LLM Reasoning

LLM: Large Language Model

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68 papers in the last four weeks, up 143% on the four weeks before. 0.7% of all new papers.

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Sep 28, 2026cs.CL

Learning from Teacher Continuations at Student States

We present OLIVE (OnLine InterVEntion). At each iteration, the evolving student policy generates a new prefix, the teacher continues it autoregressively, and the student is updated using cross-entropy computed on the teacher-generated tokens. Each design choice targets a corresponding limitation of existing distillation methods: (1) sequential covariate shift in offline supervised fine-tuning (SFT) on fixed teacher trajectories, (2) fragmented supervision under prefix failure in token-level on-policy distillation (OPD), and (3) the need for access to teacher token probabilities in distribution-matching distillation. OLIVE achieves higher reasoning performance than OPD (with a top-16 KL approximation) at comparable GPU-hour cost. Our asynchronous implementation further reduces OLIVE's total training time by 23.8%. We evaluate OLIVE on both hard reasoning tasks and agentic tasks which reflects modern post-training scenarios, and it consistently outperforms existing distillation methods under the same training budget. By regenerating prefixes from the evolving student, OLIVE continues improving after offline distillation plateaus while better preserving the general capabilities and plasticity of the student. Using only text from GPT-5.4-mini, continuously training with OLIVE outperforms offline SFT from the same teacher by 13% on ScienceWorld. These results support OLIVE as an effective and efficient approach to online language-model distillation.

Haojin Wang, Dylan Zhang, Huaibo Chen +8

University of Illinois at Urbana-Champaign · Massachusetts Institute of Technology · University of Pennsylvania +2

Language Model Distillation On-Policy Distillation Knowledge Distillation LLM Reasoning

Sep 28, 2026cs.CL

When Confidence Rises Too Early: Detecting Shortcut Reasoning via Premature Answer Commitment

The reasoning trajectory of a Large Language Model (LLM) is often treated as a verbalized description of its internal reasoning. However, such trajectories can be unfaithful: a model may rely on shortcuts to reach an answer and then post-rationalize the decision with a seemingly coherent chain of thought. Detecting this shortcut reasoning is challenging because existing monitors and verifiers mainly inspect textual traces or final outcomes, rather than how the model's belief in its answer develops during generation. We introduce ConfLens, a framework that tracks the evolution of confidence in the final answer throughout reasoning. Across three shortcut reasoning settings, we observe a common pattern of premature confidence, where shortcut samples become highly confident in the final answer at early reasoning stages. Existing confidence estimation methods, however, show limited generalizability, reliability, or efficiency for detecting this behavior. We therefore propose the Distributional Answer Commitment Score (DACS), a distributional confidence estimator that measures the entropy of the model's probability distribution over answer commitment at each reasoning step. DACS captures how concentrated the model's answer belief is without requiring ground-truth answers or task-specific verifiers. We further convert ConfLens detection results into interpretable signals for reward models to reduce their preference for shortcut reasoning. Experiments on mathematical and code reasoning tasks show that ConfLens with DACS improves shortcut reasoning detection by over 4.3% F1 compared with strong baselines and reduces the mismatch between faithfulness and correctness in reward model preferences.

Zhaohan Zhang, Junjie Liu, Chengzhengxu Li +6

Queen Mary University of London · Tongyi Lab, Alibaba Group · Xi’an Jiaotong University

Faithfulness of Language Model Explanations Confidence Estimation in Language Models LLM Uncertainty Estimation LLM Reasoning

Sep 28, 2026cs.LG

Teach to Learn: Hint Annealing for Self-improving LLM Reasoning

Group Relative Policy Optimization (GRPO) improves language-model reasoning by comparing verified rewards among multiple solution rollouts for each query. However, difficult training queries can yield only incorrect rollouts, leaving GRPO with no reward contrast or learning signal. Prior hint-based methods construct auxiliary hints from solution evidence and use them to re-solve failed queries, recovering learning signal. Yet the resulting trajectories are typically treated as ordinary solution trajectories despite being generated under an assisted condition unavailable at evaluation. We discover hinted reward shift: recovered reward contrast can concentrate policy updates on hinted trajectories, limiting improvement without hints. This also creates a trade-off: increasing hinted trajectories can accelerate early learning but intensify reward shift later. To address this problem, we propose HATCH (Hint-Annealed Self-Teaching), an online single-policy framework that learns from both generating and using its own hints to improve reasoning without assistance. To mitigate hinted reward shift, we introduce online weighting to anneal the contribution of hinted trajectories. However, learning to generate hints can conflict with improving query solving. We therefore use gradient projection to remove the opposing component of hint-generation updates. Together, these designs support self-improvement by enabling the policy to create learning opportunities for itself and turn them into stronger reasoning without hints. We evaluate our method on mathematical reasoning benchmarks and outperform state-of-the-art methods by 1.02 pp on Llama-3.2-1B-Instruct, 2.84 pp on Qwen3-1.7B, and 4.32 pp on Qwen3-8B.

Zile Wang, Zijian Li, Haodong Wang +5

The Hong Kong University of Science and Technology · Yuanbao Team, Tencent

Reinforcement Learning Self-Training for Language Models RL for Language Model Reasoning LLM Reasoning

Sep 28, 2026cs.CL

Rewarding Novel Deductions: Solver-guided Process Supervision for Logical Reasoning

Logical reasoning remains a major challenge for large language models (LLMs), particularly on structured problems that require precise constraint tracking, consistency preservation, and multi-step deduction. This challenge is especially acute for small-scale LLMs, which are more prone to producing inconsistent, redundant, or brittle reasoning trajectories. Existing approaches for improving logical reasoning largely optimize for final-answer correctness, providing only weak supervision over the intermediate reasoning process. In this work, we propose SPRING: (Solver-guided Process Rewards for Novel LogIcal ReasoNing Step Generation). SPRING uses SMT solver as a training-time verifier of intermediate reasoning steps to provide process-level supervision. It introduces the notion of a novel reasoning step, namely, a step that is logically valid, consistent with the evolving reasoning state, and not already implied by previously accepted non-contradictory deductions. Based on this solver-based assessment, it designs process rewards that encourage novel inferential progress while penalizing contradictory and uninformative reasoning steps. Evaluation across three logical reasoning benchmarks, ZebraLogic, AR-LSAT, and Knights and Knaves, and four LLMs shows that SPRING consistently outperforms base LLMs, outcome-only reward baselines, and Logic-LM. On ZebraLogic, SPRING improves puzzle accuracy by up to 49.71 and 15.43 points over the base LLM and strongest outcome-only baseline, respectively. On AR-LSAT, it improves overall accuracy by up to 64.93 and 12.14 points, respectively. On Knights and Knaves, SPRING achieves up to 93.14 puzzle accuracy and 96.05 person accuracy.

Muhammad Asif Ali, Wenqing Wang, Huan Wang +1

FORTE Lab, Faculty of Science, Information Technology University, Lahore, Pakistan · College of Informatics, Huazhong Agricultural University, Wuhan, China · Qatar Computing Research Institute, Hamad Bin Khalifa University, Doha, Qatar

RL for Language Model Reasoning Process Supervision LLM Reasoning

Sep 28, 2026cs.AI

Knowing When Thinking Is Not Enough: Teaching Small Reasoning Models to Reason Beyond Their Parametric Knowledge

Scaling test-time computation is a powerful way to improve language-model reasoning, and is particularly appealing for small reasoning models (sRMs) that are cheap to serve. However, is additional thinking always the right operation? By intervening at intermediate reasoning states across two model families and multiple scales, we find that self-refinement largely consolidates probability mass onto solutions already reachable from the current state, rather than making new ones reachable. These interventions reveal two failure regimes: execution bottlenecks, where the correct path is reachable and reflection can recover it, and knowledge bottlenecks, where relevant external information makes it reachable. Motivated by this distinction, we introduce FlyBy, a selective querying framework, and train 4B and 8B variants to reason first, diagnose what remains unresolved, and, at a knowledge bottleneck, query stronger models whose parametric knowledge extends beyond its own. Supervised fine-tuning bootstraps a multi-depth query action, and cost-aware reinforcement learning calibrates whether to query, what to ask, and how much to spend. On 1,158 hard problems across six benchmarks, FlyBy-4B achieves 45.96% pass@8, surpassing Qwen3-14B (41.64%) at 2.7 times lower serving cost, while also exceeding Qwen3-8B in pass@1 (16.85% vs. 15.31%). Scaling to FlyBy-8B further improves pass@8 to 51.81%.

Chanuk Lee, Minki Kang, Sangwoo Park +3

KAIST

Cost-Aware Inference Efficient Language Model Reasoning LLM Routing LLM Reasoning

Sep 28, 2026cs.LG

Direct Self-Evolving Optimization: Evolving LLMs without Challenger Training

Self-evolving language models improve by generating tasks and learning from their own feedback, but adapting the task generator often requires a separate challenger-training loop. Can we generate tasks adapted to the current solver without explicitly training a challenger? We introduce \textbf{D}irect Self-\textbf{E}volving \textbf{O}ptimization (DEO), which replaces challenger parameter updates with solver-guided task sampling. The KL-regularized challenger objective defines an exponential tilt of a fixed base task distribution. DEO uses this distribution as a sampling target: a frozen LLM generates and mutates tasks, the solver scores them, and an approximate Metropolis selection rule refines the training pool. Only the solver is trained. Theoretically, for an idealized variant that samples exactly from the tilted distribution, and under regularity, local gradient-dominance, and initialization conditions, we show that DEO learns distributionally robust reasoning ability. In experiments, DEO achieves reasoning performance competitive with R-Zero while using over

50\%

less wall-clock training time, and improves reasoning accuracy over a no-walk ablation. Replacing the task generator with a frozen API-only LLM further improves the local solver, illustrating a capability enabled by removing challenger training.

Yuyang Deng, Yu Wang, Jiayun Wang

Accenture, Center for Advanced AI · Georgia Institute of Technology

Self-Training for Language Models Large Language Model-Guided Optimization Distributionally Robust Optimization Language Model Self-Improvement LLM Training LLM Reasoning

Sep 28, 2026cs.CY

Investigating Human--AI Discrepancies via Multiple-Solution Problems

Frontier artificial intelligence (AI) models are benchmarked on whether they reach a correct answer. Yet many problems admit several correct answers and repeated attempts, by different people or by the same model resampled, trace out a distribution over them. In this work, we ask whether human and model reasoning lead to different distributions over valid solutions. Our testbed comprises 270 reasoning puzzles across five puzzle families. These multiple-solution puzzles each have 3 to 8 valid solutions and are simple enough that humans and models can solve them reliably. The resulting distributions differ markedly: models differ from one another, yet resemble each other far more than they resemble humans. Model distributions are, moreover, within every puzzle family, less diverse than human ones. We compare these discrepancies across puzzle categories, and trace how they respond to reasoning-effort settings, to prompting, and to perturbations of the puzzle that leave its solutions unchanged. Together, these results point at significant differences between human and AI problem-solving processes, and their choice among equally defensible solutions. As progressive deployment of AI systems in society comes into focus, evaluating such differences (beyond one-dimensional accuracy metrics) is increasingly important. Data and code are available at https://hai-discrepancies.github.io/

Zihao Wang, Francesco Insulla, Andrea Montanari

Department of Mathematics, Stanford University · Institute of Computational and Mathematical Engineering, Stanford University · Department of Statistics and Department of Mathematics, Stanford University

Generative AI Evaluation LLM Reasoning

Sep 27, 2026cs.AI

How code helps different tasks? A decompositional lens on LLM post-training

Evaluating code data as a single corpus can obscure which types of code data benefit which models and downstream tasks. Effective data selection requires understanding both the benefits of individual categories and whether these benefits persist when categories are combined. We introduce a decompositional lens for studying these effects in LLM post-training. We first decompose an execution-verified code corpus into interpretable categories based on the computational patterns of its solutions. Through controlled fine-tuning experiments, we compare individual categories with a balanced mixture across instruction-tuned models on question answering, mathematics, and code generation. The resulting response maps reveal recurring gains in average question-answering performance, while the same category can improve one model or task and degrade another. The best-performing category also varies with the starting model and target task. We then compose compact mixtures guided by these results and examine whether benefits observed in individual categories persist under joint training. On selected model--task pairs, mixtures whose constituents each improve the target task outperform both their best constituent and full-corpus training while using roughly 10--15% of the full corpus. These exploratory findings illustrate a \emph{less is more} pattern and highlight how the value of code data in post training depends on which categories are combined for which model and task.

Zheng Yu, Yiwei Li, Yishen Chen +4

Sun Yat-sen University · Shenzhen Loop Area Institute · The Chinese University of Hong Kong, Shenzhen +1

LLM Fine-Tuning Instruction-Tuning Data Selection Training Data Selection LLM Post-Training LLM Code Generation LLM Reasoning

Sep 27, 2026cs.LG

Selecting Diverse SFT Traces Improves Post-RL Generalization

Verified solutions are not equally useful for preparing reasoning models for reinforcement learning (RL). We present a comprehensive study of route diversity, the variation in the sequences of reasoning steps in supervised fine-tuning (SFT) data, and propose a lightweight, rule-based fingerprint to select for it. From one pool at one budget, with matched training recipes and checkpoints, selecting diverse rather than similar routes improves post-RL problem coverage across puzzles and mathematics, including on problems harder than those seen in either training stage. In synthetic experiments, route-diverse SFT improves OLMo3-7B's pass@8 by 16.9 points on environments held out from SFT. In a single-model condition, where one model writes every candidate, diverse selection gains up to 6.2 points of mean pass@8 across 10 mathematics benchmarks. Pre-RL diagnostics suggest why: diverse SFT can produce both successful and failed attempts on more prompts despite slightly lower mean accuracy, giving group-relative RL more prompts with a learning signal. On 3 open-source corpora, our CPU-only selector, without model calls, outperforms more expensive alternatives in every comparison of mean post-RL performance. These results identify reasoning-route diversity as a practical criterion for selecting SFT data that better prepares models for RL.

Dylan Zhang, Mingyuan Wu, Jinning Li

University of Illinois Urbana-Champaign, work done at Google · Google

Reasoning Diversity RL for Language Model Reasoning Training Data Selection RL Post-Training LLM Reasoning

Sep 27, 2026cs.CL

Rethinking Token Reweighting for SFT: Suppress, Reverse, and Extrapolate Learned Features

Supervised fine-tuning (SFT) learns most aggressively from tokens that the model deems least likely. This helps acquire new behaviors, but also amplifies noisy or conflicting supervision and can overwrite useful pretrained knowledge. Through a unified policy-loss view, we revisit existing token-reweighting methods and show that they assign nonnegative coefficients to demonstrated tokens. Consequently, they can suppress or amplify supervised updates, but cannot reverse harmful features once learned. Moreover, larger training weights do not amount to feature extrapolation, since they change the optimization trajectory rather than scale a fixed SFT direction. We argue that reversal and extrapolation require a stable reference frame defined by a fixed SFT delta. Motivated by this, we propose SCALE (Selective Control of Adaptation via Local Entropy), an entropy-guided adaptation-strength-control method that freezes the pretrained model and the SFT delta and learns bounded token- and module-specific gates by minimizing predictive entropy alone. These gates suppress, reverse, or extrapolate frozen SFT features according to their alignment with entropy reduction. Across Qwen2.5-Math-1.5B, Qwen2.5-Math-7B, and Qwen3-4B-Base, SCALE achieves mathematical-reasoning averages of 37.84, 43.60, and 36.57, exceeding the strongest corresponding baselines while remaining competitive on general-retention benchmarks. It also attains the best average code-generation performance across HumanEval, HumanEval+, and MBPP for all three models. These results suggest that effective SFT correction can benefit from controlling how already learned residuals are used, rather than only modifying how they are learned.

Cunchun Li, Haonan He, Yifan Gao +4

Shanghai AI Laboratory · University of Science and Technology of China · Fudan University +2

Supervised Fine-Tuning Adaptive Loss Weighting Selective Fine-Tuning LLM Reasoning

Sep 24, 2026cs.AI

EnigmaForge: The Question Is Hidden in the Story

Most benchmarks hand the model a question. EnigmaForge hands it a stack of old documents and no question at all. Buried in the letters, receipts, and logbook margins is a small logic puzzle whose solution is unique - proved by a SAT solver at generation time, with an ablation certificate showing every clue is load-bearing. Because instances are generated rather than collected, the corpus renews forever. The headline measure is intuition: task success when handed only the story, with world reconstruction as the secondary axis. Twenty-five frontier models ran over 600 instances (17,400 scored records) under three matched conditions. Intuition reshuffles the leaderboard: a 22x spread where fact recovery spans 1.6x, the second-best fact-recoverer ranks fourteenth, one model is indifferent to being told the question, and another is significantly better without it. Several models were blocked by their own content filters before reaching the puzzle - any benchmark scoring refusals as failure is quietly measuring filter behavior.

Daniel Eisner

Question Answering Synthetic Benchmark Generation LLM Reasoning

Sep 24, 2026cs.CL

No More Free Lunch: Corpus Task Complexity Matters as Corpora Grow

Given a large corpus, the questions one might ask can vary -- from "When was the first human heart transplant?" to "What are all the contradictory claims in this literature?" -- but what makes some questions more challenging than others? In this work, we define a notion of Corpus Task Complexity (CTC) that characterizes tasks by how their difficulty grows with corpus size; for instance, a retrieval query only requires a single linear pass over a corpus, while finding contradictions requires checking a quadratically growing set of claim pairs. Observing that prior work has largely only studied tasks whose difficulty grows linearly with corpus size, which we call low CTC tasks, we introduce 10 new tasks belonging to a class of high CTC whose difficulty grows quadratically or more in corpus size. We find that high-CTC tasks not only grow much more challenging on average at longer contexts for LCLMs, they reverse many modeling conclusions drawn solely from low-CTC evaluations. For instance, efficient block-sparse and hybrid attention approaches consistently match full attention performance on low-CTC tasks, but degrade much more on high-CTC tasks. Large-corpus high-CTC reasoning thus remains an open challenge as full attention is too costly to scale, motivating future research on these tasks. We release our code, data, and 22-task suite (CTC-Bench), to facilitate future research in this area.

Prasann Singhal, Amanda Bertsch, Jacob Steinhardt +1

UC Berkeley · Carnegie Mellon University · Allen Institute for AI

Long-Context Language Model Evaluation LLM Reasoning

Sep 24, 2026cs.CL

ELF-REG: Scaling Continuous Diffusion Language Models to Reasoning Tasks

Fully continuous diffusion language models (dLMs) denoise continuous representations without intermediate discretization, then decode all response tokens in parallel at the final step. Their performance on challenging reasoning tasks remains less established than that of autoregressive (AR) LLMs and masked dLMs. We scale Embedded Language Flows (ELF) to mathematical reasoning and code generation on GSM8K, MATH-500, HumanEval, and MBPP. We introduce ELF-REG, which improves learning with representation alignment and entanglement (REPA+REG), where a frozen AR teacher supervises intermediate denoiser features and supplies a global representation that is jointly denoised with the response. ELF-REG-L achieves 55.96% pass@1 on GSM8K at 64 network function evaluations (NFE), and 13.39% on MATH-500 and 22.56% on HumanEval at 128 NFE. It outperforms the evaluated comparable-scale dLMs in pass@1 on GSM8K and code, and improves MATH-500 pass@1 from 10.55% for the ELF-L baseline to 13.39% with ELF-REG-L. Without few-step training, the same task-specific checkpoints support strong low-NFE performance through early-stop, which decodes an intermediate clean prediction without completing the denoising trajectory. At 16 NFE, ELF-REG-L reaches 41.21% HumanEval pass@10, outperforming recent continuous dLMs of comparable scale.

Zeyu Michael Li, William Xingxu Chen, Bingshuo Qian +2

Duke University · Tsinghua University

Code Generation Diffusion Language Models Continuous Diffusion Language Models LLM Reasoning

Sep 23, 2026cs.SE

Can LLMs Reason About Runtime Behavior? A Repository-Level Dynamic Benchmark

Large language models (LLMs) are increasingly used in coding tasks, but their ability to reason about code execution remains unclear. Existing repository-level QA benchmarks mainly evaluate static code understanding and often rely on LLM-based evaluation, while execution-reasoning benchmarks are mostly limited to snippets or functions. We introduce SWE-Flux, a repository-level benchmark for dynamic execution reasoning containing 480 execution-grounded instances across 12 real Python repositories, with gold answers automatically harvested from instrumented test executions rather than written manually or judged by LLMs. The benchmark covers singletest and multi-test questions over control flow, loops, program state, dataflow, exceptions, and program invariants. Evaluating five LLMs shows that this task remains challenging. The best model achieves only 37% accuracy. Models perform better on localized behavior such as invariants, intra-procedural control flow, exceptions, and simple loops, but struggle with dataflow, inter-procedural execution, precise state reasoning, and suite-level aggregation. Finally, we show that the oracle-harvesting pipeline can generate fresh benchmark variants using input perturbation. It successfully harvests valid variants for almost 90% of the selected instances, and the resulting variants are substantially more challenging for the evaluated models.

Hamed Taherkhani, Mohammad Abdollahi, Melika Sepidband +3

York University Toronto, Canada · The University of Texas at Dallas Texas, USA

LLM Evaluation Software Engineering Benchmarks LLM Reasoning

Sep 23, 2026cs.CL

Planned Test-Time Scaling with Coordinated Reasoning Paths

Test-time scaling with parallel branches is widely adopted to improve performance on challenging reasoning tasks. The predominant approach, repeated sampling, draws branches independently from a single policy, which can produce redundant attempts and thereby limit the gains from additional inference compute. To address this limitation, we propose Planned Test-Time Scaling (PTTS), which replaces independent sampling with a coordinated joint policy: a planner generates a solution outline for each branch, steering the branches toward distinct reasoning paths, and an executor produces a full solution conditioned on each outline. Formally, we show that PTTS strictly generalizes repeated sampling and, in a stylized setting, provably promotes coverage of complementary reasoning modes and yields better pass@k scaling. We instantiate PTTS on top of strong reasoning models, keeping them fixed as executors while replacing repeated sampling with PTTS inference to further enhance test-time scaling. Concretely, we develop two variants: PTTS-ZS prompts a model to jointly generate outlines for all branches in a single autoregressive pass, while PTTS-RL directly optimizes the planner against the pass@k reward using truncated execution rollouts for efficient training and a sharper reward signal. Across five mathematical reasoning benchmarks with Qwen3-1.7B and 4B, PTTS-ZS improves pass@64 over repeated sampling by up to 6.7 points, while PTTS-RL further increases the gain to up to 13.4 points. Further analysis indicates that broader coverage of distinct reasoning paths contributes to these gains. Overall, PTTS provides a general framework for improving test-time scaling by coordinating reasoning branches, with zero-shot and trainable instantiations that yield substantial performance gains.

Xueqing Wu, Langxing Bai, Hritik Bansal +5

University of California, Los Angeles · Amazon

RL for Language Model Reasoning Test-Time Scaling LLM Reasoning

Sep 23, 2026cs.CL

LOCKR: A Hidden-State Trajectory-Guided Planner for Detecting and Repairing Stable-but-Wrong Lock-In in Diffusion Language Models

Diffusion language models generate text through iterative denoising, exposing intermediate trajectories before final answers are produced. We identify a recurring reasoning failure, stable-but-wrong lock-in, where an answer stabilizes early around an incorrect value while substantial denoising remains. Surface-level decoding signals such as confidence, entropy, margin, and answer stability are insufficient to reliably distinguish correct from erroneous lock-in. We formulate selective reasoning repair as a lightweight test-time planning problem and propose LOCKR, a hidden-state trajectory-guided planner that decides when to allocate additional computation, expands a structured set of targeted repair branches, and selects the most promising continuation using trajectory-aware verification. Across two diffusion language models and three mathematical reasoning benchmarks, hidden-state trajectories consistently outperform surface signals and single hidden snapshots for both wrong-lock-in detection and repair selection. On natural evaluation distributions, LOCKR yields absolute accuracy gains of 2.21--5.37 percentage points across all five evaluated settings, with repair rates ranging from 22% to 41%. These results establish hidden diffusion trajectories as actionable signals for selective test-time reasoning repair.

Guoshenghui Zhao, Tan Yu, Weijie Zhao

Rochester Institute of Technology · NVIDIA Corporation

Diffusion Language Model Inference Diffusion Language Models LLM Reasoning

Sep 22, 2026cs.CL

Beyond Repeated Sampling: Learning Search Policies for LLM Reasoning

Large language models increasingly tackle hard reasoning problems by spending more test-time compute, yet the dominant strategy remains naive repeated sampling: draw many independent solutions and hope one is correct. Because such sampling explores only through local decoding noise, it tends to produce many near duplicate attempts rather than genuinely different ideas. We ask whether exploration can instead be steered at a semantic level, by first sampling problem specific concepts, hints, or strategies and then conditioning answer generation on them. We refine this into a simple, more exploratory procedure that emits many diverse concepts in a single trajectory, and evaluate it on hard problems where repeated sampling struggles. We then go a step further and make concept generation trainable: a small concept generator is optimized with reinforcement learning so that its concepts maximize the downstream success of a larger, frozen answer generator. On hard mathematical reasoning problems, the trained concept generator substantially improves the answer generator's pass@k over naive repeated sampling at the same answer generation allocation, surpasses concepts drawn from much larger untuned models, and transfers to answer generators it was never trained against, including a model from a different family. A small model can thus be trained into an effective, reusable search policy for a much larger one.

Ismail Labiad, Matthieu Kowalski, Marc Schoenauer +2

Meta FAIR · Université Paris-Saclay, LISN, Inria, CNRS · NYU Courant Institute and CDS

RL for Language Model Reasoning LLM Reasoning

Sep 22, 2026cs.AI

Ladders of Thought: A Self-Evolving Curriculum of Progressively Simplified Reasoning Traces

Large language models (LLMs) excel at reasoning when scaled to hundreds of billions of parameters, but small- and mid-scale models remain brittle reasoners even with knowledge distillation (KD). We present Ladders-of-Thought (LoT), a framework that improves reasoning by combining progressive question rewrites with a self-evolving curriculum. LoT automatically generates semantically faithful but easier variants of reasoning problems, organizes them into difficulty buckets using step-based measures, and employs a self-evolving bandit scheduler to allocate training adaptively. Evaluated on two reasoning domains, math and multi-hop reasoning, across 1-8B models from different families, LoT consistently improves over KD. It delivers large gains on arithmetic tasks (e.g., +32 percentage points on AddSub, +25pp on SVAMP), +2-8pp improvements on in-domain test splits, and strong though dataset-dependent benefits on multi-hop reasoning (e.g., +16pp on QASC, +25pp on StrategyQA). LoT also converges faster than staged curricula, highlighting the value of adaptive progression. These results show that progressive rewrites coupled with adaptive curricula provide a simple yet effective recipe for strengthening reasoning in smaller LLMs.

Minghui Liu, Thomas Magelinski, Dehao Yuan +2

University of Maryland, College Park · Capital One

Numerical Reasoning in Language Models Curriculum Learning Multi-Hop Reasoning LLM Reasoning

Sep 21, 2026cs.AI

Robust Failure, Conservative Repair: Textual Knowledge Distillation from Cross-Model Failures

Failure-based textual knowledge distillation aims to discover gaps in a model's knowledge by examining its task errors. The distilled knowledge can be useful for the reasoning of both this model ("source model") and other models. However, this transfer of knowledge may not be stable. We define a rule atom to be a standalone rule injected into a model's textual input at inference time. A rule atom can encode transferable task knowledge or model-specific reasoning patches that can confuse other models. Also, the injected rule atoms can be misapplied to unrelated cases, causing the model to incorrectly flip its answer based on irrelevant information. Building on a pipeline that distills training examples into task-specific cheat sheets that aid model reasoning, we examine when failure-derived rules can improve these cheat sheets. Our early experiment shows rule distillation from a single model's failures underperforms the baseline cheat sheet on non-source model families. This motivates Robust Failure, Conservative Repair (RFCR), a textual distillation procedure that derives rules from failures shared across models, sharpens their application boundaries using boundary cases, and abstains when no useful rule is found. On a 400-item BIG-Bench Hard task set, RFCR improves the baseline cheat sheets from 68.50% to 71.25% (+2.75 pp; 95% CI [+1.25,+4.50]) without performance degradation on previously correct cases. Ablations and cross-model diagnostics support that accuracy gains come from both new knowledge injection and strict rule-application control.

Andrew Ren, Haokun Liu, Chenhao Tan

University of Chicago

Knowledge Distillation LLM Reasoning

Sep 21, 2026cs.CL

Efficient Reasoning Exploration via State-Conditioned Latent Steering with Progress Guidance

Best-of-

N

is a widely used inference strategy for complex reasoning, whose effectiveness depends on whether sampled candidates can cover diverse and high-quality reasoning paths. However, post-trained reasoning models often suffer from \emph{exploration collapse}, where independent rollouts repeatedly follow similar reasoning paths and limit the gains from increasing the rollout budget. Existing methods alleviate this issue by promoting broader exploration, but do not explicitly guide exploration toward continuations that make meaningful progress, resulting in limited exploration efficiency. To address this, we propose \emph{\underline{S}tate-conditioned \underline{P}rogress-guided \underline{S}teering} (SPS), a training-free latent steering framework. Specifically, SPS constructs a state-conditioned Direction Bank containing multiple progress-guided steering vectors for different prefix-state regions. During online inference, SPS retrieves a suitable steering vector based on the current prefix state and applies it at high-uncertainty transitions to guide the next reasoning step toward meaningful progress. Extensive experiments across multiple model scales and benchmarks demonstrate that SPS consistently outperforms strong baselines. Further analyses validate the effectiveness of its key designs and offer valuable insights for future research. The code is available at https://github.com/rattlesnakey/SPS.

Hengyuan Zhang, Chenming Shang, Zunhai Su +10

The University of Hong Kong · University of California, Los Angeles · Arizona State University +3

Best-of-N Sampling Inference-Time Guidance LLM Reasoning

Sep 17, 2026cs.CL

What Does Privileged Information Add to On-Policy Self-Distillation?

On-policy self-distillation (OPSD) lets a language model learn from a frozen copy of itself that sees an answer or a worked solution. Giving the teacher this extra information seems to offer the student more to learn, but how much does it add beyond distillation itself? To isolate that contribution, we construct AMPLE-Math, a reusable suite of 5,319 mathematical problems with six reasoning views that share the same answer, and compare each view with matched reference-free distillation. With a thinking-enabled teacher supervising direct-response rollouts, reference-free distillation accounts for much of Qwen3-1.7B's improvement under thinking-enabled evaluation, both in domain and on external benchmarks. Evidence for an additional reference benefit is modest in Qwen, strongest for a polished solution, whereas complete traces add two percentage points in SmolLM3-3B at step 50. These benefits depend on the student being trained. At the same checkpoint, replacing short direct-response rollouts with long thinking-enabled rollouts turns gains into losses in both families while the problems, references, and evaluation stay fixed. Teacher profiles and matched loss interventions in Qwen further show that changing token-level supervision can leave student behavior largely unchanged. Together, these findings suggest that OPSD can improve access to existing reasoning capabilities through parameters shared by direct-response and thinking-enabled inference. The value of a privileged reference is what it adds to this cross-mode transfer, not how much of the solution it reveals.

XiuYu Zhang, Wei Chow, Junfeng Fang +2

National University of Singapore

On-Policy Self-Distillation Learning Using Privileged Information LLM Reasoning

Sep 17, 2026cs.IR

Think Thrice Before Reranking: Multi-perspective Evidence and Reasoning Integration for Text Reranking

Reasoning-based reranking with Large Language Models (LLMs) has shown promising improvements in text ranking. However, current methods predominantly rely on a single reasoning trajectory, resulting in rankings that are susceptible to reasoning errors and inherently constrained in modeling the multifaceted signals underlying document relevance. To resolve this dilemma, we propose MERIT-Rank(Multi-perspective Evidence and Reasoning Integration for Text Reranking), a framework that models complementary reasoning trajectories to improve reranking robustness. MERIT-Rank formulates a Multi-Trajectory Reasoning Space (MTRS) that evaluates query-document relevance from multiple perspectives and introduces a joint reranker that consolidates these reasoning paths into a unified ranking decision. We further develop Progressive Rank Policy Optimization (PRPO), a progressive training framework that stabilizes reasoning trajectories while continually improving ranking quality through staged optimization objectives. Experiments on both reasoning-intensive and traditional retrieval benchmarks show that MERIT-Rank consistently achieves superior performance over competitive baselines. The 4B model notably outperforms most 7B and even 32B rerankers on BRIGHT.

Lijun Liu, Zhengzong Chen, Wenyan Li +2

Honor Device Co., Ltd

Learning to Rank RL for Language Model Reasoning LLM Reranking LLM Reasoning

Sep 17, 2026cs.AI

LLM-as-an-Improver: Turning Verification into Better Candidates

Verifier-based selection improves LLM performance by generating multiple candidate solutions and using a verifier to select the most promising one. However, existing methods typically treat verification only as a ranking step and discard its feedback once a fixed candidate pool has been evaluated. In this paper, we ask whether verification can also improve the candidate set itself. To this end, we introduce LLM-as-an-Improver and propose Verify--Repair--Reselect (VRR), which uses verification feedback to generate and reselect improved candidates. VRR retains the initial winner while conditionally generating three complementary alternatives: repaired versions of the winner and runner-up, and a solution based on a new approach. It filters invalid and duplicate candidates using only inference-time information and then reselects the final answer under the original evaluation criteria. Across diverse models and code-generation and reasoning benchmarks, VRR improves over fixed-pool verifier-based selection in many settings and can recover correct solutions even when all candidates in the initial pool are incorrect. These results highlight a broader role for LLMs as improvers: verification feedback can not only select among existing solutions but also construct stronger candidates beyond the initial pool.

Akiyoshi Tomihari, Yuma Ichikawa

Fujitsu Limited Department of Computer Science The University of Tokyo · Fujitsu Limited RIKEN center for AIP

LLM Answer Verification LLM Reranking LLM Reasoning

Sep 16, 2026cs.AI

Clueing up LLMs with Tool-Augmented Deductive Reasoning

Despite recent advances in large language models (LLMs), performing logically consistent deductive reasoning over extended interactions remains challenging. Tasks that require integrating evidence across multiple reasoning steps, maintaining consistency with prior inferences, and updating beliefs under new constraints can surface limitations in current models while providing a useful testbed for evaluating reasoning enhancements. In this paper, we implement a text-based, multi-agent version of the classic board game Clue as an environment to evaluate multi-step, agentic deductive reasoning. In this setting, agents must infer hidden information from a sequence of observations, maintain consistency across turns, and reason over an evolving set of logical constraints. We instantiate six LLM-based agents (GPT-4o-mini and Gemini-2.5-Flash) as players that engage in turn-based gameplay; using three agents per model family, we establish baseline performance across repeated games. We then introduce a tool-augmented approach in which a structured possibility matrix converts implicit game state from generated reasoning logs into an explicit representation of remaining possibilities. The possibility matrix encodes extended-turn memory and deductive constraints, offloading these tasks from the agent. We compare this approach against the baseline to evaluate how tool augmentation supports reasoning quality and task success for autonomous agents in a strategic reasoning environment.

Rebecca Ansell, Autumn Toney-Wails

Georgetown University · Syntheos, Corp · UNU-MERIT

Multi-Agent LLM Systems AI Agent Benchmarks Agentic Reasoning LLM Reasoning

Sep 16, 2026cs.AI

What Counts as Strategic Reasoning? A Systematic Mapping of Chess Research on Humans, Engines, and Language Models

Chess has long served as a model domain for studying search, expertise, decision-making, and artificial intelligence. The emergence of large language models (LLMs) has renewed the relevance of chess as a controlled environment for investigating strategic reasoning and comparing human and artificial decision-making. We present a systematic mapping study of recent research spanning human players, classical chess engines, neural and reinforcement-learning systems, LLMs, and hybrid approaches. The final map comprises 84 core study families, classified according to agent type, strategic-reasoning stages, and evaluation dimensions. The map reveals a literature strongly concentrated on situation assessment, evaluation, and action selection, while explicit planning, explanation, metacognition, and human--AI collaboration remain less explored. LLM research places particular emphasis on state representation and generalization, whereas grounded explanation appears more frequently in hybrid approaches combining language models with engines, expert knowledge, or other external structures. Two distinctions emerge that the map aggregates rather than resolves: hybrid systems differ in where and when heterogeneous capabilities combine, and evaluations that show improved human performance do not thereby establish human--AI synergy. We propose both as extensions of the mapping framework. We argue that chess provides a useful bridge between cognitive and computational perspectives on strategic reasoning, and identify explicit planning, grounded and faithful explanation, metacognitive calibration, and human--AI complementarity as directions for future research.

Paolo Ciancarini, Remo Pareschi

Department of Computer Science and Engineering, University of Bologna, Bologna, Italy · Stake Lab, University of Molise, Campobasso, Italy

Chess Human-AI Decision Making LLM Reasoning

Sep 14, 2026cs.LG

Bellman Policy Optimization

Reinforcement learning with verifiable rewards (RLVR) improves the reasoning capabilities of large language models (LLMs). We introduce Bellman Policy Optimization (BPO), a critic-free method derived from Policy Mirror Descent (PMD). For autoregressive generation with terminal rewards, BPO uses the Bellman equations to reformulate PMD as a trajectory-level objective. The reformulation avoids estimating state values at intermediate states. We prove that it has the same unique optimal solution as the original PMD objective. We derive the practical BPO loss by approximating this objective. Its mismatch-correction weight is a smoothed ratio of complementary token probabilities. Experiments on mathematical reasoning benchmarks demonstrate the effectiveness of BPO.

Zhuoqing Song, Haotian Xu, Xikun Zhang +1

1Apodex US, Inc. · 2Princeton University

Reinforcement Learning RL for Language Model Reasoning Policy Optimization Critic-Free RL Reinforcement Learning with Verifiable Rewards Policy Learning+1

Sep 14, 2026cs.AI

Stellar Colosseum: A Many-Agent Harness for Long-Horizon Research in Mathematics and Theoretical Computer Science

Language models can produce plausible short proofs, but may still be unreliable on long-horizon research problems, where progress depends on a sequence of uncertain and interdependent decisions. We introduce Stellar Colosseum, a model-agnostic harness for allocating inference across research in mathematics and theoretical computer science. Colosseum explores alternative strategies before proof construction, uses a readiness gate to decide when a route is mature enough to decompose, represents the proof plan as interdependent section-level subproblems, and routes verifier findings back to the affected part of the argument. Across these stages, it generates candidates in parallel, attacks them with targeted falsification, and combines candidates and their critiques into a single research artifact through overlapping random-sample tree aggregation. The Colosseum workflow has been integrated into Google Antigravity's Teamwork framework as the Long Proof pattern. We demonstrate the capabilities of Colosseum through open-ended research and evaluations on theorem-proving and competitive programming benchmarks. Using Colosseum with Gemini 3.1 Pro, we obtain several new results that address open problems arising from papers published at top venues such as FOCS and JMLR. On TCS-Bench, a benchmark of research-level theorem-proving tasks drawn from papers published at FOCS, STOC, and SODA, Colosseum achieves 71.0% accuracy using Gemini 3.1 Pro and Gemini 3.7 Flash. In a separate Codeforces evaluation using Gemini 3.1 Pro, the proof-oriented pipeline with execution feedback solves 218 of 222 problems.

Honghao Lin, David P. Woodruff, Yuan Deng +3

1Google Research. · 2Carnegie Mellon University.

Inference-Time Search Automated Theorem Proving Multi-Agent Reasoning Autonomous Research Agents LLM Reasoning

Sep 14, 2026cs.LG

Discrete Beckmann Transport Models for One-Step Language Modeling and Reasoning

Discrete diffusion and flow models are a promising alternative to autoregressive language models, but compressing many-step sampling into fewer steps typically requires distilling a pretrained teacher model. This caps the student at the teacher's quality and requires a costly two-stage training pipeline. We introduce Discrete Beckmann Transport Models (DBTM), built on a time-independent flow whose autonomous transport map provably carries any point in the ambient space to a fixed point on the vertices of the simplex in a single step. We show that this fixed-point property is characterized by a conservation equation whose residual can be minimized directly from data, removing the requirement for a teacher flow and time conditioning. Under this construction, a partially trained map corresponds to the flow truncated at finite time, so generation reduces to iterating one map until it reaches a fixed point. We further extend the map to a partial-context interpolant where additional function evaluations act as refinement steps rather than ODE integration steps. On language modeling and reasoning tasks, DBTM enables one- and few-step generation that improves quality and accuracy over discrete diffusion and continuous flow baselines.

Sophia Tang, Shiyi Wang

University of Pennsylvania · Harvard University · Kempner Institute +1

One-Step Generative Modeling Flow-Based Generative Modeling Diffusion Language Models LLM Reasoning

Sep 14, 2026cs.AI

HISPO: Hierarchical Importance-Sampling Policy Optimization with Entropy-Derived Segments

Reinforcement learning with verifiable rewards (RLVR) has become a central approach for improving mathematical reasoning in language models, but long-form completions introduce a difficult credit-assignment problem: different parts of a solution trace may contribute unevenly to final correctness. Existing policyoptimization objectives for RLVR commonly apply importance-sampling correction at either the token level (GRPO, DAPO) or the sequence level (GSPO), imposing different granularities for assigning credit across a response. We introduce Hierarchical Importance-Sampling Policy Optimization (HISPO), a segment-level policy-optimization method that constructs rollout-time entropy-derived contiguous segments, assigns soft entropy-based saliency weights, and applies clipped importance-sampling correction at the segment granularity. This provides an intermediate correction unit between token-level GRPO/DAPO and sequence-level GSPO. We evaluate HISPO by fine-tuning Qwen3-1.7B-Base on mathematical reasoning tasks. Across six benchmarks, HISPO improves Pass@8 over the strongest baseline on all benchmarks and matches or exceeds the strongest baseline in Acc@8 on five of them. On AIME25, HISPO improves over GRPO by +3.75 Acc@8 and +3.78 Pass@8, and over GSPO by +2.50 Acc@8 and +1.27 Pass@8. These results suggest that segment-level correction is a promising granularity for RLVR in long-form mathematical reasoning.

Quoc-Vinh Lai-Dang, Hyo-Sang Shin

Cho Chun Shik Graduate School of Mobility KAIST

RL for Language Model Reasoning Credit Assignment in RL Policy Optimization Reinforcement Learning with Verifiable Rewards LLM Reasoning

Sep 14, 2026cs.AI

CWM: Controllable White-Box Meta-Prompting for Adaptive Retrieval-Augmented Generation and Reasoning Ability

Recently, Large Language Models (LLMs) have gained significant attention due to their strong language understanding and generation capabilities, demonstrating impressive reasoning abilities as well as effective utilization of external knowledge. Many studies have proposed methods that specialize in improving performance for individual tasks. However, ironically, only a limited number of attempts have explored general-purpose, task-agnostic methods. In this work, we present a unified framework integrating reasoning and Retrieval-Augmented Generation (RAG) tasks. We further propose Controllable White-Box Meta-Prompting (CWM), a low-cost white-box method for adaptive RAG tasks previously dominated by black-box approaches, without requiring external decision modules or multi-sampling. CWM achieves state-of-the-art performance on three adaptive RAG benchmarks across recent LLMs, including GPT-oss-20b, Qwen3-14b, and Llama3.1-8b, while also demonstrating strong generality by extending to reasoning tasks. In addition, CWM provides controllability by enabling retrieval decisions to be regulated through the manipulation of internal model signals. Our code is available at https://github.com/JeongEunhye00/CWM.

Keuntae Kim, Eunhye Jeong, Yong Suk Choi

Department of Computer Science, Hanyang University, Seoul, Korea · Department of Artificial Intelligence, Hanyang University, Seoul, Korea

LLM Prompting Adaptive RAG LLM Reasoning