NeurIPS 2026 论文列表

Large language models (LLMs) can translate natural language into optimization code, but *silent failures* pose a critical risk: code that executes and returns solver-feasible solutions may encode semantically incorrect formulations—a feasibility–correctness gap reaching 90 percentage points on compositional problems. We introduce **ReLoop**, which addresses this gap through two complementary mechanisms. *Structured generation* decomposes code production into a four-stage reasoning chain (understand, formalize, synthesize, verify), preventing formulation errors at their source. *Behavioral verification* detects errors that survive generation by testing whether the formulation responds correctly to solver-based parameter perturbation—an external semantic signal that bypasses LLM self-review and requires no ground truth. The two mechanisms are complementary by error structure: structured generation drives the largest gains on compositional problems (**+8.5pp** accuracy on RetailOpt-190 with Claude Opus 4.6), while behavioral verification dominates on localized defects (**+4.4pp** on MAMO-ComplexLP, its largest contribution across benchmarks). Combined with diagnostic execution recovery, ReLoop reaches **100% executable code** on Claude Opus 4.6 and consistently improves accuracy on chat-tuned foundation models across three benchmarks; we further identify a known limitation of narrowly-tuned SFT models, whose learned output formats are brittle to chain-of-thought prompts—an interaction we document and analyze. We release **RetailOpt-190**, 190 compositional retail optimization scenarios targeting the multi-constraint interactions where LLMs most frequently fail. Code and benchmark will be released upon acceptance.

Neural scaling laws for transformer language models predict smooth improvements in pretraining loss with increasing parameters, but downstream capabilities such as in-context learning are known to emerge abruptly past a certain model scale. In this paper, we show that emergent capabilities arise at variable intervals throughout training, with larger models acquiring capabilities earlier on average. We demonstrate that the emergence of capabilities such as pattern completion and indirect object identification corresponds to the abrupt learning of task-relevant attention patterns. To isolate this phenomenon, we train transformer models on synthetic linear map and cellular automata datasets, and we show that the difficulty of learning attention patterns depends on context length and pattern sparsity. Moreover, scaling the number of attention heads improves learning efficiency on our synthetic tasks, while increasing the head dimension yields diminishing returns past a minimum capacity. We additionally investigate architectures with alternative attention mechanisms, showing that MLP-Mixer outperforms a transformer on linear map tasks with complex attention patterns. Our findings provide a mechanistic insight into emergence, showing that downstream capabilities arise abruptly due to the intrinsic difficulty of learning sparse attention patterns in transformer models.

Large language models (LLMs) have demonstrated promising capabilities in tool calling. However, existing benchmarks predominantly evaluate models in an idealized setting where ground-truth tool definitions are provided in context. This assumption diverges significantly from real-world deployment scenarios, where the model must first identify user intent and retrieve relevant tools from a large, heterogeneous tool repository before invoking them. In this work, we introduce a Retrieval-augmented Tool-calling Benchmark (RTCBench). In RTCBench, we collect 1,840 tasks from existing benchmarks and augment them with two tool environments: 1) None: no available tools provided in the prompt and 2) Distractor: strong distractor tools, while the target tools are excluded. By removing oracle tool access, RTCBench compels LLMs to actively retrieve relevant tools from a large-scale repository via a unified search tool before making tool calls, thereby faithfully simulating the end-to-end complexity of real-world tool-use pipelines. Through comprehensive evaluation of diverse LLMs ranging from 4B-parameter models to proprietary frontier models, we identify two core deficiencies: unreliable tool discovery, where models fail to initiate effective retrieval actions, and post-retrieval grounding failures, where models cannot reliably select and invoke the correct tools from semantically similar retrieved candidates. Furthermore, to mitigate these issues, we release 13,278 retrieval-augmented tool-calling expert trajectories with high-quality chain-of-thought reasoning for LLM post-training. Experiments show that a 4B-parameter model post-trained with GRPO improves its tool-calling accuracy on RTCBench from approximately 47.9\% to over 85.8\%, approaching the performance of the state-of-the-art model Gemini-3.1-Pro.

Vision-Language Models (VLMs) have achieved remarkable advances in general autonomous driving. Nevertheless, effectively exploiting the reasoning capability of Chain-of-Thought (CoT) to enhance the robustness and accuracy of decision and planning in long-tail scenarios still remains a challenging open problem. To this end, we propose a \textbf{R}easoning-\textbf{S}upervised \textbf{P}olicy \textbf{O}ptimization (RSPO) algorithm to boost reasoning and decision-making performance under long-tail driving scenarios. Concretely, we first conduct an empirical analysis of the core challenges faced by current VLMs in autonomous driving decision and planning tasks, and formally define reasoning and decision-making tasks tailored to long-tail scenarios. On this basis, we design a curriculum-guided supervised fine-tuning strategy to enable the model to rapidly fit the mean distribution of model outputs. Furthermore, we propose a reasoning-supervised optimization algorithm, which enhances the robustness and accuracy of reasoning and decision in long-tail scenarios by guiding the optimality consistency between reasoning processes and final decisions. Finally, we construct multiple verifiable autonomous driving reasoning and decision datasets based on open-source benchmarks and conduct extensive multi-dimensional comparative experiments. Experimental results show that the proposed algorithm achieves consistent improvements in prediction accuracy across multiple datasets compared with existing methods. In particular, it achieves a 6.7\% relative improvement over the strong baseline on the CODA-LM task and also yields lower trajectory-prediction errors on downstream planning tasks.

Retrieval is increasingly moving from one-shot matching toward interactive reasoning, where language agents iteratively inspect evidence, reformulate queries, and search again. Training such agents raises a credit-assignment challenge: executable actions such as queries or summaries can be directly evaluated by the retriever, while latent reasoning steps are not directly observable and only affect future executable actions. This asymmetry makes outcome-level reward assignment unreliable, as the same final reward may credit reasoning steps that did not actually shape retrieval success. We propose RICE-PO, a critic-free policy optimization framework that converts retrieval interactions into localized learning signals. RICE-PO selects high-uncertainty executable actions as anchors, evaluates local counterfactual branches using retrieval metrics, and propagates credit to latent reasoning steps only when reasoning-to-action influence is strong and future residual effects are stable. On BRIGHT and BEIR, RICE-PO consistently outperforms prompt-based agents and group-based RL baselines under the same retriever setting. These results show that the structure of agent-environment interaction itself can provide useful supervision for training reasoning-based retrieval.

Long chain-of-thought reasoning improves vision-language models (VLMs), but it also exposes a temporal grounding failure: as generation unfolds, models may drift from image evidence while reinforcement learning still provides only a final-answer reward. We study this gap through visual revisit, a temporally localized reactivation of image evidence during reasoning. Across three VLM backbones, revisit peaks are predictive of correctness and causally linked to performance: masking them degrades accuracy more than masking non-peaks, while injecting revisit-like peaks into failed rollouts partially restores correct answers. Control analyses show that this signal is not explained by raw attention strength, uncertainty, logit margin, or hidden-state norm. We propose RECAP, a GRPO-compatible training method that turns detached revisit traces into a credit-assignment signal. RECAP uses revisit-conditioned advantage estimation, dynamic discounting, and gated value prediction to propagate final rewards through visually important reasoning steps, without extra rewards, additional rollouts, or inference-time changes. Across Qwen2.5-VL-7B, InternVL3-8B, and LLaVA-OV-7B, RECAP consistently improves over GRPO and VPPO, yielding $+6.1$--$+6.5$ HallusionBench gains over the SFT base while preserving reasoning and text-only performance. Results on larger LoRA-tuned models, Chinese zero-shot benchmarks, visual perturbations, and human evaluation further demonstrate robust improvements in image-grounded reasoning.

Post-training quantization (PTQ) is widely used to deploy large language models efficiently, but its effect on reasoning models is not well understood. Across math, coding, and science QA, we find that aggressive PTQ reduces accuracy while increasing chain-of-thought (CoT) length. Surprisingly, we show that in up to 52% of the quantized models' failures, models reach the right answer in intermediate reasoning steps but do not output it as a final answer. To understand why quantization leads to this increase in overthinking errors, we measure the token-level KL divergence between quantized and full-precision output distributions. Positions with high KL divergence correlate strongly with high next-token entropy, and at these positions quantized models disproportionately sample overthinking markers such as “wait", “but", and “alternatively". We show that simply introducing a training-free logit penalty on a curated set of overthinking markers can reduce CoT length by 12--23% while preserving or improving accuracy across 5 models (1.5B--32B parameters), 3 quantization methods, and 5 benchmarks, yielding the best Pareto frontier of accuracy against reasoning cost. Overthinking errors produced by quantized models are particularly reduced by up to 58%.

Beam-search–based test-time methods provide an effective way to improve large language model (LLM) performance on long-horizon generation by pruning invalid reasoning paths early, leading to significantly improved reasoning efficiency and more favorable test-time cost scaling. Despite strong empirical success, the theoretical understanding of beam search remains limited. In this paper, we study the test-time compute guarantee of the commonly used beam search framework that uses the model's internal log-likelihood for intermediate scoring, while relying on an external reward model only after a complete response is generated. We first establish a lower bound for vanilla beam search, showing that at least $\Omega(C^\star(x)^2)$ samples are required for the optimal response to survive, where $C^\star(x)$ is the token-level coverage coefficient for prompt $x$. This motivates our modified confidence-filtered beam search (CF-Beam), which provably reduces the sample size by a factor of $C^\star(x)$. We then show that the regret of CF-Beam is upper-bounded by the probability of rare failure events and the reward estimation error scaled by a path-level coverage coefficient, where the rare-failure term vanishes as per-step sampling increases. Our results highlight a fundamental advantage of beam search over sequence-level inference methods such as Best-of-N and Best-of-Majority. While the guarantees of these approaches typically involve coverage coefficients that grow exponentially with the horizon $L$, CF-Beam controls the dominant search-induced term through a token-level coverage coefficient that scales polynomially with $L$. Our numerical experiments further confirm that beam search is more robust on hard instances and under increasing reasoning horizons.

Large language models (LLMs) increasingly solve difficult problems by producing reasoning traces before emitting a final response. However, it remains unclear how accuracy and decision commitment evolve along a reasoning trajectory, and whether intermediate trace segments provide answer-relevant information beyond generic length or stylistic effects. Here, we propose a trajectory-probing protocol for evaluating how a reasoning model's predicted answer evolves along a partial reasoning trace. The protocol 1) generates a model's full reasoning trace, 2) truncates it at fixed token-percentiles, and 3) injects each partial trace back into the model, measuring the model's induced answer distribution. We apply the protocol to five open-source reasoning models (Qwen3-4B/-8B/-14B and gpt-oss-20b/-120b) across three benchmarks (GPQA Diamond, MMLU-Pro, and Omni-MATH-2). The protocol reveals that accuracy and decision commitment consistently increase as the percentage of provided reasoning tokens grows, and length, form, and token-identity controls confirm that gains stem from instance-specific semantic content rather than context length or generic reasoning style effects. Furthermore, weak-to-strong cross-model probing experiments reveal when stronger models recover from incorrect partial traces and when they instead anchor to them. Together, these results provide a reproducible, model-agnostic measurement of reasoning-trace dynamics that generalizes across answer formats and can reveal model-specific failure modes invisible to aggregate accuracy.

Tiny Recursive Models (TRM) solve complex reasoning tasks with a fraction of the parameters of modern large language models (LLMs) by iteratively refining a latent state and final answer. While powerful, their deterministic recursion can lead to convergence at suboptimal solutions, without escape mechanism. A common workaround relies on task-specific input perturbations at test time combined with answer aggregation via voting. We introduce Probabilistic TRM (PTRM), a task-agnostic framework for test-time compute scaling that addresses this limitation through stochastic exploration. PTRM injects Gaussian noise at each deep recursion step, enabling parallel trajectories to explore diverse solution basins, and selects among them using the model’s existing Q head (used for early stopping in the original TRM). Without requiring retraining or task-specific augmentations, PTRM enables substantial accuracy gains across benchmarks, including Sudoku-Extreme (87.4% to 98.75%) and on various puzzles from Pencil Puzzle Bench (65% to 91%). On the latter, PTRM achieves nearly double the accuracy of frontier LLMs (91% vs. 55%) at less than 0.0001x the cost, using only 7M parameters.

How should future neural reasoning systems implement extended computation? Recursive Reasoning Models (RRMs) offer a promising alternative to autoregressive sequence extension by performing iterative latent-state refinement with shared transition functions. Yet existing RRMs are largely deterministic, following a single latent trajectory and converging to a single prediction. We introduce Generative Recursive reAsoning Models (GRAM), a framework that turns recursive latent reasoning into probabilistic multi-trajectory computation. GRAM models reasoning as a stochastic latent trajectory, enabling multiple hypotheses, alternative solution strategies, and inference-time scaling through both recursive depth and parallel trajectory sampling. This yields a latent-variable generative model supporting conditional reasoning via $p_\theta(y \mid x)$ and, with fixed or absent inputs, unconditional generation via $p_\theta(x)$. Trained with amortized variational inference, GRAM improves over deterministic recurrent and recursive baselines on structured reasoning and multi-solution constraint satisfaction tasks, while demonstrating an unconditional generation capability.

Code generation is typically trained in the \emph{primal} space of programs: a model produces a candidate solution and receives sparse execution feedback, often a single pass/fail bit. Test-time scaling enriches the inference procedure by sampling multiple candidates and judging among them, but the comparative information this process reveals is discarded after inference. We argue that this information defines a \emph{dual} judgment space that provides a far richer training signal: the model learns not from an isolated success or failure, but from the relative correctness structure across its own plausible attempts, identifying which succeed, which fail, and what distinguishes them. We introduce \textbf{DuST} (\textbf{Du}al \textbf{S}elf-\textbf{T}raining), a framework for self-training from the dual judgment space. DuST samples candidate programs from the model's own distribution, labels them through sandbox execution, retains groups containing both successes and failures, and trains the model to rank candidates by execution correctness using GRPO. The objective is purely discriminative: the model is never directly rewarded for generating correct programs. Dual self-training improves both judgment and generation. Across five models spanning two families and three scales (4B to 30B), DuST consistently improves Best-of-4 test-time scaling on LiveCodeBench. For Qwen3-30B-Thinking on LiveCodeBench v6, judgment quality improves by +6.2 NDCG, single-sample pass@1 improves by +3.1, and Best-of-4 accuracy improves by +4.1. The trained model's single rollout matches the base model's Best-of-4 performance. SFT on the same ranking data improves judgment without improving generation, confirming that on-policy RL is the mechanism that transfers dual-space learning back into primal generation.

Test-time scaling has emerged as a critical avenue for enhancing the reasoning capabilities of Large Language Models (LLMs). Though the straight-forward ``best-of-$N$'' (BoN) strategy has already demonstrated significant improvements in performance, it lacks principled guidance on the choice of $N$, budget allocation, and multi-stage decision-making, thereby leaving substantial room for optimization. While many works have explored such optimization, rigorous theoretical guarantees remain limited. In this work, we propose new methodologies to predict and improve scaling properties via tail-guided search. By estimating the tail distribution of rewards, our method predicts the scaling law of LLMs without the need for exhaustive evaluations. Leveraging this prediction tool, we introduce Scaling-Law Guided (SLG) Search, a new test-time algorithm that dynamically allocates compute to identify and exploit intermediate states with the highest predicted potential. We theoretically show that SLG approaches a full-information oracle at a reduced scale and, under additional regularity conditions, achieves vanishing matched-budget regret; in a Gaussian two-stage model, SLG can also match BoN with a polynomially larger sampling budget. Empirically, we validate our framework across different LLMs and reward models, confirming that tail-guided allocation consistently achieves higher reward yields than Best-of-$N$ under identical compute budgets.

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.

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 ability of neural networks to generalize is fundamentally shaped by their computational units. While the perceptron provides a first-order, linear inductive bias and the radial basis function (RBF) unit offers an isotropic curved bias, we identify a critical opportunity for a structured extension: the Generative Matching Unit (GMU). Each individual GMU captures complex dependencies by treating the forward pass as an inference problem; its internal generative model optimizes instance-specific latent parameters to compute a reconstruction error, effectively measuring a point-to-manifold distance as opposed to the point-to-point distance in RBFs. We focus on linear GMUs, which yield closed-form analytical expressions for fast computation and extend naturally to convolutional architectures. Our theoretical analysis demonstrates that linear GMUs are highly flexible universal approximators capable of recovering structured class posteriors. We prove that while a single GMU can exactly emulate an RBF kernel and two can emulate the decision boundary of a perceptron, emulating a single $k$-order GMU’s decision boundary requires a hidden layer of standard units that scales polynomially or exponentially with input dimensionality. Furthermore, we prove that the GMU’s point-to-manifold distance remains discriminative in high dimensions where standard Euclidean distances fail, offering unique robustness to the curse of dimensionality. Finally, we show that GMUs offer superior flexibility and efficiency in learning smooth manifold decision boundaries compared to MLPs and RBFs. Motivated by the theoretical results, we place GMUs in the first network layer like RBFs, where their role is to enhance linear separability for subsequent layers. This avoids the typical gradient collapse problem with stacking RBF-like units while ensuring the generalization benefits remain. We find that across extensive experiments involving 27 tabular datasets, five vision datasets evaluated across 34 test-time corruption settings, and 30 synthetic scenarios, GMU networks demonstrate statistically significant improvements in generalization and robustness.

Perturbation experiments are central to understanding cellular mechanisms, but remain costly and sparse, motivating prediction of gene expression responses for unobserved conditions. A promising recent direction leverages large language models (LLMs) as “virtual cell” simulators—using stepwise, knowledge-grounded mechanistic reasoning to infer differential expression—pointing toward an interpretable, knowledge-driven paradigm that transcends purely data-driven approaches. However, we find that plausibility is not prediction: despite producing biologically plausible explanations, these methods fail to capture perturbation-specific effects — systematically overestimating differential expression, often underperforming a simple gene‑frequency baseline in aggregate evaluations, and collapsing to chance-level performance at the per-gene level. This reveals a reliance on intrinsic gene response tendencies rather than true perturbation reasoning. We trace this failure to how evidence is presented: existing methods evaluate perturbation–gene pairs in isolation, without exposing how related perturbations differ in their effects on the same gene. To address this limitation, we introduce **CORE** (**C**ontrastive **O**rganization of **R**elational **E**vidence), which reframes prediction as a comparison task by organizing evidence into positive and negative outcomes from related perturbations. Using a biomedical knowledge graph for evidence retrieval, CORE improves calibration and substantially boosts perturbation-specific prediction in both LLM-based and non-LLM settings: for example, on drug-perturbation data, CORE-Reasoning improves Qwen3.5-9B aggregate metrics by up to 28.6\%, while on generic perturbation data, CORE-Voting raises macro-per-gene AUROC from chance to 0.711. This highlights contrastive evidence organization as essential to reliable LLM-based perturbation reasoning.

Recently, Muon and related spectral optimizers have demonstrated strong empirical performance as scalable stochastic methods, often outperforming Adam. Yet their behaviour remains poorly understood. We analyze stochastic spectral optimizers, including Muon, on a high-dimensional matrix-valued least squares problem. We derive explicit deterministic dynamics that provide a tractable framework for studying learning behaviour with a focus on (stochastic) SignSVD and (stochastic) SignSGD, the latter serving as a proxy for Adam. Our analysis shows that for large batch size, SignSVD performs a square-root preconditioning with respect to the data covariance spectrum, while for small batch size smaller eigenmodes behave like SGD, slowing down convergence. We contrast with SignSGD which for generic covariance performs no preconditioning and has no transition, leading to different optimal learning rates and convergence characteristics. The two methods match up to a constant factor with isotropic data, but behave differently with anisotropic data. An analysis of a power law covariance model with data exponent $\alpha$ and target exponent $\beta$, and show there are three phases in the $(\alpha,\beta)$ plane: one where SignSGD is uniformly favored, one where SignSVD is uniformly favored, and a third where the two methods exhibit a trade-off in performance.

Evaluating machine learning in scientific domains requires separating correct predictions from correct reasons under realistic distribution shifts. We introduce PerturbReason, a knowledge‑grounded benchmark for cell‑state--conditioned reasoning about perturbation effects. It tests the models to generate mechanistically faithful explanations and assesses their robustness against complex shifts, such as new cells, unseen perturbations, and cross-modal or combinatorial extrapolations. PerturbReason combines single‑cell genetic and chemical perturbation data across multiple cell lines with knowledge graphs, and dynamically conditions pathways on cell‑specific basal states to avoid generic memorization. Evaluations on state-of-the-art models reveal systematic gaps between predictive accuracy and mechanistic reasoning. Specifically, these models exhibit failure modes largely invisible to standard benchmarks, such as deriving correct answers through flawed logic, ignoring cellular context, and generating directionally inconsistent mechanisms. As a reference probe of the benchmark, we present PerturbRM, a large language model trained to align outcome predictions with context-specific regulatory reasoning. PerturbReason thus provides a rigorous diagnostic benchmark for studying and improving faithful, generalizable reasoning in data-rich scientific systems.