art scaffolding methods across four hard benchmarks: grounded multi-hop reasoning, synthetic long-chain question answering, long-context aggregation, and deep research-style information seeking. DOLORES outperforms all evaluated scaffolds across four benchmarks, three model sizes, and two model families, improving over the strongest evaluated scaffold baseline by 24.8% on average, including methods tailored to individual benchmark families. Trace and token analyses suggest that while baseline scaffolds fail by overloading individual LLM calls, DOLORES succeeds by distributing cognition across structured, lower-load reasoning threads, thereby reducing premature termination and hallucination. This advantage can even bridge the scaling gap, with an 8B version surpassing all evaluated 32B baselines from the same family in more than half the settings. These results point toward future agentic systems that treat scaffolding as adaptive reasoning, constructing the structure each task requires just-in-time.

Large Reasoning Models (LRMs) exhibit backtracking and self-verification mechanisms that enable them to revise intermediate steps and reach correct solutions, yielding strong performance on complex logical benchmarks. We hypothesize that such behaviors are beneficial only when the model has sufficiently strong “critique” ability to detect its own mistakes. This work systematically investigates how current LRMs recover from errors by inserting arithmetic mistakes in their intermediate reasoning steps. Notably, we discover a peculiar yet important phenomenon: despite the error propagating throughout the entire chain-of-thought (CoT) without any verbalized correction, the model still reaches the correct final answer after the thinking process finishes. This recovery implies the existence of an internal mechanism helping the model to detect errors and trigger self-correction, which we refer to as the hidden critique ability. Building on feature space analysis, we identify a highly interpretable critique vector representing this behavior. Extensive experiments across multiple model scales and families demonstrate that steering latent representations with this vector improves the model’s error detection capability and enhances the performance of test-time scaling at no extra training cost. Our findings provide a valuable understanding of LRMs’ critique behavior, suggesting a promising direction to control and improve their self-verification mechanism.

Recent work has identified a set of emergent symbolic mechanisms that support abstract reasoning in large language models, but it remains unclear what factors drive the emergence of these mechanisms. To address this question, we trained neural networks from scratch on abstract sequence tasks, varying both architectural and data distributional factors, and investigated the effects of these factors on the emergence of symbolic mechanisms. Using a combination of representational, attentional, and casual mediation analyses, we first confirmed that transformer language models trained from scratch on our task developed symbolic mechanisms, partially capturing the set of mechanisms learned by large-scale pretrained models. We then investigated the effect of data diversity, operationalized as vocabulary size, on the emergence of these mechanisms, finding that mechanistic and behavioral signatures of emergent symbol processing scaled with data diversity, including downstream measures of systematic (i.e., out-of-distribution) generalization. Surprisingly, we found that the emergence of symbolic mechanisms was not driven by architectural inductive biases, as the same mechanistic and behavioral signatures emerged in modified transformer architectures and even multilayer perceptrons. These results suggest that data diversity, rather than architectural inductive biases, is the primary driver of emergent symbolic computation in neural networks.

Diagram question answering (DQA) requires models to interpret structured visual representations such as charts, maps, infographics, circuit schematics, and scientific diagrams. Recent vision-language models (VLMs) often achieve high answer accuracy on these tasks, yet correct answers do not guarantee that models ground their reasoning in the diagram regions that support the prediction. Models may instead rely on textual correlations or dataset artifacts without identifying the visual evidence required to verify the answer. This limitation prevents reliable evaluation of diagram reasoning and reduces interpretability. We introduce **DRAGON**, a benchmark for evaluating evidence-grounded visual reasoning in diagrams. Given a diagram, a question, and the correct answer, a model must predict bounding boxes that correspond to the visual elements required to justify the answer. These evidence regions may include answer-bearing components, textual labels, legends, axes, connectors, and other supporting structures involved in the reasoning process. The DRAGON dataset contains 11,664 annotated question instances from six diagram QA datasets: ChartQA, Circuit-VQA, InfographicsVQA, MapIQ, MapWise, and AI2D, with a 2,445-instance test set carrying human-verified evidence annotations and a standardized evaluation framework. Our evaluation on recent VLMs reveals that even Claude Opus 4.6 achieves a Grounding IoU of only 23.8% on AI2D, showing that faithful visual grounding remains an open challenge. DRAGON supports future research on models that ground their predictions in visual evidence.

Reinforcement learning with verifiable rewards (RLVR) has become a dominant recipe for improving mathematical and code reasoning in open-weight language models, but existing methods rely on fixed hyperparameters despite highly non-stationary training dynamics. We present DACE-RL (Diagnosis-Aware Compute-Efficient RL), a closed-loop framework that promotes training diagnostics to first-class signals. DACE-RL tracks four lightweight statistics—token entropy, sample diversity, advantage saturation, and answer consistency—and feeds their EMA-smoothed state to a controller that adaptively sets per-prompt rollout budget, sampling temperature, asymmetric clipping bounds, and entropy regularization strength. We formalize adaptive rollout allocation as a difficulty-conditioned multi-armed bandit and provide a regret bound that improves over uniform-budget GRPO under heterogeneous prompt difficulty; we also give a stability result for the dual-loop entropy-diversity controller. Across three small base models (Qwen2.5-Math-1.5B, Qwen2.5-7B, and Llama-3.1-8B-Instruct) and six math reasoning benchmarks, DACE-RL matches or improves Pass@1 while reducing rollout-GPU-hours by 38–52%, and improves Pass@32 by 4.7 absolute points on average. Pilot analysis further shows that diagnostic inflection signals appear 100–300 update steps before reward plateau, indicating that diagnosis-aware control is a key lever for compute-efficient RLVR.

We introduce CurveBench, a benchmark for hierarchical topological reasoning from visual input. CurveBench consists of $\textbf{756 images}$ of pairwise non-intersecting Jordan curves across easy, polygonal, topographic-inspired, maze-like, and dense counting configurations. Each image is annotated with a rooted tree encoding the containment relations between planar regions. We formulate the task as structured prediction: given an image, a model must recover the full rooted containment tree induced by the curves. Despite the visual simplicity of the task, the strongest evaluated model, $\texttt{Gemini-3.1-Pro-Preview}$, achieves only $\textbf{71.1\\%}$ tree-generation accuracy on CurveBench-Easy and $\textbf{19.1\\%}$ on CurveBench-Hard. We further demonstrate benchmark utility through RLVR-style fine-tuning of open-weight vision-language models. Our trained $\texttt{Qwen3-VL-8B}$ model improves over $\texttt{Qwen3-VL-8B-Thinking}$ from $\textbf{2.8\\%}$ to $\textbf{33.3\\%}$ tree-generation accuracy on CurveBench-Easy, exceeding $\texttt{GPT-5.4}$ and $\texttt{Claude-Opus-4.5}$ under our evaluation protocol. The remaining gap, especially on CurveBench-Hard, shows that exact topology-aware visual reasoning remains far from solved.

Cryptanalysis---the task of finding attacks against cryptographic schemes---sits at the intersection of mathematical reasoning and programming, two areas where LLMs have made rapid progress. Just like math and programming, cryptanalytic attacks are formally defined and can be unambiguously verified. This raises the question if cryptanalysis might experience a similar acceleration in progress through LLMs. In this paper we introduce $\texttt{CryptanalysisBench}$, a benchmark of 113 tasks spanning six families of cryptographic primitives (block ciphers, hash functions, etc) drawn primarily from four NIST standardization competitions. Each task asks an agent to break an implementation of a cryptographic primitive by winning a formal security game. The benchmark has three tiers: (1) primitives with known practical breaks; (2) scaled-down variants of primitives without one; (3) a challenge set of unbroken production primitives. We evaluate Claude Opus 4.7 and GPT-5.5: both solve a majority of Tier 1 (71.4\% and 78.5\%, respectively), while Tier 2 remains largely out of reach. For Tier 1 successes, we provide a fine-grained analysis distinguishing paper recall from source-level rediscovery. We release $\texttt{CryptanalysisBench}$ both as a forecasting tool to track when AI cryptanalytic capability becomes a serious factor, and as scaffolding for subjecting candidate schemes to more attacks before they are deployed.

Reinforcement learning with verifiable rewards (RLVR) post-trains language models on multi-step reasoning by assigning a single outcome reward uniformly across all tokens in a trajectory, regardless of which steps contributed to success or failure. Improving credit assignment can address this limitation by enabling targeted refinement of faulty reasoning steps, rather than updating entire trajectories uniformly. Resets are one such simple mechanism, enabling more precise credit assignment by returning to an intermediate state and resampling its continuation, so that outcome differences can be attributed to decisions made at that point. We propose two such methods: Random-Reset Policy Optimization (RRPO), where reset states are drawn randomly from reasoning steps, and Self-Reset Policy Optimization (SRPO), where the model self-localizes the erroneous step in an incorrect trajectory and resets there. We analyze these methods within a Conservative Policy Iteration (CPI) framework. We extend it with a credit-assignment oracle that targets improvable states, defined as those whose advantage exceeds a threshold, and show that it yields provable improvements over random resets. Across models and reasoning benchmarks, SRPO consistently outperforms standard GRPO and RRPO by sampling multiple suffix continuations at a self-localized reset and learning from their rewards, using only the model itself with no external supervision.

While Diffusion Language Models (DLMs) are theoretically well-suited for iterative refinement due to their non-causal structure, off-the-shelf masked diffusion language models (MDLMs) often fail to reliably revise incorrect tokens in practice. The key challenge lies in the model's inability to distinguish between correct and erroneous tokens in a visible sequence. Standard MDLM training is restricted to the objective of unmasking, undermining the effectiveness of refinement guided by confidence. Based on this observation, we study corrective behavior in DLMs, defined as the ability to assign lower confidence to incorrect tokens and iteratively refine them while preserving correct content. Under matched compute and data, we show that this capability is not induced by conventional masked diffusion objectives and propose a post-training principle oriented by correction that explicitly supervises visible incorrect tokens, enabling discriminative confidence and targeted refinement. To evaluate corrective behavior, we introduce the Code Revision Benchmark, a controllable and executable benchmark for assessing error localization and in-place correction. Beyond improving in-place correction, our post-training principle yields stronger general generation as a direct consequence: the same error-aware confidence that drives reliable revision also makes parallel decoding more effective and improves answer quality on standard generation tasks. We validate this dual benefit across three distinct domains, code completion, mathematical reasoning, and high-entropy parallel decoding (ParallelBench), where models trained with our objective consistently outperform both the base model and standard masked-diffusion fine-tuning.

Small language models deployed under cost, latency, or privacy constraints cannot simply switch to larger models when reasoning fails. Multi-candidate generate then-rerank offers a natural test-time scaling route. However, more candidates do not always yield higher accuracy. We identify a previously overlooked bottleneck between generation and selection: a correct answer may appear in the candidate pool yet fail to be selected because it is incomplete, unparseable, or misaligned with the answer mode the fixed selector expects. We term this loss the hidden interface tax and formalize a coverage–conversion decomposition that distinguishes raw oracle coverage from selectable coverage, the subset of problems where a correct candidate can actually be consumed by the selector. We propose Compatibility Aware Candidate Construction (CACC), an interface layer between the candidate source and the fixed selector that repairs fragments, aligns answer modes, and removes selector-confusing noise without retraining either component. On numeric reasoning (GSM8K, competition_math), CACC raises both oracle coverage and final accuracy. On GPQA Diamond, CACC alone improves final accuracy from 5.6% to 19.2% (+13.6pp); combined with proposer-side strengthening it reaches 25.8% (+20.2pp). On MMLU-Pro, CACC exposes a coverage–conversion gap: answer-mode-compatible construction raises oracle coverage, but final gains require additional proposer-side distribution shaping.