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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Latest papers 650

Aug 5, 2026cs.CL

NOLLI: A Difficulty-Calibrated Puzzle Benchmark for Diagnosing the English-Korean Performance Gap

We introduce NOLLI, a procedurally generated English-Korean puzzle benchmark designed to diagnose where Korean performance gaps arise. It comprises 15 puzzle types (25 tasks; 7,500 items), with every instance seed-regenerable, verified to have a unique solution, and scored deterministically. Rather than equating harder with bigger, we calibrate difficulty behaviorally, tuning each generator until a fixed reference model lands in target accuracy bands. Its three-level design combines matched direct translations, script adaptations over Hangul jamo (sub-syllabic letters), and Korean-only tasks grounded in Korean culture or orthography. We evaluate 15 frontier, open-weight, and Korean-developed models; among the 12 above a 3% overall-accuracy floor, matched English-Korean accuracy is statistically equivalent within a +/- 10 pp margin (TOST), suggesting little cost from presentation language alone. Writing-system-intensive tasks show sharper gaps: Korean Cipher falls behind English by up to 68.7 pp, whereas Cryptarithmetic over the same jamo shows no systematic penalty, and Jamo Composition accuracy predicts Korean Cipher accuracy. These contrasts are diagnostic rather than causal, consistent with difficulty in multi-step sub-syllabic execution. Korean-only tasks separate rule-application deficits, which vary in sign, from a Kinship deficit positive in all 12. Finally, a salient size measure fails to grow from Easy to Hard in 7 of 15 types, making structural size an unreliable proxy for empirical difficulty.

Dasol Choi, Joonyong Park, Daegon Yu +3

AIM Intelligence · HAERAE LAB · KT Corp. +3

Multilingual Language Model Evaluation Benchmark Validity LLM Reasoning Cross-Lingual Transfer

Aug 4, 2026cs.LG

Test-Time Scaling in Reasoning LLMs: Inference Regimes, Evaluation, and Reproducibility

Large language models can solve harder reasoning problems with more inference-time compute. The term "test-time scaling," however, covers several inference algorithms: extending deliberation along one trajectory, sampling completed candidates and aggregating them by voting or verification, and searching over partial states. These algorithms differ in statistical structure, compute requirements, and failure modes. Treating them as interchangeable under a scalar "budget," or reporting accuracy without specifying the inference protocol, makes results difficult to compare across studies. We study test-time scaling along three axes. First, we formalize it as budgeted inference over the implicit prefix tree of an autoregressive model and distinguish single-trajectory sequential scaling, leaf-level scaling with terminal reduction, and prefix-level scaling. Second, we treat the full inference system as the evaluated object and separate end-to-end performance from candidate-bank diagnostics. We introduce an evaluation profile whose coordinates and simple functionals recover or bound common repeated-sampling metrics, and require compute accounting and uncertainty estimates that match the protocol. Third, we distinguish exact replay from distributional reproducibility and state the requirements for each. We also organize open-weight reasoning models by model-side and interface mechanisms. Our empirical study covers broad knowledge, symbolic reasoning, and competition mathematics, and we publicly release 1,403,520 sampled model attempts. The project website is available at https://mohsenhariri.github.io/scorio/tts. The released datasets are Trace (https://huggingface.co/datasets/harimo/scorio-trace), Lite (https://huggingface.co/datasets/harimo/scorio-lite), Math (https://huggingface.co/buckets/harimo/scorio-math), and SuperGPQA (https://huggingface.co/buckets/harimo/scorio-gpqa).

Mohsen Hariri, Weicong Chen, Nahal Shahini +11

Case Western Reserve University

LLM Evaluation Test-Time Scaling ML Reproducibility LLM Reasoning

Aug 4, 2026cs.CL

LoopMTP: A looped transformer guided by latent multi-token prediction

Looped transformers have emerged as a parameter-efficient alternative to scaling depth for strong reasoning. By reusing one stack of layers across

T

iterations, they attain the effective depth and reasoning capabilities of larger models at a fixed parameter count. Yet existing approaches suffer from latent overthinking and undifferentiated computation, largely because intermediate representations receive no guidance across loops. Multi-token prediction (MTP) supplies exactly the dense, forward-looking supervision the loop is missing. We propose \textsc{LoopMTP}, which links the two through a structural correspondence in latent space: a model that loops

T

times can anticipate

T

future tokens. \textsc{LoopMTP} realizes this by softly aligning the hidden state of loop

t

with the embedding of the token

t

steps ahead, while a lightweight gate preserves useful information across iterations. \textsc{LoopMTP} improves average accuracy by up to 8.1% (relative) over the non-looped baseline, with training remaining stable for up to 15 loops.

Behzad Shomali, Markus Frey, David Berghaus +2

Lamarr Institute · University of Bonn · Fraunhofer IAIS

Multi-Token Prediction Recurrent Transformers LLM Reasoning

Aug 3, 2026cs.LG

GradCuit: Credit-Assigned Gradient Flow Enables Robust and Interpretable Test-Time Latent Reasoning

Optimization-based latent reasoning improves large language model outputs by optimizing instance-specific continuous states at test time while keeping model parameters frozen. Existing methods, however, typically connect these states to the reasoning trajectory through decoded tokens, making sequence-level credit assignment indirect and obscuring how latent updates shape subsequent reasoning. We introduce GradCuit (gradient through circuit), which inserts optimizable latent states at a selected Transformer layer between the hidden representations of the prompt and the generated continuation. Causal self-attention provides every continuation-token log-probability with a differentiable path to every preceding latent state through the remaining Transformer blocks, enabling reward-weighted gradients from the entire continuation to be assigned directly to the latents. Across five instruction-tuned backbones, three reasoning benchmarks, and two answer formats, GradCuit achieves an average accuracy of 64.5%, outperforming chain-of-thought prompting by 6.6 percentage points and the strongest competing method by 2.4 points. GradCuit also demonstrates greater robustness: across seven learning-rate settings, it consistently outperforms LatentSeek while reducing the standard deviation of accuracy from 1.53 to 0.82, and even its random-walk variant remains competitive with LatentSeek. For interpretability, token-level gradient attribution reveals that latent influence concentrates on reasoning-connector tokens, while layer analysis identifies early-to-middle Transformer layers as the most effective optimization space. By directly optimizing internal reasoning from outcome feedback, GradCuit opens a new axis of robust and interpretable test-time scaling, where LLMs adapt how they reason rather than merely regenerate, sample, or rerank outputs.

Zhaoxin Yu, Qi Shen, Hengli Li +4

NLCo Lab, Beijing Institute for General Artificial Intelligence · School of Artificial Intelligence, Beijing University of Posts and Telecommunications · School of Artificial Intelligence for Science, Peking University

Test-Time Optimization LLM Interpretability Continuous Latent Reasoning Language Model Robustness LLM Reasoning Latent Reasoning

Aug 3, 2026cs.AI

Beyond the Mean: Multi-Moment Policy Optimization for LLM Reasoning

Reinforcement learning has become a central paradigm for improving the reasoning capabilities of large language models. Existing methods generally aim to reduce the failure probabilities induced across problems. In this paper, we introduce a moment-based perspective on policy optimization for LLM reasoning by treating the failure probability of a randomly sampled problem as a random variable and characterizing optimization objectives through its moments. Under this perspective, many existing methods optimize only a single moment of the failure-probability distribution, leaving its broader distributional structure largely uncharacterized. We propose \textbf{M}ulti-\textbf{M}oment \textbf{P}olicy \textbf{O}ptimization (MMPO), a novel policy optimization framework that jointly minimizes multiple moments of the failure-probability distribution. MMPO admits a direct operational interpretation as minimizing the expected truncated time required to obtain the first successful response. Beyond MMPO, we further develop a general moment-transformation framework that systematically induces different moment profiles and provides a unified view of a broader family of policy optimization objectives. Experiments across five mathematical reasoning benchmarks and models of different scales demonstrate that MMPO consistently outperforms strong baselines. We hope this moment-based perspective offers new insights into the design of policy optimization objectives for LLM reasoning.

Yijun Zhang, Yule Xie, Jiaxin Ding +4

Shanghai Jiao Tong University

RL for Language Model Reasoning Policy Optimization LLM Reasoning

Aug 3, 2026cs.AI

HPFA: Hypergraph-Based Paired Failure Attribution for LLM Reasoning

Reflection is a powerful mechanism for LLM reasoning, yet its effectiveness hinges on accurately attributing failures to specific reasoning steps, a capability that current models notably lack. Existing failure attribution methods either require expensive step-by-step counterfactual testing that scales poorly with trajectory length, or treat reasoning traces as flat sequences that ignore the inherent non-linear logical dependencies. We propose a hypergraph-based paired failure attribution (HPFA) framework that attributes the failure root cause by comparing the hyperedges of the targeted failure reasoning path against a reference successful path. By reducing the search space, our method efficiently localizes root causes and enables scalable synthesis of attribution data for training a lightweight attributor model via supervised fine-tuning and reinforcement learning. Experiments on mathematical reasoning and agentic coding tasks demonstrate that HPFA can dramatically increase attribution accuracy and efficiency, and the trained attributor consistently improves reasoning accuracy at test time, outperforming baselines that lack graph structure or paired analysis.

Runchuan Zhu, Hongbin Lai, Bowen Jiang +4

National University of Singapore · Peking University · University of Texas at Austin +1

LLM Reasoning Reasoning Trace Analysis

Aug 3, 2026cs.CV

AdaThinkV: Adaptive Thinking for Token-Efficient Video Reasoning

Chain-of-thought (CoT) reasoning can improve performance on difficult video questions but often wastes decoding tokens on simple ones. We study whether a video multimodal large language model can adapt its reasoning effort to each question. We propose AdaThinkV, an adaptive framework for video reasoning that learns whether to reason explicitly without offline difficulty labels, manually tuned confidence thresholds, or an external router. During reinforcement learning, AdaThinkV samples matched rollouts in explicit reasoning and direct answering modes for each prompt. ThinkGain estimates the prompt-level utility of explicit reasoning by balancing its accuracy gain against additional response length, providing supervision for both conditional response generation and autonomous mode selection. For difficult prompts, limited rollout exploration can yield groups in which every response is unsuccessful and accuracy rewards show little variation, providing insufficient signal for learning. We therefore introduce Variance Recovery Policy Optimization (VRPO), which retains and progressively expands these groups to recover informative signals from prompts that are difficult yet solvable. At inference, AdaThinkV selects a response mode and generates the response in a single autoregressive sequence. Across a unified suite of video reasoning evaluations, AdaThinkV achieves a mean accuracy of 40.79 with an average of 257.20 output tokens, outperforming the strongest evaluated adaptive baseline by 2.98 points while using 22.7% fewer tokens. Project page: https://trilarflagz.github.io/AdaThinkV/

Jingqi Tian, Haoji Zhang, Lin Chen +7

Tsinghua Shenzhen International Graduate School, Tsinghua University · Alibaba Group · Peking University

Efficient VLM Inference RL for Language Model Reasoning Video Reasoning Multimodal CoT Reasoning LLM Reasoning

Aug 3, 2026cs.CL

Does Accuracy Equal Evidence? Reasoning Faithfulness under KV Cache Compression

KV cache compression is commonly evaluated by final-answer accuracy, implicitly assuming that preserving the answer also preserves the reasoning that supports it. We test this assumption for large reasoning models and show that it can fail: under compression, correct answers and the validity of their visible supporting rationales can be preserved at different rates. We study this failure with a controlled fixed-trace replay protocol, which holds reasoning content fixed and isolates whether compression preserves usable information from an already available trace. We evaluate ten token-eviction KV compression methods and one quantization method on three models across mathematical reasoning, scientific QA, clinical calculation, and long-context retrieval. We measure final accuracy, answer-chain consistency, and perturbation faithfulness. Across tasks, token-eviction methods can preserve competitive final-answer accuracy while substantially degrading chain support or perturbation faithfulness. We call this the answer-evidence gap. A coverage-preserving quantization control is substantially less affected, suggesting that the failure is tied less to KV memory reduction itself than to losing access to parts of the reasoning trace. Code is available at https://github.com/famous-blue-raincoat/Safe_KV_Compress.

Mengting Ai, Jingrui He, Yue Guo

University of Illinois Urbana-Champaign

CoT Faithfulness Reasoning Evaluation KV Caching KV-Cache Compression KV-Cache Quantization LLM Reasoning

Aug 2, 2026cs.CV

Recursive Vision Language Models for General Symbolic Reasoning

Hard symbolic-reasoning tasks such as Sudoku, maze pathfinding, and ARC remain challenging for LLMs due to their fixed-depth autoregressive reasoning, which limits systematic search, refinement, and backtracking. While recursive models such as Hierarchical Reasoning Model (HRM) and Tiny Recursive Model (TRM) address this limitation through iterative latent-state refinement, they are typically task-specific and do not leverage pretrained language priors. We propose R-Qwen, a recursive reasoning framework built upon a pretrained Qwen backbone. R-Qwen repeatedly refines a candidate solution through programmatic self-recursion and deep supervision, combining the structured iterative computation of recursive models with the linguistic and reasoning priors of pretrained LLMs. We further adapt Hierarchical Supervision Weighting (HSW) to autoregressive models by exponentially weighting losses across recursive steps. HSW reduces gradient variance by at least 50%, improves the signal-to-noise ratio of stochastic gradients, and accelerates convergence. Across eight challenging benchmarks, R-Qwen consistently outperforms prior recursive reasoning models and substantially larger LLMs while using a comparable number of trainable parameters. Notably, on ARC-AGI dataset, our model achieves a 27.6% improvement over the baseline, highlighting the effectiveness of recursive refinement for general symbolic reasoning. These results suggest that recursive reasoning mechanisms and pretrained language model priors are complementary approaches for improving symbolic puzzle-solving. Code and models will be released after acceptance.

Omid Nejati Manzari, Guillaume Lajoie, Hassan Rivaz

Concordia University, Montreal, Canada · Mila — Quebec AI Institute · Université de Montréal

Symbolic Reasoning Implicit Reasoning in Language Models Algorithmic Reasoning LLM Reasoning

Aug 2, 2026cs.AI

Cognitive Demand Steering for Adaptive Meta-Reasoning in Large Language Models

Recent meta-reasoning frameworks improve LLM reasoning by wrapping chain-of-thought generation in an iterative control loop, allowing more effective backtracking, termination of reasoning loops, and injection of promising reasoning patterns, among other strategy adjustments. Despite promising results, methods often rely on backward-looking reward functions, utilize coarse search actions, or require additional reasoning controller training requiring many-shot supervision. We introduce Cognitive Demand Steering (CDS), a training-free meta-reasoning framework equipped with residual demand assessment: at each step, an LLM-based progress evaluator characterizes the residual reasoning required to arrive at a solution rather than merely evaluating the previous step. This allows a meta-controller to select reasoning interventions comprising both general-purpose exemplars and actions (e.g., general guidance for quantitative reasoning) that directly tackle this forward-looking demand signal. This shift eliminates the need for any trained component while enabling zero-shot transfer across models and tasks with no adaptation. Rather than relying on coarse characterizations, we employ cognitive scales to both design interventions as well as profile initial problem complexity and residual demand signal over 16 dimensions motivated by cognitive science (e.g., attention and scan, learning and abstraction, spatio-physical reasoning), giving the controller a fine-grained vocabulary for diagnosing. Averaged across three frontier LLMs and six reasoning benchmarks, CDS improves accuracy by

21.9\%

over direct calls and

9\%

over standard CoT reasoning, with the largest gains on difficult mathematics and coding tasks.

John Scoville, Shengzhuang Chen, Yejin Bang +2

Thomson Reuters Foundational Research · Imperial College London

Metacognition in Language Models LLM Reasoning

Jul 31, 2026cs.CL

BLADE: Boundary-Expanded and Layer-Adaptive Dynamic Exit for Efficient LLM Reasoning

Large language models often improve task performance by generating long reasoning traces, but the resulting computation is frequently wasted on redundant verification and revision. Existing probe-based early-exit approaches mainly inspect explicit self-doubt expressions, leaving many earlier termination opportunities undetected. Expanding inspection to ordinary reasoning boundaries improves coverage, but also exposes highly diverse intermediate states whose predictive information may reside in different hidden layers. We present Boundary-Expanded and Layer-Adaptive Dynamic Exit for Efficient LLM Reasoning (BLADE), a lightweight framework that dynamically terminates reasoning by estimating whether the generated prefix is sufficient for correct answering. BLADE constructs multi-granular checkpoints from sentence, self-doubt, and paragraph boundaries, and derives robust training labels through repeated answer completions. It further learns a compact subset of informative probe layers instead of relying on fixed choices or expensive representations from all layers. At inference time, calibrated predictions are combined with checkpoint-specific confirmation rules to balance responsiveness and premature-exit risk. Experiments on five benchmarks and two Qwen3 reasoning models show that BLADE preserves near-baseline accuracy while reducing generated tokens by 24.8% on Qwen3-8B and 15.8% on Qwen3-4B. Ablation studies further confirm the benefits of diverse checkpoints and automatic layer selection, demonstrating an effective approach to more efficient LLM reasoning.

Keshu Fu, Keqin Peng, Jun Bai +6

School of Computer Science and Engineering, Beihang University · Beijing Institute for General Artificial Intelligence, BIGAI · Academy for Advanced Interdisciplinary Studies, Peking University +1

Efficient Language Model Reasoning Efficient Language Model Inference Language Model Probing LLM Reasoning Early-Exit Neural Networks

Jul 30, 2026cs.CL

Would You Walk to the Car Wash? Revealing the Salience Bias of Large Language Models in Commonsense Reasoning

As large language models (LLMs) continue to advance in complex reasoning tasks, they have learned to heavily prioritize explicit conditions provided in the input. However, in everyday commonsense reasoning, this mechanism exposes a critical vulnerability which we term Salience Bias: models become easily hijacked by useless explicit distractors (e.g., numerical values), leading them to ignore the implicit physical or commonsense prerequisites of a task. A critical open question is whether this failure reflects a genuine gap in commonsense knowledge or merely its suppression under misleading task framing. To investigate this, we construct the SaliTrap Benchmark, a high-quality dataset across four trap dimensions. Evaluating 12 state-of-the-art LLMs, we find that all mainstream models suffer significantly from salience bias, with severity scaling with distractor density and detecting the trap often decoupled from actually avoiding it. Crucially, by re-eliciting the same models with the task framing stripped away, we show that this is overwhelmingly a failure of \textbf{knowledge suppression rather than knowledge absence}: a context-free knowledge probe alone recovers over 90% of sycophantic-compliance failures, revealing that the requisite commonsense is intrinsically present but actively crowded out by salient distractors that lure the model into over-compliant, unnecessary computation. Building on this diagnosis, we further show that lightweight, inference-time prompting alone substantially closes the gap without any retraining. Our findings relocate the bottleneck of commonsense reasoning failures from model competence to elicitation, and we release SaliTrap as a testbed for this blind spot. The codes are available at https://github.com/Wuzheng02/SaliTrap.

Zheng Wu, Chenhao Xue, Shijie Zheng +3

School of Computer Science, Shanghai Jiao Tong University · ByteDance Inc

Implicit Reasoning in Language Models LLM Reasoning

Jul 30, 2026cs.CL

Lightning OPD 2.0: Mitigating Style Bias in Cross-Teacher On-Policy Distillation for Large Reasoning Models

On-policy distillation (OPD) provides dense token-level supervision from a teacher, but its effectiveness can depend on teacher consistency, meaning that the model providing OPD supervision should also have generated the demonstrations used to train the supervised fine-tuning (SFT) reference. However, this condition is frequently violated in practice when SFT data have mixed or unknown provenance or when different models are preferred for SFT data generation and subsequent distillation. In such cross-teacher settings, even a stronger OPD teacher can yield little improvement over the SFT reference. We find that raw teacher--reference disagreement contains potentially useful context-specific teacher evidence as well as a recurring component associated with differences in wording, formatting, and reasoning cadence. We introduce Lightning OPD 2.0 with cross-fitted style residualization, which uses rollout-level cross-fitting to estimate this recurring component as an operational proxy for style-token bias and subtracts it before constructing the token-level OPD update. Across mathematical reasoning and code generation benchmarks, Lightning OPD 2.0 consistently outperforms Lightning OPD in cross-teacher settings. Starting from Klear-Reasoner-8B-SFT, Lightning OPD 2.0 reaches 82.4% on AIME 2024 and 63.0% on LiveCodeBench v5. Together, these results establish Lightning OPD 2.0 as a practical approach to cross-teacher OPD, relaxing teacher consistency as a prerequisite and allowing the SFT data generator and distillation teacher to be selected independently. Code will be released soon.

Yecheng Wu, Song Han, Han Cai

NVIDIA

Language Model Distillation On-Policy Distillation Knowledge Distillation LLM Reasoning

Jul 30, 2026cs.AI

Not All Tokens Deserve Equal Credit: Counterfactual Sensitivity Credit Reallocation for Long-CoT Reasoning

Reinforcement learning with verifiable rewards (RLVR) is central to improving long-CoT reasoning in large language models. Critic-free methods such as GRPO convert response-level rewards into advantages and uniformly broadcast them across tokens, overlooking their unequal contributions to the final outcome. On-policy self-distillation (OPSD) instead provides dense distributional supervision by minimizing the forward KL divergence between an unprivileged policy and a privileged self-teacher, implicitly assuming that the resulting likelihood shifts encode reliable answer-aligned information. We test this premise by fixing each sampled trajectory and re-scoring it under two opposing outcome conditions, one asserting correctness and the other incorrectness. Most affected tokens shift in the same direction under both conditions, with few sign reversals and substantial overlap in the induced optimization signals. Large shifts also concentrate on highly substitutable surface-form tokens, whereas tokens carrying problem-specific reasoning content are less sensitive. These findings show that privileged shifts fail to provide reliable answer-aligned directions, while their magnitudes primarily reflect counterfactual sensitivity rather than token-level learning value. Based on these observations, we propose Counterfactual Sensitivity Credit Reallocation (CSCR), a simple extension of GRPO that reduces credit for highly sensitive tokens and renormalizes token-level advantages to preserve both the original credit budget and verifier-determined direction. On long-CoT mathematical reasoning benchmarks, CSCR consistently outperforms GRPO baseline with the same number of policy updates. Targeted ablations further corroborate our diagnosis: privilege-induced directions are unreliable, moderate downweighting is most effective, and stronger modulation destabilizes optimization.

Qiangqiang He, Zhongheng Wu, ZiJian Wang

State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China · Institute of Wireless Communications Technology, Shanghai Jiao Tong University, Shanghai, China

Token-Level Credit Assignment RL for Language Model Reasoning Step-Level Credit Assignment in RL Reinforcement Learning with Verifiable Rewards Counterfactual Credit Assignment LLM Reasoning

Jul 30, 2026cs.AR

ARES: Adaptive Reasoning-Effort Steering for PPA- and Cost-Aware RTL Optimization with LLM Agents

Large language model (LLM) agents optimize the power, performance, and area (PPA) of register-transfer-level (RTL) designs by iterating over edits, synthesis, and PPA analysis, paying a dollar cost for every LLM call. Prior agents report the quality reached without its normalized cost, attribute that quality to an engineered cross-design memory, and hold the reasoning effort of every call fixed. We propose Ares with three corresponding innovations. (1) We introduce a normalized dollar cost per LLM call reported alongside the figure of merit (FoM), enabling fair comparison across effort levels and optimizers. (2) Using this accounting, we find the construction of the long-term memory matters little. An engineered memory brings no dependable gain over a plain concatenation of the same experience. (3) We instead adapt the per-call reasoning effort by escalating to deeper reasoning only once progress at a lower effort stalls, via a patience counter fit on 21 training designs, allocating reasoning where it pays rather than uniformly across all iterations. On three test designs unseen during training, the effort policy lowers the FoM by 23-27% where the best fixed effort reaches 16-23%, at equal normalized cost. Ares closes up to 83% of the gap from an LLM-drafted multiply-accumulate unit to its highly hand-optimized counterpart, and reaches a 25% deeper FoM than state-of-the-art Dr. RTL at 12% of its tokens.

Stef Cuyckens, Mihaela Jivanescu, Jun Yin +2

KU Leuven Leuven, Belgium · Nokia Bell Labs Antwerp, Belgium

Inference-Time Optimization Large Language Model-Guided Optimization Cost-Aware Inference LLM Reasoning Memory-Augmented Language Model Agents

Jul 30, 2026cs.LG

LoRA Scaffolded Policy Optimization (LSPO): A Sampling-Time Low-Rank Scaffold for Recovering Reinforcement-Learning Gradient on Zero-Reward Cliff Prompts

Reinforcement learning from verifiable rewards (RLVR) for mathematical reasoning suffers from a structural blind spot: on "cliff" prompts-those on which every sampled rollout in a group fails-the group-normalized advantage is identically zero, so GRPO produces no gradient on precisely the prompts at the frontier of the model's capability. We introduce LoRA Scaffolded Policy Optimization (LSPO), a sampling-time mechanism that recovers this lost gradient. Each RL step, LSPO detects cliff prompts, fits a small low-rank (LoRA) adapter by a brief supervised step on their ground-truth solutions, re-rolls the cliffs with the base-plus-adapter model, splices the now-successful completions back into the RL batch with an importance-sampling correction, and takes a GRPO step on the base alone; the adapter receives only the supervised gradient and is discarded at checkpoint, yielding a base-only model. On DeepMath-103K with DeepSeek-R1-Distill-Qwen-1.5B, evaluated over n=5 paired seeds per arm at a matched 1000-step reporting horizon, LSPO's 5-seed mean matches or beats a DAPO baseline on all 16 (benchmark, pass@k) cells (15 strict wins and one exact tie), with gains of up to +10.7 points on AIME24/pass@4, +6.7 points on AIME24 and AIME26 at pass@16, and +2.4 points on MATH500/pass@1; averaged over the 16 cells the improvement is +3.8 points.

Ken Ding

NVIDIA

Reinforcement Learning RL for Language Model Reasoning Group Relative Policy Optimization Reinforcement Learning with Verifiable Rewards Policy Learning LLM Reasoning

Jul 30, 2026cs.CL

Reasoning Consensus: Structural Ensembling of LLM Reasoning via Weighted DAG Aggregation

Large Language Models (LLMs) explore problems through chain-of-thought, but this exploration is buried in unstructured prose. On high-stakes tasks, users cannot tell which steps are well-supported, which alternatives were seriously considered, or how the final conclusion compares to those the model discarded. We propose a framework that ensembles the reasoning structure, not just the answers, of multiple LLMs by weighted merging of Directed Acyclic Graphs (DAGs) extracted from reasoning chains. We weight each step by how many traces independently attest to it, to return "Consensus Reasoning". Across six benchmarks spanning statutory interpretation, graduate-level science, narrative multi-hop reasoning, and first-order logic, our ensemble outperforms a matched-budget majority-vote baseline, with a maximum accuracy gain of 3.1% on MuSR-MM (narrative multi-hop reasoning). On a single model, the framework matches or exceeds self-consistency at the same trace budget while additionally exposing an inspectable consensus reasoning graph. Ensemble weights correlate with LLM-judge rankings of reasoning quality at Spearman

ρ= 0.30

-

0.51

, and consensus subgraphs are preferred over alternatives leading to the majority-vote answer in 54.4-65.4% of head-to-head comparisons across five of six datasets. We observe that our framework can also be used to analyze diverse reasoning perspectives for a problem.

Amruta Parulekar, Jinu Lee, Dilek Hakkani-Tür +1

University of Illinois Urbana-Champaign

LLM Reasoning with Graphs LLM Interpretability Structured Reasoning Language Model Ensembles Multi-Agent Reasoning LLM Reasoning

Jul 30, 2026cs.GT

Strategy, Not Payoffs: A Behavioural Embedding of Normal-Form Games

Learning a strategic task changes more than what is directly taught: fine-tuning on one game can either enhance or degrade an agent's ability to reason in another. Understanding and predicting this transfer of strategic capabilities, however, remains a key challenge for large language models (LLMs). Normal-form games provide an ideal testbed for analyzing this phenomenon, as they feature explicitly defined payoffs and well-characterized equilibrium behaviours. In this work, we investigate whether game embeddings can explain and predict changes in LLM strategic capabilities following fine-tuning across different games. We propose a lightweight two-feature embedding that captures fundamental behavioural demands: the entropy of the Nash equilibrium and the sensitivity of optimal responses to an opponent's action. We show that while existing published structural embeddings primarily memorize game identities and fail to generalize, our behavioural embedding reliably predicts performance changes on held-out games. These results demonstrate that the transfer of strategic capabilities in LLMs is not dictated by the payoff geometry of a game, but by the underlying structure of the decision-making behaviour it requires.

Joshua Caiata, Sreepriya Pulyassary, Xiang Li +1

University of Waterloo

LLM Fine-Tuning Strategic Reasoning Risks in Language Models Transfer Learning LLM Reasoning

Jul 29, 2026cs.CL

Benchmarking LLM Competence on Logical Inference over Probability Operators

Both expressions of uncertainty and inferences are ubiquitous in natural language, and valid inferences over natural-language expressions of uncertainty are necessary for not only everyday conversations but also for high-stakes domains such as medicine and law. While large language models are increasingly evaluated on logical reasoning tasks, disentangling principled, symbolic reasoning from clever surface-level pattern matching is fraught with difficulty. We introduce a benchmark for reasoning over probability operators--inference over sentences with gradable epistemic modals (e.g., probably, might, must) containing 14,320 procedurally-generated English prompts across fifteen inference templates, systematically varying question form, negation strategy, and surface content. Evaluating 29 models, we find that most show answer biases independent of the logical form, a systematic preference for Yes or No. We summarize this with a competence floor: the worse of a model's accuracy on Yes-correct and No-correct items. Only 9 of 29 models exceed random chance. We also test variations in question form, verb phrases/activity, and both the gender and origin of names used in the prompts, finding biases across every axis.

Nayera Hasan, Jack Greff, Alvin Grissom

Haverford College

Probabilistic Logic LLM Evaluation Language Model Bias Evaluation LLM Reasoning

Jul 29, 2026cs.LG

ReCo: Reweighting GRPO Against Distributional Concentration

Group Relative Policy Optimization (GRPO) has become a standard reinforcement learning method for post-training language models. Recent work shows that GRPO can reduce the base model's reasoning capacity and underperform it in Pass@k when k is large, indicating reduced coverage of reasoning paths. We find that this reduction is associated with GRPO concentrating on responses that the base model already generates with high probability. We trace this concentration to two mechanisms in the GRPO update. At the response level, high-probability responses dominate the group gradient through repeated occurrence. At the token level, GRPO's importance ratio scales gradients, further reinforcing tokens that become more likely under the current policy. We propose ReCo, a reweighting method that addresses both effects. Response contributions are normalized by their expected occurrence within the rollout group, and the token-level importance ratio is replaced with a variance-based ratio that gives larger update scale to non-saturated decision points where alternative token choices remain plausible. Across Qwen2.5-Math-1.5B/7B and Llama-3.1-8B-Instruct on five mathematical reasoning benchmarks, ReCo improves Pass@k for large values of k and is comparable to GRPO for small values of k.

Junoh Park, Junseo Hwang, Wonguk Cho +1

Graduate School of Data Science, Seoul National University

Reasoning Diversity RL for Language Model Reasoning Group Relative Policy Optimization Importance Weighting RL Post-Training LLM Reasoning

Jul 29, 2026cs.CL

Knowledge before Reasoning: EC-Reason-Bench, a Training-Free Diagnostic Benchmark for LLM Enzyme Classification

Enzyme function prediction is a hierarchical, knowledge-intensive form of protein function classification. Existing benchmarks expose an anomaly: general LLMs often get the coarse first level right, yet once asked for a complete EC number their accuracy at levels two through four drops to almost zero, while specialized models and tools stay usable. We propose EC-Reason-Bench, a training-free, diagnostic evaluation protocol built to answer two questions: why general LLMs score close to nothing on EC number prediction, and how much of that loss can be recovered without updating a single weight. We break enzyme classification ability into four orthogonal levers that can each be measured on their own: output structure, external knowledge, reasoning structure, and reasoning robustness. We test each lever with an inference-time method against a shared zero-shot baseline reproducing previously reported near-zero performance. Experiments with several strong reasoning LLMs yield four main findings. First, external knowledge is decisive and must precede reasoning: uniformly low closed-book performance rises sharply with open-book access, narrowing model gaps. Second, in closed-book settings, whether cascading and chain-of-thought help or hurt depends on a model's tendency to abstain. Third, once evidence is available the aggregate score of the best LLM setting is indistinguishable from simply voting the EC numbers of the nearest retrieved neighbors; that tie is an artifact of averaging, and it hides a large gain on adversarial evidence set against an equally large loss on multi-functional enzymes. Reasoning over evidence therefore acts as an arbiter of conflicting neighbors rather than as a source of knowledge, and no single-number leaderboard can see it. Fourth, accuracy obeys a law of homology availability.

Linyu Li, Zhi Jin, Yichi Zhang +6

School of Computer Science, Peking University, Beijing, China · College of Computer Science and Technology, Zhejiang University, Hangzhou, China · School of Computer Science, Tibet University, Lhasa, China

Retrieval-Augmented Generation LLM Evaluation Classification Molecular Property Prediction LLM Reasoning

Jul 26, 2026cs.CL

Do Diagrams Help Large Language Models Reason? Evidence from Syllogistic Reasoning

Diagrams are widely used to support logical reasoning, and prior studies suggest that representations such as Euler diagrams can improve human reasoning performance. Recent work has also explored their effects on large language models (LLMs). In this paper, we compare four representational conditions for syllogistic reasoning: natural language, logical notation, linear diagrams, and Euler diagrams. Using 285 problems from Ando et al. (2024), we evaluate two contemporary LLMs, Claude 3.5~Sonnet and GPT-4o-mini. Our results show that diagrammatic representations do not consistently improve performance. Although the models perform well on entailment and contradiction problems, they struggle with neutral problems and often make systematic conversion errors. Overall, the results suggest that the tested models gain limited benefit from diagrams in logical reasoning tasks.

Risako Ando, Koji Mineshima

Keio University, 2-15-45 Mita, Minato-ku, Tokyo 108-8345, Japan

LLM Evaluation LLM Reasoning

Jul 26, 2026cs.CL

Reasoning or Memorization: Can LLMs Understand and Generate Chinese Xiehouyu Riddles?

In this paper, we push the boundary of LLM reasoning by testing them in a Chinese language game, xiehouyu, with novel xiehouyu created by linguists that had not existed before to avoid data contamination. We use multiple-choice questions (MCQ), free-form explanation generation, and new xiehouyu creation to evaluate LLMs' ability to understand and create xiehouyu. In MCQ, we use the delta of accuracy (

Δ_{acc}

) between existing but low-frequency xiehouyu and novel ones as an index for memorization.

Δ_{acc}

for native speakers is very low, suggesting similar processing mechanisms. However, we found that frontier Chinese models have on average a

Δ_{acc}

of 23.6%, while English-centric models tested have a mean

Δ_{acc}

of 5.1%, suggesting that frontier Chinese models are likely trained with much larger Chinese data, thus memorizing more low-frequency xiehouyu. For novel xiehouyu, Gemini 3.1 Pro demonstrated remarkable ability with acc 92.6, which is 24% higher than human accuracy. In xiehouyu creation, those created by LLMs receive much worse ratings than those by humans. These results suggest that claims about the reasoning abilities of LLMs may need careful re-examination considering the data contamination issue, and that LLMs' creativity in language-related tasks may still be behind human experts, at least in Chinese xiehouyu.

Hai Hu, Siyuan Song, Chongtian Shao +3

1The Hong Kong Polytechnic University · 2The University of Texas at Austin · 3Shanghai Jiao Tong University

LLM Evaluation Memorization in Language Models Text Generation LLM Reasoning

Jul 25, 2026cs.AI

Confidently Wrong: Exception Chain Collapse in Frontier LLM Rule Evaluation

We document a failure class in frontier large language models -- exception chain collapse -- observed in eligibility evaluation under nested conditional rules of the form "A is required UNLESS B applies, UNLESS C overrides B". The failure reproduces at first observation, but its empirical surface is unstable: between March and April 2026 several failure cells closed silently under the same model alias, with no version bump (GPT-5.4 on construction insurance moved from 96.6% to 100%, same prompt and harness). For regulated workflows, frontier-model accuracy is a moving compliance boundary that shifts without notice. We present the Aethis Eligibility Module, a neuro-symbolic architecture in which LLMs author rules from authoritative sources and an SMT-based layer executes them deterministically, consistent with the authored specification regardless of model drift, reasoning-effort defaults, or prompt format. Three evidence bases: (i) a controlled benchmark of 225 scenarios across four regulatory domains documents the pattern and, in replication, the drift that partially closed it; (ii) a 20-scenario adversarial extension on construction insurance, where the engine scores 20/20, as does one of four frontier configurations (GPT-5.4 at low reasoning effort), while the other three, including Anthropic's strongest model at evaluation time, fail the same coverage-gap edge case; (iii) external validation on nine peer-reviewed LegalBench tasks, 949 held-out cases, where the engine is significantly more accurate than all three frontier models (combined McNemar's p <= 0.003), with margins up to +41 points on the curated multi-prong tasks against the Anthropic models. The contribution is to relocate uncertainty from the inference boundary, where it is silent, to the specification boundary, where it is deliberate and audited. All scenarios, rule encodings, and results are public and reproducible.

Paul Simpson, John Kozak, Lisa Doake

Aethis (aethis.ai)

LLM Reliability Neuro-Symbolic AI LLM Reasoning

Jul 25, 2026cs.AI

SymStep: Symbolic Step Verification for Logical Reasoning

Chain-of-thought (CoT) prompting can fail severely on constraint-dense logical reasoning tasks, where unverified errors accumulate silently across steps. We introduce SymStep: an LLM makes one atomic claim at a time (DEDUCE: Alice, pet, Cat), then a lightweight constraint propagator checks the claim for consistency with prior accepted deductions, rejects contradictions, and cascades implied facts automatically. SymStep+G additionally provides MRV guidance after each accepted step, directing the LLM toward the most constrained unresolved variable. On a 35-puzzle retained subset of ZebraLogicBench, a benchmark of 1,000 Einstein-style logic puzzles, Direct and CoT both achieve 0%, while SymStep+G reaches 97%. On AR-LSAT analytical reasoning problems, SymStep achieves 100% vs. CoT's 87%. On LGP-14, SymStep+G achieves 100% vs. 0% for CoT and Logic-LM, the strongest prior symbolic+LLM baseline we compare against. Ablation studies reveal that MRV guidance is a key mechanism for reducing directionless cycling, while consistency checking provides a safety net against explicit contradictions. Across six benchmarks spanning five task domains, SymStep variants match or exceed every baseline on constraint-dense and arithmetic tasks. Experiments on AQUA-RAT algebra confirm the advantage is constraint-density-specific.

Aida Usmanova, Rui Gao, Dilshod Azizov +2

Leuphana University of Lüneburg · Mohamed bin Zayed University of Artificial Intelligence

Symbolic Reasoning Structured Reasoning Neuro-Symbolic Reasoning Constraint Satisfaction LLM Reasoning

Jul 24, 2026cs.CL

J-CoT: Chain-of-Thought in J-Space

Chain-of-thought prompting improves language-model reasoning by carrying intermediate states across successive computation steps. However, relying on natural language as the only recurrent interface is overly restrictive, since many transient computations do not need to be fully verbalized. Existing latent-reasoning methods remove this constraint by recurrently propagating continuous hidden states. However, these methods pass a dense hidden vector as a whole, without an explicit mechanism for selecting and organizing the information needed by the next reasoning step. This motivates an intermediate interface that remains linguistically grounded without requiring a decoded sentence. We introduce \textbf{J-CoT}, a recurrent reasoning framework built on \emph{J-space}, a vocabulary-indexed coordinate system within the model's hidden representations. Within each cycle, the model computes in its full hidden space. At the cycle boundary, J-CoT expresses the intermediate state as vocabulary-indexed coefficients, carries these coefficients forward as a \emph{J-thought}, and maps them back into the model's hidden representation for the next cycle. J-CoT therefore requires neither a fluent intermediate rationale nor recurrence over the complete hidden state. Under matched backbone and inference settings, J-CoT-Zero matches or exceeds the strongest evaluated latent-reasoning baseline on every benchmark, while J-CoT-Train obtains the highest score across the evaluated mathematical, scientific, coding, and structured path-reasoning tasks.

Junde Wu, Jiayuan Zhu, Fengling Liu +2

University of Oxford · Stanford University

LLM Reasoning Latent Reasoning

Jul 24, 2026cs.AI

Semiotic logical hexagon theory for LLM logical reasoning

Large language models (LLMs) have become powerful tools for language understanding and logical reasoning. However, they still make mistakes when a problem requires both understanding meaning and following logic. A key reason is that natural-language statements often carry implicit semantic relations before any formal reasoning begins. If these hidden meanings are not properly organized, the model may reach incorrect conclusions even when the subsequent reasoning process appears logically valid. Existing methods improve reasoning through decomposition, symbolic translation, external solvers, or self-verification, but pay comparatively less attention to the semantic structure on which reasoning depends. In this paper, we further investigate how semantic organization influences logical reasoning in LLMs. To this end, we propose HexLogicAgent, a framework that first organizes the meaning of natural-language statements and then guides logical reasoning through structured verification. In our investigation, we also make two observations. First, incomplete semantic representations, rather than deductive inference itself, are a major source of logical reasoning failures in LLMs. Second, explicitly modeling the complete structure of semantic opposition substantially delays the degradation of reasoning performance as logical complexity increases. Experiments on challenging logical reasoning benchmarks demonstrate that HexLogicAgent consistently improves reasoning reliability across multiple LLMs. The core idea is supported by a logical hexagon theory, which explains why a complete structure of opposing meanings is necessary for reliable reasoning.

Yunyao Zhang, Xinglang Zhang, Zeliang Chen +2

aHuazhong University of Science and Technology, , Wuhan, 430074, Hubei, China

Logical Reasoning LLM Reliability LLM Reasoning

Jul 23, 2026cs.AI

Euclid-MCP: A Model Context Protocol Server for Deterministic Logical Reasoning via Prolog

Large Language Models (LLMs) excel at natural language understanding and generation but remain unreliable for multi-step logical reasoning, especially in safety-critical or compliance-sensitive domains. Recent neuro-symbolic approaches address this gap by coupling neural models with external symbolic engines, yet most integrations are bespoke and lack a standardized interface for tool-augmented agents. This paper presents Euclid-MCP, an open-source MCP server that provides deterministic logical reasoning via SWI-Prolog. Euclid-MCP introduces Euclid-IR, an engine-agnostic intermediate representation for Horn-clause logic that is human-readable, easy for LLMs to generate, and straightforward to compile into Prolog or alternative backends. The server exposes a compact tool interface that supports a translate-run-inspect-repair loop, enabling LLM clients to delegate inference while retaining full access to proof traces and derivation logs. We evaluate Euclid-MCP on a realistic IT security and compliance use case. Results show that while LLMs alone are sufficient on small knowledge bases, they hallucinate systematically on larger problems, whereas Euclid-MCP delivers exact answers with lower latency and more compact outputs. We argue that semantic RAG is fundamentally unsuited for rule enforcement, and that Euclid-MCP can serve as a stable, shared reasoning substrate for both RAG-based assistants and agentic systems.

Bartolomeo Bogliolo

Logic Programming LLM Reliability Model Context Protocol Neuro-Symbolic Reasoning LLM Reasoning

Jul 23, 2026cs.AI

AdaKP: Online Adaptive Knowledge-Point Selection for Reasoning-Oriented Reinforcement Learning

Reinforcement learning with verifiable rewards is a powerful paradigm for eliciting reasoning in large language models, yet it suffers from severe reward sparsity on competition-level mathematics. A common remedy injects atomic knowledge points (KPs) - short natural-language hints distilled from gold solutions - into the prompt. Existing methods, however, either fix this selection once offline or merely scale the monolithic quantity of injected text, leaving untouched the most informative axis of choice: which subset of atomic KPs to inject, and when. We introduce AdaKP, an online selector that re-chooses each problem's KP subset over the course of RL training. At its core is an entropy proxy that scores a KP by the reduction in next-token entropy it induces - a single inexpensive forward pass, with a provable bound on its truncation bias - in place of expensive rollout-based estimation. Three lightweight mechanisms make this signal usable online: a momentum smoother that absorbs per-step noise, a retirement-and-revival manager that prunes weak KPs while preserving exploration, and an adaptive scheduler that front-loads re-evaluations into early training. AdaKP further contributes a pre-flight validation gate that certifies the proxy against a leave-one-out ground truth before any expensive run is launched, turning method-level risk into a falsifiable check. Realized as a fully additive fork of a standard DAPO+GRPO trainer with no optimizer changes, AdaKP improves over a strong static-selection baseline on all eight competition-mathematics benchmarks at negligible added cost, positioning online, validated KP-subset selection as a practical and as-yet under-explored axis for reasoning-oriented reinforcement learning.

Zibin Meng, Zhenyu Zhao, Chunqiang Run

The Hong Kong University of Science and Technology · University of the Chinese Academy of Sciences

Knowledge Augmentation for Language Models RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards Adaptive Learning LLM Reasoning

Jul 22, 2026cs.CL

Notes to Self: Can LLMs Benefit from Experiential Abstractions?

Humans distill experience into reusable abstractions, e.g., strategies and cautionary reminders, and apply them to gradually solve problems more effectively. We study whether Large Language Models (LLMs) can similarly benefit from such experiential abstractions. From LLMs' solution traces on the MATH training set, a stronger teacher or the LLMs themselves extract natural-language abstractions into a retrievable library. We explore two usage modes: (1) inference-time retrieval and (2) reinforcement learning (RL) with abstraction-augmented training prompts. Experiential abstractions improve LLM performance on mathematical and logical reasoning benchmarks. Self-extracted abstractions match teacher-extracted ones, and our abstraction usage framework can transfer to other datasets and models. These findings suggest LLMs can extract and apply experiential abstractions much as humans leverage distilled experience.

Chang Liu, Xinyu Li, Artur Dubrawski

Auton Lab, Carnegie Mellon University

Knowledge Augmentation for Language Models LLM Reasoning