LLM Reasoning

LLM: Large Language Model

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Overview

This field asks how language models can carry out multi-step inference across mathematics, coding, logic, science, and real-world tasks, and how to tell robust reasoning from pattern matching. Common approaches include chain-of-thought prompting, self-consistency and tree search at inference time, tool use and symbolic verification, and post-training with supervised traces, reinforcement learning from verifiable rewards, or process feedback. Researchers are also exploring latent and recurrent computation to reduce reliance on long written traces, alongside benchmarks that test compositionality, robustness, and long-horizon execution. A central tension is that more computation can improve accuracy but raise cost, while plausible explanations and correct final answers do not by themselves establish faithful, reliable reasoning.

Latest papers

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931 papers105 papers in the last four weeks, up 27% on the four weeks before. 0.6% of all new papers.

Apr 24, 2026

Thinking Without Words: Efficient Latent Reasoning with Abstract Chain-of-Thought

While long, explicit chains-of-thought (CoT) have proven effective on complex reasoning tasks, they are costly to generate during inference. Non-verbal reasoning methods have emerged with shorter generation lengths by leveraging continuous representations, yet their performance lags behind verbalized CoT. We propose Abstract Chain-of-Thought\textbf{Abstract Chain-of-Thought}, a discrete latent reasoning post-training mechanism in which the language model produces a short sequence of tokens from a reserved vocabulary in lieu of a natural language CoT, before generating a response. To make previously unseen ''abstract'' tokens useful, we introduce a policy iteration-style warm-up loop that alternates between (i.) bottlenecking from a verbal CoT via masking and performing supervised fine-tuning, and (ii.) self-distillation by training the model to generate abstract tokens from the prompt alone via constrained decoding with the codebook. After warm-up, we optimize the generation of abstract sequences with warm-started reinforcement learning under constrained decoding. Abstract-CoT achieves up to 11.6×11.6\times fewer reasoning tokens while demonstrating comparable performance across mathematical reasoning, instruction-following, and multi-hop reasoning, and generalizes across language model families. We also find an emergent power law distribution over the abstract vocabulary, akin to those seen in natural language, that evolves across the training phases. Our findings highlight the potential for post-training latent reasoning mechanisms that enable efficient inference through a learned abstract reasoning language.

Keshav Ramji, Tahira Naseem, Ramón Fernandez Astudillo

IBM Research AI

Efficient Language Model ReasoningImplicit Reasoning in Language ModelsEfficient Language Model InferenceLanguage Model Post-TrainingLLM ReasoningLatent Reasoning+1
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Apr 24, 2026

Large Language Models Decide Early and Explain Later

Large Language Models often achieve strong performance by generating long intermediate chain-of-thought reasoning. However, it remains unclear when a model's final answer is actually determined during generation. If the answer is already fixed at an intermediate stage, subsequent reasoning tokens may constitute post-decision explanation, increasing inference cost and latency without improving correctness. We study the evolution of predicted answers over reasoning steps using forced answer completion, which elicits the model's intermediate predictions at partial reasoning prefixes. Focusing on Qwen3-4B and averaging results across all datasets considered, we find that predicted answers change in only 32% of queries. Moreover, once the final answer switch occurs, the model generates an average of 760 additional reasoning tokens per query, accounting for a substantial fraction of the total reasoning budget. Motivated by these findings, we investigate early stopping strategies that halt generation once the answer has stabilized. We show that simple heuristics, including probe-based stopping, can reduce reasoning token usage by 500 tokens per query while incurring only a 2% drop in accuracy. Together, our results indicate that a large portion of chain-of-thought generation is redundant and can be reduced with minimal impact on performance.

Ayan Datta, Zhixue Zhao, Bhuvanesh Verma +3

IIIT Hyderabad · University of Sheffield, UK · Goethe University, Frankfurt am Main, Germany

Efficient Language Model ReasoningLLM Inference AccelerationEarly Stopping for Language Model ReasoningLLM ReasoningReasoning Trace Analysis
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Apr 24, 2026

Calibration Drift Under Reasoning: How Chain-of-Thought Budgets Induce Overconfidence in Large Language Models

The ability of large language models (LLMs) to express calibrated uncertainty is important for safe deployment. Chain-of-thought (CoT) reasoning is widely used to improve accuracy and reliability, but its effect on calibration is not fully understood. We show that this picture is incomplete: in some settings, increasing the reasoning budget beyond a task-specific threshold can cause models to become systematically overconfident, assigning high confidence to incorrect answers. We call this phenomenon Calibration Drift Under Reasoning (CDUR) and study it both theoretically and empirically. We define reasoning budget B and analyze conditions under which Expected Calibration Error ECE(B) follows a non-monotonic pattern: it first decreases as reasoning corrects errors, then increases as longer reasoning produces internally consistent but incorrect explanations. We propose a Hypothesis Lock-In model based on autoregressive generation to explain this behavior. We evaluate Llama-3.1-8B and Llama-3.3-70B on 47 reasoning-trap questions across four reasoning budgets and three seeds (1,368 API calls; 574 valid responses). The 8B model shows non-monotonic calibration behavior, while results for the 70B model are limited to baseline evaluation and are inconclusive for budget-dependent effects. We introduce CABStop, a calibration-aware stopping rule that halts reasoning when confidence diverges from an auxiliary accuracy estimate. These results suggest that increasing reasoning depth does not always improve reliability and should be monitored carefully.

Prakul Sunil Hiremath, Harshit R. Hiremath

Department of Computer Science and Engineering Visvesvaraya Technological University, Belagavi · Department of Computer Science and Business System SG Balekundri Institute of Technology, Belagavi

Confidence Estimation in Language ModelsCoT ReasoningLanguage Model CalibrationLLM ReliabilityLLM Uncertainty EstimationLLM Reasoning
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Apr 23, 2026

Thinking with Reasoning Skills: Fewer Tokens, More Accuracy

Reasoning LLMs often spend substantial tokens on long intermediate reasoning traces (e.g., chain-of-thought) when solving new problems. We propose to summarize and store reusable reasoning skills distilled from extensive deliberation and trial-and-error exploration, and to retrieve these skills at inference time to guide future reasoning. Unlike the prevailing reasoning from scratch paradigm, our approach first recalls relevant skills for each query, helping the model avoid redundant detours and focus on effective solution paths. We evaluate our method on coding and mathematical reasoning tasks, and find that it significantly reduces reasoning tokens while improving overall performance. The resulting lower per-request cost indicates strong practical and economic potential for real-world deployment.

Guangxiang Zhao, Qilong Shi, Xusen Xiao +3

Qiyuan Tech · Tsinghua University · The University of Hong Kong +1

Efficient Language Model ReasoningEfficient Language Model InferenceLLM Mathematical ReasoningLLM Reasoning
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Apr 23, 2026

To See the Unseen: on the Generalization Ability of Transformers in Symbolic Reasoning

We investigate the ability of decoder-only transformer models to perform abstract symbolic reasoning; specifically solving propositional logic reasoning problems given in-context. Previous work demonstrated that models fail to generalize to problems involving variable names that were not observed during training, and it was shown that one reason behind this is the difficulty of copying (or generating) unseen tokens. We show both theoretically and empirically that a particular representational collapse also has a crucial role: the unembeddings (last-layer weights) of unseen tokens collapse to nearly the same vector during training. The collapse makes distinguishing multiple unseen variables difficult for the model (especially when the embedding and unembedding parameters are shared), and provides a mechanistic explanation for the effectiveness of existing heuristic interventions like "active forgetting", which periodically reset the token (un)embeddings. Based on these observations, we devise a combination of techniques, involving a small architecture change facilitating copying, data diversity, and freezing or resetting (un)embeddings, that achieves generalization to unseen tokens. We support our claims with extensive controlled experiments on propositional logic reasoning problems. Beyond synthetic experiments, we also observe evidence of (un)embedding collapse in the open-weight models in the Gemma 3 family, which includes 99 unused tokens reserved for downstream use. Empirically we find that the correlated embeddings of these tokens are a poor initialization for finetuning applications.

Nevena Lazić, Liam Fowl, András György +1

Logical ReasoningDecoder-Only Language ModelsSymbolic ReasoningCompositional GeneralizationLLM Reasoning
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Apr 23, 2026

Process Supervision via Verbal Critique Improves Reasoning in Large Language Models

Inference-time scaling for LLM reasoning has focused on three axes: chain depth, sample breadth, and learned step-scorers (PRMs). We introduce a fourth axis, granularity of external verbal supervision, via Verbal Process Supervision (VPS), a training-free framework that uses structured natural-language critique from a stronger supervisor to guide an iterative generate-critique-refine loop up to a round budget R. Across GPQA Diamond, AIME 2025, and LiveCodeBench V6 (covering both closed and open models), VPS yields three key results. First, on GPQA Diamond, GPT-5.4 (High) | GPT-5.4 (Low) reaches 94.9% at R=4, surpassing the 94.1% state of the art without gradient updates. Second, on AIME 2025, VPS enables strong weak-actor rescue, boosting scores from 11.7-26.7% to 63.3-90.0% (up to +63.3 points). Third, at matched compute, VPS outperforms Reflexion by +8.5 to +12.1 points and Self-Consistency@5 by +5.0 pp (GPQA) and +8.3 pp (LiveCodeBench), isolating critique granularity as the key driver. Performance scales with the supervisor-actor capability gap (Pearson r=0.90) and degrades when errors are not linguistically expressible (e.g., code synthesis), motivating hybrid verbal-executable methods. These results establish critique granularity as a new axis of inference-time scaling.

Hao-Yuan Chen

Mindify AI Research · University of London · Senate House, Malet Street, London WC1E 7HU, United Kingdom

Inference-Time ScalingProcess SupervisionLLM Reasoning
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Apr 23, 2026

CoFEE: Reasoning Control for LLM-Based Feature Discovery

Feature discovery from complex unstructured data is fundamentally a reasoning problem: it requires identifying abstractions that are predictive of a target outcome while avoiding leakage, proxies, and post-outcome signals. With the introduction of ever-improving Large Language Models (LLMs), our method provides a structured method for addressing this challenge. LLMs are well suited for this task by being able to process large amounts of information, but unconstrained feature generation can lead to weak features. In this work, we study reasoning control in LLMs by inducing cognitive behaviors for improving feature discovery. We introduce CoFEE (Cognitive Feature Engineering Engine), a reasoning control framework that enforces cognitive behaviors in how the LLM reasons during feature discovery. From a machine learning perspective, these cognitive behaviors act as structured inductive biases over the space of candidate features generated by the model. These behaviors have been exploited with success in ML models, and include backward chaining from outcomes, subgoal decomposition, verification against observability and leakage criteria, and explicit backtracking of rejected reasoning paths. In a controlled comparison, we show that enforcing cognitive behaviors yields features with higher empirical predictability than those under unconstrained vanilla LLM prompts. CoFEE achieves an average Success Rate Score that is 15.2% higher than the vanilla approach, while generating 29% fewer features and reducing costs by 53.3%. Using held-out feature evaluation, we assess whether cognitively induced features generalize beyond the data used for discovery. Our results indicate that, in our evaluated setting, reasoning control is associated with improvements in quality and efficiency of LLM-based feature discovery.

Maximilian Westermann, Ben Griffin, Aaron Ontoyin Yin +6

University of Oxford · Vela Research · Amazon

LLM PromptingAutomated Feature EngineeringLLM ReasoningLarge Language Model-Based Feature Engineering
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Apr 23, 2026

Reasoning Primitives in Hybrid and Non-Hybrid LLMs: Do Architectural Differences Yield Advantages in State-Tracking and Recall?

Reasoning in large language models is often discussed as a single capability, but some of its gains may stem from simpler underlying operations. We examine two such primitives, recall and state-tracking, through five controlled task families centered on state-based recall, and compare matched transformer and hybrid architectures with and without reasoning augmentation. Across the suite, reasoning-augmented variants substantially outperform instruction-only variants, often by large margins. This pattern is consistent with the State over Tokens view: externalized reasoning traces help because they carry the intermediate state forward in token space. By contrast, hybrid inductive bias does not yield a uniform advantage in accuracy once reasoning tokens are available. When architectural differences do appear, they follow task structure: the hybrid Think model is more robust on strictly sequential chained updates, whereas the transformer Think model is more robust on flat multi-hop retrieval. We therefore cast the main contribution of this study as a descriptive account of what drives performance on state-based recall tasks: reasoning-token augmentation appears to be the dominant factor, while hybrid advantages are narrower, task-dependent, and potentially more about inference efficiency than overall capability. We also release the codebase and data required to reproduce these results.

Shivam Rawat, Lucie Flek, Florian Mai +1

Lamarr Institute for Machine Learning and Artificial Intelligence · Rheinische Friedrich-Wilhelms-Universität Bonn

CoT ReasoningLLM MemoryLanguage ModelingLLM ReasoningHybrid Language Models
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Apr 23, 2026

On Reasoning Behind Next Occupation Recommendation

In this work, we develop a novel reasoning approach to enhance the performance of large language models (LLMs) in future occupation prediction. In this approach, a reason generator first derives a ``reason'' for a user using his/her past education and career history. The reason summarizes the user's preference and is used as the input of an occupation predictor to recommend the user's next occupation. This two-step occupation prediction approach is, however, non-trivial as LLMs are not aligned with career paths or the unobserved reasons behind each occupation decision. We therefore propose to fine-tune LLMs improving their reasoning and occupation prediction performance. We first derive high-quality oracle reasons, as measured by factuality, coherence and utility criteria, using a LLM-as-a-Judge. These oracle reasons are then used to fine-tune small LLMs to perform reason generation and next occupation prediction. Our extensive experiments show that: (a) our approach effectively enhances LLM's accuracy in next occupation prediction making them comparable to fully supervised methods and outperforming unsupervised methods; (b) a single LLM fine-tuned to perform reason generation and occupation prediction outperforms two LLMs fine-tuned to perform the tasks separately; and (c) the next occupation prediction accuracy depends on the quality of generated reasons. Our code is available at https://github.com/Sarasarahhhhh/job_prediction.

Shan Dong, Palakorn Achananuparp, Hieu Hien Mai +3

Singapore Management University · Columbia University

Large Language Model-Based RecommendationLanguage Model Post-TrainingLLM Reasoning
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Apr 22, 2026

TRACES: Tagging Reasoning Steps for Adaptive Cost-Efficient Early-Stopping

The field of Language Reasoning Models (LRMs) has been very active over the past few years with advances in training and inference techniques enabling LRMs to reason longer, and more accurately. However, a growing body of studies show that LRMs are still inefficient, over-generating verification and reflection steps. Additionally, the high-level role of each reasoning step and how different step types contribute to the generation of correct answers, is largely underexplored. To address this challenge, we introduce TRACES (Tagging of the Reasoning steps enabling Adaptive Cost-Efficient early-Stopping), a lightweight framework that tags reasoning steps in real-time, and enable adaptive, cost-efficient early stopping of large-language-model inferences. Building on this framework we monitor reasoning behaviors during inferences, and we find that LRMs tend to shift their reasoning behavior after reaching a correct answer. We demonstrate that the monitoring of the specific type of steps can produce effective interpretable early stopping criteria. We evaluate the TRACES framework on three mathematical reasoning benchmarks, namely, MATH500, GSM8K, AIME and two knowledge and reasoning benchmarks, MMLU and GPQA respectively. We achieve 20 to 50% token reduction while maintaining comparable accuracy to standard generation.

Yannis Belkhiter, Seshu Tirupathi, Giulio Zizzo +1

IBM Research Europe · Trinity College Dublin · Dublin, Ireland +1

Reasoning Trace AnalysisEarly StoppingEfficient Language Model ReasoningLLM Inference EfficiencyEfficient Language Model InferenceLLM Reasoning+2
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Apr 22, 2026

Where Reasoning Breaks: Logic-Aware Path Selection by Controlling Logical Connectives in LLMs Reasoning Chains

While LLMs demonstrate impressive reasoning capabilities, they remain fragile in multi-step logical deduction, where a single transition error can propagate through the entire reasoning chain, leading to unstable performance. In this work, we identify logical connectives as primary points of this structural fragility. Through empirical analysis, we show that connective tokens function as high entropy forking points, at which models frequently struggle to determine the correct logical direction. Motivated by this observation, we hypothesize that intervening in logical connective selection can guide LLMs toward more correct logical direction, thereby improving the overall reasoning chain. To validate this hypothesis, we propose a multi-layered framework that intervenes specifically at these logic-critical junctions in the reasoning process. Our framework includes (1) Gradient-based Logical Steering to guide LLMs internal representations towards valid reasoning subspaces, (2) Localized Branching to resolve ambiguity via targeted look-ahead search, and (3) Targeted Transition Preference Optimization, a surgical reinforcement learning objective that selectively optimizes single-token preferences at logical pivots. Crucially, by concentrating intervention solely on logic-critical transitions, our framework achieves a favorable accuracy--efficiency trade-off compared to global inference time scaling methods like beam search and self-consistency.

Seunghyun Park, Yuanyuan Lei

Independent Researcher · University of Florida Gainesville, FL, United States

Inference-Time SearchRL for Language Model ReasoningCausal Interventions in Language ModelsLLM Reasoning
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Apr 22, 2026

LLM StructCore: Schema-Guided Reasoning Condensation and Deterministic Compilation

Automatically filling Case Report Forms (CRFs) from clinical notes is challenging due to noisy language, strict output contracts, and the high cost of false positives. We describe our CL4Health 2026 submission for Dyspnea CRF filling (134 items) using a contract-driven two-stage design grounded in Schema-Guided Reasoning (SGR). The key task property is extreme sparsity: the majority of fields are unknown, and official scoring penalizes both empty values and unsupported predictions. We shift from a single-step "LLM predicts 134 fields" approach to a decomposition where (i) Stage 1 produces a stable SGR-style JSON summary with exactly 9 domain keys, and (ii) Stage 2 is a fully deterministic, 0-LLM compiler that parses the Stage 1 summary, canonicalizes item names, normalizes predictions to the official controlled vocabulary, applies evidence-gated false-positive filters, and expands the output into the required 134-item format. On the dev80 split, the best teacher configuration achieves macro-F1 0.6543 (EN) and 0.6905 (IT); on the hidden test200, the submitted English variant scores 0.63 on Codabench. The pipeline is language-agnostic: Italian results match or exceed English with no language-specific engineering.

Serhii Zabolotnii

Cherkasy State Business College2026 Cherkasy, Ukraine

HealthcareClinical Information ExtractionMedical LLMsLLM Reasoning
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Apr 22, 2026

Early-Stage Product Line Validation Using LLMs: A Study on Semi-Formal Blueprint Analysis

We study whether Large Language Models (LLMs) can perform feature model analysis operations (AOs) directly on semi-formal textual blueprints, i.e., concise constrained-language descriptions of feature hierarchies and constraints, enabling early validation in Software Product Line scoping. Using 12 state-of-the-art LLMs and 16 standard AOs, we compare their outputs against the solver-based oracle FLAMA. Results show that reasoning-optimized models (e.g., Grok 4 Fast Reasoning, Gemini 2.5 Pro) achieve 88-89% average accuracy across all evaluated blueprints and operations, approaching solver correctness. We identify systematic errors in structural parsing and constraint reasoning, and highlight accuracy-cost trade-offs that inform model selection. These findings position LLMs as lightweight assistants for early variability validation.

Viet-Man Le, Thi Ngoc Trang Tran, Sebastian Lubos +2

Graz University of Technology Graz, Austria

Software EngineeringLLM EvaluationLLM Reasoning
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Apr 22, 2026

Self-Awareness before Action: Mitigating Logical Inertia via Proactive Cognitive Awareness

Large language models perform well on many reasoning tasks, yet they often lack awareness of whether their current knowledge or reasoning state is complete. In non-interactive puzzle settings, the narrative is fixed and the underlying structure is hidden; once a model forms an early hypothesis under incomplete premises, it can propagate that error throughout the reasoning process, leading to unstable conclusions. To address this issue, we propose SABA, a reasoning framework that explicitly introduces self-awareness of missing premises before making the final decision. SABA formulates reasoning as a recursive process that alternates between structured state construction and obstacle resolution: it first applies Information Fusion to consolidate the narrative into a verifiable base state, and then uses Query-driven Structured Reasoning to identify and resolve missing or underspecified premises by turning them into queries and progressively completing the reasoning state through hypothesis construction and state refinement. Across multiple evaluation metrics, SABA achieves the best performance on all three difficulty splits of the non-interactive Detective Puzzle benchmark, and it also maintains leading results on multiple public benchmarks.

Fulong Fan, Peilin Liu, Fengzhe Liu +2

School of Software, Jilin University · School of Computer Science, Jilin University

Abductive ReasoningStructured ReasoningLLM Reasoning
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Apr 22, 2026

HiPO: Hierarchical Preference Optimization for Adaptive Reasoning in LLMs

Direct Preference Optimization (DPO) is an effective framework for aligning large language models with human preferences, but it struggles with complex reasoning tasks. DPO optimizes for the likelihood of generating preferred over dispreferred responses in their entirety and lacks the granularity to provide feedback on subsections of many-step solutions typical of reasoning tasks. Existing methods excel at either stable preference learning (e.g., DPO variants like KTO and RSO) or structured reasoning (e.g., ReMA's multi-agent RL framework, Tree of Thoughts), but fail to merge these complementary strengths. We propose HiPO (Hierarchical Preference Optimization), an extension of DPO that separates responses into reasoning segments (query clarification and context, reasoning steps, and answer) and computes loss as a weighted sum of the DPO loss for each segment. Our approach enables segment-specific training while maintaining DPO's computational efficiency and training stability. We demonstrate that for multiple 7B LLMs fine-tuned using HiPO and DPO on the Math Stack Exchange preference dataset, the models trained with HiPO outperform the others on a variety of common math benchmarks and achieve greater organization, logical flow, and consistency as measured by GPT-4.1.

Darsh Kachroo, Arjun Prasaath Anbazhagan, Adriana Caraeni +2

Vellore Institute of Technology, Chennai · Northwestern University · University of Massachusetts Amherst +2

LLM AlignmentDirect Preference OptimizationMathematical ReasoningPreference OptimizationLLM Reasoning
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Apr 22, 2026

Differentiable Conformal Training for LLM Reasoning Factuality

Large Language Models (LLMs) frequently hallucinate, limiting their reliability in critical applications. Conformal Prediction (CP) addresses this by calibrating error rates on held-out data to provide statistically valid confidence guarantees. Recent work extends CP to LLM factuality to filter out risky claims, ensuring that hallucination rates remain below a user-specified level (e.g., 10%). While prior methods treat claims independently, Coherent Factuality extends to multi-step reasoning by representing outputs as dependency graphs and jointly validating claims with their logical ancestors. A key limitation is that Coherent Factuality is not differentiable, requiring hand-crafted scorers that at high reliability levels remove nearly 60% of true claims. We introduce Differentiable Coherent Factuality (DCF), a fully differentiable relaxation that enables learning improved scorers while provably recovering the original algorithm's guarantees. Experiments on two benchmark reasoning datasets demonstrate DCF achieves up to 141% improvement in claim retention while maintaining reliability guarantees, representing a significant step towards reliable conformal LLM systems.

Nathan Hittesdorf, Marco Salzetta, Lu Cheng

Department of Computer Science, University of Illinois at Chicago, Chicago, United States · Department of Physics, University of Illinois at Urbana-Champaign, Urbana, United States

LLM Hallucination MitigationConformal PredictionConformal Prediction for Language ModelsLLM ReliabilityLLM Reasoning
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Apr 21, 2026

Separable Pathways for Causal Reasoning: How Architectural Scaffolding Enables Hypothesis-Space Restructuring in LLM Agents

Causal discovery through experimentation and intervention is fundamental to robust problem solving. It requires not just updating beliefs within a fixed framework but revising the hypothesis space itself, a capacity current AI agents lack when evidence demands representations they have not previously constructed. We extend the blicket detector paradigm from developmental science to test this capacity in AI agents equipped with architectural scaffolding that targets hypothesis-space restructuring. Our compositional architecture has two discrete components: context graphs, which structure exploration as typed state machines, and dynamic behaviors, which monitor for evidence that the current hypothesis space is inadequate and expand it at runtime. Across 1,085 experimental trials, these components make orthogonal contributions: context graphs drive reasoning quality within the post-switch hypothesis space, accounting for 94% of the accuracy gain, while dynamic behaviors drive reasoning eligibility by detecting regime changes and preventing premature commitment to outdated hypotheses.

John Alderete, Sebastian Benthal, Connie Xu +1

Amigo AI · Simon Fraser University · International Computer Science Institute

Causal DiscoveryLLM AgentsCausal Interventions in Language ModelsLLM Reasoning
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Apr 21, 2026

Discovering a Shared Logical Subspace: Steering LLM Logical Reasoning via Alignment of Natural-Language and Symbolic Views

Large Language Models (LLMs) still struggle with multi-step logical reasoning. Existing approaches either purely refine the reasoning chain in natural language form or attach a symbolic solver as an external module. In this work, we instead ask whether LLMs contain a shared internal logical subspace that simultaneously aligns natural-language and symbolic-language views of the reasoning process. Our hypothesis is that this logical subspace captures logical reasoning capabilities in LLMs that are shared across views while remaining independent of surface forms. To verify this, we employ Canonical Correlation Analysis on the paired residual activations from natural-language and symbolic-language reasoning chains, learning a low-dimensional subspace with maximum cross-view correlation. Furthermore, we design a training-free approach that steers LLMs reasoning chain along this logical subspace, thereby leveraging the complementary reasoning signals from both views. Experiments on four logical reasoning benchmarks demonstrate the effectiveness of our approach, improving accuracy by up to 11 percentage points and generalizing well on out-of-domain problems.

Feihao Fang, My T. Thai, Yuanyuan Lei

University of Illinois Urbana-Champaign, Champaign, IL · Computer & Information Science and Engineering, University of Florida, Gainesville, FL

Symbolic ReasoningNeuro-Symbolic ReasoningActivation SteeringLLM Reasoning
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Apr 21, 2026

CoDA: Towards Effective Cross-domain Knowledge Transfer via CoT-guided Domain Adaptation

Large language models (LLMs) have achieved substantial advances in logical reasoning, yet they continue to lag behind human-level performance. In-context learning provides a viable solution that boosts the model's performance via prompting its input with expert-curated, in-domain exemplars. However, in many real-world, expertise-scarce domains, such as low-resource scientific disciplines, emerging biomedical subfields, or niche legal jurisdictions, such high-quality in-domain demonstrations are inherently limited or entirely unavailable, thereby constraining the general applicability of these approaches. To mitigate this limitation, recent efforts have explored the retrieval of cross-domain samples as surrogate in-context demonstrations. Nevertheless, the resulting gains remain modest. This is largely attributable to the pronounced domain shift between source and target distributions, which impedes the model's ability to effectively identify and exploit underlying shared structures or latent reasoning patterns. Consequently, when relying solely on raw textual prompting, LLMs struggle to abstract and transfer such cross-domain knowledge in a robust and systematic manner. To address these issues, we propose CoDA, which employs a lightweight adapter to directly intervene in the intermediate hidden states. By combining feature-based distillation of CoT-enriched reference representations with Maximum Mean Discrepancy (MMD) for kernelized distribution matching, our method aligns the latent reasoning representation of the source and target domains. Extensive experimental results on multiple logical reasoning tasks across various model families validate the efficacy of CoDA by significantly outperforming the previous state-of-the-art baselines by a large margin.

Jianzhi Yan, Le Liu, Buzhou Tang +3

Harbin Institute of Technology, Shenzhen, 518100, China · Pengcheng Laboratory, Shenzhen, 518100, China

Domain AdaptationCross-Domain Transfer LearningDomain Adaptation for LLMsLLM Reasoning
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Apr 21, 2026

Do LLMs Game Formalization? Evaluating Faithfulness in Logical Reasoning

Formal verification guarantees proof validity but not formalization faithfulness. For natural-language logical reasoning, where models construct axiom systems from scratch without library constraints, this gap between valid proofs and faithful translations is especially acute. We investigate whether frontier models exploit this gap when generating Lean 4 proofs, a behavior we term formalization gaming. We evaluate GPT-5 and DeepSeek-R1 on 303 first-order logic problems (203 from FOLIO, 100 from Multi-LogiEval), comparing unified generation against a two-stage pipeline that separates formalization from proving. Despite compilation rates of 87-99%, we find no evidence of systematic gaming in unified generation: models prefer reporting failure over forcing proofs, even under prompting designed to encourage it. However, unfaithfulness that evades our detection signals may still occur. The two-stage pipeline reveals two distinct modes of unfaithfulness: GPT-5 fabricates axioms during proof generation, a reactive fallback detectable via cross-stage comparison, while DeepSeek-R1 mistranslates premises during formalization, producing internally consistent outputs that evade detection entirely. These findings show that high compilation rates or accuracies should not be equated with faithful reasoning. Code and data are available at https://github.com/koreankiwi99/formalization-gaming.

Kyuhee Kim, Auguste Poiroux, Antoine Bosselut

EPFL

Formal VerificationLean Theorem ProvingAutoformalizationLLM Reasoning
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Apr 21, 2026

How Do Answer Tokens Read Reasoning Traces? Self-Reading Patterns in Thinking LLMs for Quantitative Reasoning

Thinking LLMs produce reasoning traces before answering. Prior activation steering work mainly targets on shaping these traces. It remains less understood how answer tokens actually read and integrate the reasoning to produce reliable outcomes. Focusing on quantitative reasoning, we analyze the answer-to-reasoning attention and observe a benign self-reading pattern aligned with correctness, characterized by a forward drift of the reading focus along the reasoning trace and a persistent concentration on key semantic anchors, whereas incorrect solutions exhibit diffuse and irregular attention pattern. We interpret this as internal certainty during answer decoding, where the model commits to a viable solution branch and integrates key evidence. Following this, we propose a training-free steering method driven by Self-Reading Quality (SRQ) scores combining geometric metrics for process control with semantic metrics for content monitoring. SRQ selects data to build steering vectors that guide inference toward benign self-reading and away from uncertain and disorganized reading. Experiments show that our method yields consistent accuracy gains.

Haoyang Chen, Yi Liu, Jianzhi Shao +3

State Key Laboratory for Novel Software Technology, Nanjing University, China · Alibaba Group, China · Ant Group, China

LLM InterpretabilityMathematical ReasoningActivation SteeringLLM ReasoningReasoning Trace Analysis
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Apr 21, 2026

How Much Thinking is Enough? Quantifying and Understanding Redundancy in LLM Reasoning

Reasoning-capable large language models solve hard problems by emitting long chains of thought, paying heavily in latency, GPU time, and energy. Casual inspection of their traces reveals extensive reformulation, verification, and circular self-reflection, yet how much of this deliberation is actually necessary has never been measured at scale or explained from first principles. This paper closes both gaps. We formalise reasoning redundancy directly in terms of the reasoning model itself: the redundancy of a correct trace is the largest fraction of its trailing segmented steps that can be truncated while ππ, forced to terminate thinking and emit a final answer, still produces the correct answer. A large-scale quantification across four frontier reasoning models and two mathematical benchmarks shows that step-level redundancy is consistently high -- between 61% and 93% across the 8 (model, benchmark) conditions we study, with the median critical prefix equal to a single segmented step in six of the eight conditions -- that the finding is robust to the choice of judge family, and that although ρρ decreases with problem difficulty on MATH-500, all four models remain substantially redundant (ρ∈[46%,85%]ρ\in [46\%, 85\%]) even on the hardest Level-5 problems. We then prove that this redundancy is a structural consequence of length-agnostic outcome rewards, not a model-specific artefact: under any such reward, no finite expected stopping time is optimal. The result holds regardless of RL algorithm, base model, data distribution, or whether the policy is obtained via RL or distillation; over-thinking is therefore not a bug to be patched in individual models but a structural property of how current reasoning models are trained. Code: https://github.com/zhiyuanZhai20/how-much-thinking-is-enough

Zhiyuan Zhai, Xinkai You, Wenjing Yan +1

Fudan University · The Chinese University of Hong Kong

LLM Inference EfficiencyRL for Language Model ReasoningEfficient Language Model ReasoningLLM Mathematical ReasoningLLM ReasoningLarge Reasoning Models+1
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Apr 20, 2026

AI scientists produce results without reasoning scientifically

Large language model (LLM)-based systems are increasingly deployed to conduct scientific research autonomously, yet whether their reasoning adheres to the epistemic norms that make scientific inquiry self-correcting is poorly understood. Here, we evaluate LLM-based scientific agents across eight domains, spanning workflow execution to hypothesis-driven inquiry, through more than 25,000 agent runs and two complementary lenses: (i) a systematic performance analysis that decomposes the contributions of the base model and the agent scaffold, and (ii) a behavioral analysis of the epistemological structure of agent reasoning. We observe that the base model is the primary determinant of both performance and behavior, accounting for 41.4% of explained variance versus 1.5% for the scaffold. Across all configurations, evidence is ignored in 68% of traces, refutation-driven belief revision occurs in 26%, and convergent multi-test evidence is rare. The same reasoning pattern appears whether the agent executes a computational workflow or conducts hypothesis-driven inquiry. They persist even when agents receive near-complete successful reasoning trajectories as context, and the resulting unreliability compounds across repeated trials in epistemically demanding domains. Thus, current LLM-based agents execute scientific workflows but do not exhibit the epistemic patterns that characterize scientific reasoning. Outcome-based evaluation cannot detect these failures, and scaffold engineering alone cannot repair them. Until reasoning itself becomes a training target, the scientific knowledge produced by such agents cannot be justified by the process that generated it.

Martiño Ríos-García, Nawaf Alampara, Chandan Gupta +5

Laboratory of Organic and Macromolecular Chemistry (IOMC), Friedrich Schiller University Jena, Humboldstr. 10, 07743 Jena, Germany · Department of Civil Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India · School of Interdisciplinary Research, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India +3

AI Agent ReliabilityScientific ReasoningLLM Agent EvaluationLLM ReliabilityAutonomous Scientific DiscoveryScientific Reasoning in Language Models+2
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Apr 20, 2026

Knowing When to Quit: A Principled Framework for Dynamic Abstention in LLM Reasoning

LLMs utilizing chain-of-thought reasoning often waste substantial compute by producing long, incorrect responses. Abstention can mitigate this by withholding outputs unlikely to be correct. While most abstention methods decide to withhold outputs before or after generation, dynamic mid-generation abstention considers early termination of unpromising reasoning traces at each token position. Prior work has explored empirical variants of this idea, but principled guidance for the abstention rule remains lacking. We present a formal analysis of dynamic abstention for LLMs, modeling abstention as an explicit action within a regularized reinforcement learning framework. An abstention reward parameter controls the trade-off between compute and information. We show that abstaining when the value function falls below this reward strictly outperforms natural baselines under general conditions. We further derive a principled and efficient method to approximate the value function. Empirical results on mathematical reasoning and toxicity avoidance tasks support our theory and demonstrate improved selective accuracy over existing methods.

Hen Davidov, Nachshon Cohen, Oren Kalinsky +4

University of Oxford. Work done partly during an internship at amazon. · 2Amazon.

RL for Language Model ReasoningLLM AbstentionLLM Reasoning
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Apr 20, 2026

Reasoning Models Know What's Important, and Encode It in Their Activations

Language models often solve complex tasks by generating long reasoning chains, consisting of many steps with varying importance. While some steps are crucial for generating the final answer, others are removable. Determining which steps matter most, and why, remains an open question central to understanding how models process reasoning. We investigate if this question is best approached through model internals or through tokens of the reasoning chain itself. We find that model activations contain more information than tokens for identifying important reasoning steps. Crucially, by training probes on model activations to predict importance, we show that models encode an internal representation of step importance, even prior to the generation of subsequent steps. The internal representations of importance in different models yield high agreement on which steps are important. The representation is distributed across layers, and does not correlate with surface-level features, such as a step's relative position or its length. Our findings suggest that analyzing activations can reveal aspects of reasoning that surface-level approaches fundamentally miss, indicating that reasoning analyses should look into model internals.

Yaniv Nikankin, Martin Tutek, Tomer Ashuach +2

Technion · University of Zagreb, FER · MIT +1

LLM InterpretabilityLLM ReasoningLarge Reasoning ModelsReasoning Trace Analysis
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Apr 20, 2026

Process Reward Models Meet Planning: Generating Precise and Scalable Datasets for Step-Level Rewards

Process Reward Models (PRMs) have emerged as a powerful tool for providing step-level feedback when evaluating the reasoning of Large Language Models (LLMs), which frequently produce chains of thought (CoTs) containing errors even when the final answer is correct. However, existing PRM datasets remain expensive to construct, prone to annotation errors, and predominantly limited to the mathematical domain. This work introduces a novel and scalable approach to PRM dataset generation based on planning logical problems expressed in the Planning Domain Definition Language (PDDL). Using this method, we generate a corpus of approximately one million reasoning steps across various PDDL domains and use it to train PRMs. Experimental results show that augmenting widely-used PRM training datasets with PDDL-derived data yields substantial improvements in both mathematical and non-mathematical reasoning, as demonstrated across multiple benchmarks. These findings indicate that planning problems constitute a scalable and effective resource for generating robust, precise, and fine-grained training data for PRMs, going beyond the classical mathematical sources that dominate this field.

Raffaele Pisano, Roberto Navigli

Babelscape · Sapienza University of Rome

Process Reward ModelsSynthetic Data GenerationLLM Reasoning
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Apr 20, 2026

SPREG: Structured Plan Repair with Entropy-Guided Test-Time Intervention for Large Language Model Reasoning

Large Language Models (LLMs) are prone to logical hallucinations and stochastic drifts during long-chain reasoning. While Classifier-Free Guidance (CFG) can improve instruction adherence, standard static implementations often cause semantic dilution and linguistic degradation. We propose SPREG (Structured Plan-guided Real-time Entropy Gating), a lightweight inference-time framework for surgical error rectification. SPREG employs an adaptive dual-threshold mechanism to monitor real-time entropy, identifying sudden ``entropy spikes'' as reliable indicators of logical failure. Upon detection, it triggers a dynamic repair by replacing uninformative null-priors with reference distributions synthesized from historical high-confidence states. By modulating guidance intensity according to structured reasoning stages (e.g., Action, Observation), SPREG steers the model back to a stable manifold without compromising fluency. Our experiments demonstrate significant gains, notably a 20.0% absolute accuracy improvement on AIME25, while effectively suppressing uncontrolled entropy drift in complex tasks.

Xuan Wang, Yu Ming, Xinhao Zhong +4

1Meituan

LLM Self-CorrectionClassifier-Free GuidanceInference-Time InterventionLLM Reasoning
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Apr 19, 2026

KnowledgeBerg: Evaluating Systematic Knowledge Coverage and Compositional Reasoning in Large Language Models

Many real-world questions appear deceptively simple yet implicitly demand two capabilities: (i) systematic coverage of a bounded knowledge universe and (ii) compositional set-based reasoning over that universe, a phenomenon we term "the tip of the iceberg." We formalize this challenge through two orthogonal dimensions: knowledge width, the cardinality of the required universe, and reasoning depth, the number of compositional set operations. We introduce KnowledgeBerg, a benchmark of 4,800 multiple-choice questions derived from 1,183 enumeration seeds spanning 10 domains and 17 languages, with universes grounded in authoritative sources to ensure reproducibility. Representative open-source LLMs demonstrate severe limitations, achieving only 5.26-36.88 F1 on universe enumeration and 16.00-44.19 accuracy on knowledge-grounded reasoning. Diagnostic analyses reveal three stages of failure: completeness, or missing knowledge; awareness, or failure to identify requirements; and application, or incorrect reasoning execution. This pattern persists across languages and model scales. Although test-time compute and retrieval augmentation yield measurable gains -- up to 4.35 and 3.78 points, respectively -- substantial gaps remain, exposing limitations in how current LLMs organize structured knowledge and execute compositional reasoning over bounded domains. The dataset is available at https://huggingface.co/datasets/2npc/KnowledgeBerg

Xiao Zhang, Qianru Meng, Yongjian Chen +2

University of Groningen · LIACS, Leiden University

LLM EvaluationCompositional ReasoningStructured ReasoningFactual Knowledge in Language ModelsKnowledge-Intensive QALLM Reasoning
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Apr 19, 2026

Beyond Fine-Tuning: In-Context Learning and Chain-of-Thought for Reasoned Distractor Generation

Distractor generation (DG) remains a labor-intensive task that still significantly depends on domain experts. The task focuses on generating plausible yet incorrect options, known as distractors, for multiple-choice questions. A reliable distractor must be contextually relevant to the question and able to mislead examinees through implicit reasoning when identifying the correct answer. While a recent method integrates fine-tuning pre-trained encoder-decoder models with contrastive learning to generate semantically relevant distractors for a given question-answer, it often fails to capture the underlying reasoning process that experts utilize when selecting distractors in benchmarks. In this paper, we explore large language models (LLMs) reasoning for DG through in-context learning with unsupervised semantic retrieval for selecting few-shot examples. We design a rationale-augmented DG framework that jointly generates distractors and their rationales for a given question-answer. Extensive experiments on six benchmarks, with varying average distractor lengths and domains, demonstrate that prompting LLMs with few-shot examples substantially improves the performance compared to recent DG models. It outperforms recent approaches and achieves state-of-the-art results in generating reasoned distractors that align with human-labeled benchmarks.

Elaf Alhazmi, Quan Z. Sheng, Wei Emma Zhang

School of Computing, Macquarie University, Australia · College of Engineering and Computing in Al-Lith, Umm Al-Qura University, Saudi Arabia · School of Computer and Mathematical Sciences, Adelaide University, Australia

LLM PromptingIn-Context LearningText GenerationLLM Reasoning
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Apr 19, 2026

Self-Consistency from Only Two Samples: CoT-PoT Ensembling for Efficient LLM Reasoning

Self-consistency (SC) is a popular technique for improving the reasoning accuracy of large language models by aggregating multiple sampled outputs, but it comes at a high computational cost due to extensive sampling. We introduce a hybrid ensembling approach that leverages the complementary strengths of two distinct modes of reasoning: Chain-of-Thought (CoT) and Program-of-Thought (PoT). We describe a general framework for combining these two forms of reasoning in self-consistency, as well as particular strategies for both full sampling and early-stopping. We show that CoT-PoT ensembling not only improves overall accuracy, but also drastically reduces the number of samples required for SC by a factor of 9.3x. In particular, the majority of tasks (78.6%) can be addressed with only two samples, which has not been possible with any prior SC methods.

Raman Saparkhan, Majd Hawasly, Md Rizwan Parvez +1

Carnegie Mellon University Qatar · Qatar Computing Research Institute

LLM Inference EfficiencySelf-Consistency DecodingCoT ReasoningEfficient Language Model ReasoningReasoning Consistency in Language ModelsLanguage Model Ensembles+3
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