Reasoning Consistency in Language Models

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Overview

The field studies whether language models preserve conclusions and sound reasoning when prompts are paraphrased, evidence changes, answers are resampled, or conversations continue. Evaluations use controlled reformulations and multi-turn tests, repeated-sample agreement, and checks of reasoning traces with formal solvers, causal interventions, or evidence-grounded verifiers across math, logic, coding, and medical tasks. Methods include self-consistency and uncertainty-based answer selection, consistency-aware training and rewards, and test-time verification, repair, or early-exit systems. A central tension is that consistency can signal stability without correctness or faithful reasoning: models may repeat the same error, abstain, or agree while relying on invalid reasoning, so reliability must be assessed alongside accuracy, faithfulness, and cost.

Latest papers

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123 papers24 papers in the last four weeks, up 60% on the four weeks before. 0.1% of all new papers.

Jun 19, 2026

Coherence Under Commitment: Probing Generalization and Vacuous Memorization in LLM Logical Reasoning

Large language models (LLMs) deployed for logical reasoning in knowledge-intensive domains exhibit a subtle but critical failure: coherence can be vacuously achieved through systematic abstention. A model that withholds commitment to either entailment or refutation satisfies negation consistency while providing no utility. We introduce Coherence Under Commitment (CUC), a dual-query evaluation paradigm that jointly measures consistency and decisiveness. CUC contributes three innovations: (1) a commitment score c(φ)=p(φ)+p(¬φ)c(\varphi) = p(\varphi) + p(\lnot\varphi) quantifying probability mass allocated to decisive outcomes; (2) a deterministic elicitation protocol via normalized YES/NO log probabilities, eliminating sampling variance; and (3) a 3-way decision framework (True/False/Uncertain) operationalizing the coherence-commitment trade-off into metrics. Experiments on four open-weight LLMs (1B-3B) across 204 FOLIO examples expose a sharp frontier. Qwen2.5-3B achieves near-zero contradiction (E[vneg]=0.025\mathbb{E}[v_{\mathrm{neg}}]{=}0.025) but only 7.4%7.4\% coverage, while TinyLlama-1.1B reaches 79.4%79.4\% coverage with violations on every example. Coherence-only evaluation would rank the abstaining model first; CUC exposes this as vacuous, and the frontier generalizes to LogiQA~v2 (ρ=0.97ρ{=}0.97). We argue that evaluation must report both coherence and non-vacuous commitment and release a toolkit for standardized assessment.

Noor Islam S. Mohammad, Mahmudul Hasan

Department of Computer Science, Informatics Institute, Istanbul Technical University, ˙Istanbul, Türkiye · School of Information Technology, Deakin University, Geelong, VIC 3220, Australia

LLM EvaluationReasoning Consistency in Language ModelsLLM AbstentionLLM Reasoning
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Jun 16, 2026

The Consistency Dilemma in LLMs: Generator-Evaluator Agreement and Vulnerability to Mistakes

Large language models are increasingly deployed in agentic pipelines that depend on the model evaluating its own outputs without external verification. The reliability of these pipelines depends on an implicit assumption: that the model applies relevant concepts the same way when it generates an output and later evaluates that output. We propose a new measure, generator-evaluator self-consistency, to test this assumption directly and apply it to 10 frontier models across 491 concepts. We find, first, that there is substantial variation in self-consistency. Second, we find that in a clinical setting with physician-validated mistakes (Proniakin et al., 2025), across models, those with higher self-consistency are linked to greater vulnerability to mistakes. Thus, even when models consistently apply concepts they may not be safe to deploy. This is evidence of a consistency dilemma in LLMs: self-consistency is operationally useful, but models that are more consistent are also more prone to mistakes.

Marina Mancoridis, Zoë Hitzig

Massachusetts Institute of Technology · Harvard Society of Fellows

LLM EvaluationReasoning Consistency in Language ModelsLLM ReliabilityMetacognition in Language ModelsSelf-Consistency in Language Models
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Jun 15, 2026

Quantifying Consistency in LLM Logical Reasoning via Structural Uncertainty

Large language models can arrive at the same answer through reasoning paths that are unstable, contradictory, or difficult to rank consistently -- a failure mode especially prevalent in multi-step deductive reasoning. Existing methods assess reliability primarily through output dispersion -- measuring how much sampled answers differ -- but this discards a complementary signal: whether the model can consistently rank competing reasoning candidates. We propose structural uncertainty, a consistency-aware framework derived from the stability of self-preference-induced rankings over sampled reasoning solutions. Given a query, we generate multiple candidate solutions and ask the model to judge pairwise preferences among its own outputs. We aggregate self-preferences into ranking distributions via Bradley-Terry modeling with PageRank, and decompose the signal into two entropy-based components: across-trial ranking instability and within-trial candidate ambiguity. Across five LLMs and eight benchmarks, structural signals provide information complementary to answer dispersion: on logical and mathematical reasoning tasks, the combination improves identification of unreliable instances, while on factual retrieval the structural signal collapses toward uniformity, diagnosing a regime boundary where reasoning-level consistency evaluation is uninformative. The two components relate differently to accuracy: within-trial ambiguity correlates positively with correctness -- consistent with settings where multiple plausible solution paths remain competitive -- while across-trial instability correlates negatively, signaling unreliable reasoning. Structural uncertainty is best understood not as a universal confidence estimator, but as a regime-sensitive evaluator of logical reasoning consistency.

Baishali Chaudhury, Mengdie Flora Wang, Hyunji Hayley Park +3

AWS Generative AI Innovation Center

Reasoning Consistency in Language ModelsLLM ReliabilityLLM Uncertainty EstimationLLM Mathematical ReasoningUncertainty DecompositionLLM Reasoning
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Jun 11, 2026

Operadic consistency: a label-free signal for compositional reasoning failures in LLMs

Detecting LLM reasoning failures at inference time without ground-truth labels has motivated a wide range of confidence baselines, including self-consistency, semantic entropy, and P(True), built on within-question sampling and self-evaluation. Operad theory, the formalism for systems built by iterated substitution, suggests a complementary diagnostic: a model's direct answer to a compositional query should agree with the answer it produces by composing a stated decomposition of the same query. We instantiate this idea as operadic consistency (OC), a per-question signal. Across twelve instruction-tuned LLMs (4B to 671B parameters, open-weights and closed-source) on four multi-hop QA datasets, OC is strongly correlated with accuracy on every dataset (Pearson r∈[0.86,0.94]r \in [0.86, 0.94], all p≤0.0004p \leq 0.0004), and is the only signal we evaluate with r≥0.85r \geq 0.85 uniformly across all four datasets. Chain-of-thought self-consistency (CoT-SC; Wang et al., 2023) matches OC on HotpotQA and DROP (r=0.93,0.87r = 0.93, 0.87) but drops to r≈0.45r \approx 0.45 on MuSiQue and StrategyQA. At the per-question level, OC contributes information beyond CoT-SC and semantic entropy on every dataset (cluster-robust p≤10−16p \leq 10^{-16} for the OC coefficient), and the conclusion is robust to additionally controlling for constructed decomposition-aware baselines (p≤10−13p \leq 10^{-13}). The same signal yields selective-prediction improvements (accuracy at fixed coverage) over a tuned CoT-SC baseline at the equal-cost K=3K = 3 budget (AUARC lifts of +0.086 to +0.096 and AUROC lifts of +0.092 to +0.164; 95% CIs exclude zero on every cell). On five frontier thinking models, where the decomposition is extracted from the model's own chain of thought, the same equal-cost comparison gives positive selective-prediction point-estimate lift on all 16 (dataset, budget, metric) cells tested, with 95% CIs excluding zero on 12 of the 16.

Nathaniel Bottman, Yinhong Liu, Kyle Richardson

Incubilate · University of Cambridge · Allen Institute for Artificial Intelligence

Compositional ReasoningReasoning Consistency in Language ModelsLLM ReliabilityLLM Uncertainty Estimation
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Jun 10, 2026

Agreement in Representation Space for Open-Ended Self-Consistency

Self-consistency improves LLM reasoning by sampling multiple outputs and selecting the most consistent answer, but existing formulations largely rely on exact matching and therefore remain limited to tasks with categorical outputs. In this work, we study self-consistency in open-ended generation tasks such as code synthesis and text summarization. We hypothesize that consistency can be understood as a geometric property of the generation space, where semantically compatible generations concentrate in similar regions of representation space. To study this hypothesis, we introduce Embedding-Based Agreement (EBA), a simple training-free operationalization that estimates agreement by clustering sampled generations in embedding space. Through experiments on mathematical reasoning, code generation, and summarization, we show that agreement in representation space provides a robust and scalable signal of self-consistency for open-ended tasks. In particular, EBA consistently outperforms random selection and exhibits more stable scaling behavior than recent selection approaches based on LLM evaluation or uncertainty estimation. We further show that these agreement signals remain stable across model families and embedding spaces, even with native hidden representations. Finally, our analysis shows that the geometric location occupied by sampled generations is strongly correlated with generation quality: generations concentrated near central regions of representation space tend to correspond to more reliable outputs, whereas peripheral generations are substantially less accurate. Overall, our findings support viewing self-consistency as a property of the geometric organization of sampled generations rather than exact symbolic overlap.

Paula Ontalvilla, Gorka Azkune, Aitor Ormazabal

HiTZ Center - Ixa, University of the Basque Country (UPV/EHU)

Open-Ended GenerationSelf-Consistency DecodingReasoning Consistency in Language ModelsText GenerationSelf-Consistency in Language ModelsLLM Reasoning
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Jun 3, 2026

Boosting Self-Consistency with Ranking

Self-consistency improves large language models by sampling multiple reasoning paths and selecting the most frequent answer, but majority voting often fails to recover correct answers that are already present among the samples. We address this limitation with Ranking-Improved Self-Consistency (RISC), which reformulates answer selection in self-consistency as a ranking problem. Instead of relying on a single uncertainty or confidence signal, RISC uses a lightweight LambdaRank model to score candidate answers with five carefully designed features that capture answer frequency, semantic centrality, and reasoning-trace consistency. We evaluate RISC on three datasets under a range of test-time budgets. Across datasets, RISC consistently achieves a better accuracy-efficiency trade-off than standard self-consistency and strong baselines, with particularly large gains on question answering benchmarks. Further analysis shows that the proposed features are individually useful and, more importantly, complementary, highlighting the value of learning to combine multiple informative signals for test-time answer selection.

Maria Marina, Daniil Moskovskiy, Sergey Pletenev +3

AIRI · Skoltech · EPFL

Self-Consistency DecodingLLM RerankingReasoning Consistency in Language ModelsSelf-Consistency in Language Models
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May 29, 2026

ConsisGuard: Aligning Safety Deliberation with Policy Enforcement in LLM Guardrails

Reasoning-based LLM guardrails improve safety moderation by generating explicit rationales before issuing final decisions. However, their rationales do not always lead to faithful enforcement: a model may recognize a harmful intent in its reasoning but still predict a safe label, or issue an unsafe decision without policy-grounded justification. We identify this safety-critical failure mode as the deliberation-to-enforcement gap. Unlike general chain-of-thought faithfulness, guardrail reliability requires policy execution consistency: the generated reasoning should be grounded in the safety policy, and the final decision should be entailed by that reasoning. We propose ConsisGuard, a consistency-aware framework for reasoning-based LLM guardrails. ConsisGuard performs Policy-to-Decision Trajectory Distillation and Functional Coupling Alignment, aligning the internal coupling between safety deliberation and decision enforcement. Experiments on prompt and response harmfulness detection benchmarks show that ConsisGuard improves detection performance while reducing policy execution failures. These results suggest that reliable reasoning-based guardrails require accurate faithful execution of safety policies.

Yan Wang, Zhixuan Chu, Zihao Xue +9

Alibaba Group · Zhejiang University · Huzhou Normal University +1

LLM GuardrailsFaithfulness of Language Model ReasoningLLM Safety AlignmentReasoning Consistency in Language Models
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May 28, 2026

Same Evidence, Different Answers: Canonical-Context On-Policy Distillation for Multi-Turn Language Models

Large language models (LLMs) often solve a task when all instructions are given in a single prompt, but fail when the same information is revealed gradually across turns. When a clean FULL prompt and a RAW-SHARDED conversation contain the same complete user evidence, the model should still arrive at the same answer. We argue that a key reason for this gap is self-anchored drift: responses produced under partial information introduce unsupported assumptions, and those assumptions later distort the final answer. To reduce this effect, we propose Canonical-Context On-Policy Distillation (CCOPD). During training, the same base model is used in two roles: a frozen teacher conditioned on the clean FULL prompt and a trainable student that receives the same evidence incrementally through a multi-turn conversation; CCOPD aligns the student's behavior on its own trajectories with the teacher's canonical full-context behavior. Trained only on math problem conversations, CCOPD yields a 32% average relative improvement in RAW-SHARDED performance over the original base model across math and five zero-shot out-of-domain task families, while largely preserving full-context performance. Further analyses suggest that CCOPD strengthens grounding in user evidence and reduces sensitivity to contamination from earlier assistant turns.

Zizhuo Lin, Quanling Liu, Jinsheng Quan +6

Zhejiang University · University of Science and Technology of China

LLM GroundingMulti-Turn Language Model ReasoningReasoning Consistency in Language ModelsLanguage Model DistillationOn-Policy DistillationLanguage Model Robustness+2
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May 27, 2026

Self-Consistency via Marginal Sharpening

Inference-time sampling can elicit strong reasoning abilities from language models without additional training. Existing power-sampling methods do so by sharpening the distribution over full generated outputs, favoring completions that are individually likely under the model. We argue that this is the wrong object to target for reasoning: a completion entangles a reasoning trace with a final answer, whereas what matters is whether an answer is supported by many plausible reasoning paths. We therefore shift the target from the full-output distribution to the sharpened answer marginal, making self-consistency an inference-time objective rather than a post-hoc voting criterion. Surprisingly, this marginal target admits an efficient approximation: we propose a simple, purely autoregressive parallel sampling algorithm that approximately samples from the sharpened answer marginal, eliciting stronger performance than standard power sampling on mathematics and coding benchmarks while being orders of magnitude faster.

Aleksei Arzhantsev, Otmane Sakhi, Nicolas Chopin

Criteo AI Lab, CREST IP Paris · Criteo AI Lab · ENSAE, Institut Polytechnique de Paris

Efficient Language Model ReasoningReasoning Consistency in Language ModelsEfficient Language Model InferenceSelf-Consistency in Language ModelsLLM Reasoning
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May 26, 2026

Do Models Know Why They Changed Their Mind? Interpretability and Faithfulness of Chain-of-Thought Under Knowledge Conflict

When a language model sees a document contradicting its training knowledge, it must choose: follow the document or trust itself. Prior work proved this choice depends on how well-known the fact is. We ask: does the model's chain-of-thought (CoT) reasoning faithfully report this mechanism? We introduce introspective faithfulness and test it across 200 questions, 8 models, and 4 prompt conditions. We find CoT reasoning is highly stable across opposite decisions: flip pairs retain 96% of same-answer similarity (d=0.34; confirmed by ROUGE-L, d=0.45). Yet self-rated confidence carries a faint genuine signal: for obscure facts where entity fame is uninformative, confidence still predicts decisions (p<0.001) and tracks item-level knowledge (r=0.134). GPT-4o is the only model with statistically reliable reasoning-decision coupling. Claude Sonnet 4.6 shows the widest confidence range (SD=1.39) but near-zero pooled correlation because the confidence-decision relationship reverses between conditions; a temperature ablation confirms this is model-specific. Internal thinking tokens show greater decision-sensitivity than user-facing CoT (p=0.033). CoT decomposes into a decision-invariant knowledge display (~96%) and a thin confidence layer with weak but real signal. For monitoring: read confidence, not the argument.

Pruthvinath Jeripity Venkata

Independent Researcher

LLM Uncertainty EstimationFaithfulness of Language Model ExplanationsConfidence Estimation in Language ModelsKnowledge Conflicts in Language ModelsLLM InterpretabilityCoT Faithfulness+3
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May 22, 2026

Convergence Without Understanding: When Language Models Agree on Representations but Disagree on Reasoning

Large language models trained under diverse objectives and architectures have been shown to develop increasingly similar internal representations, an observation formalized as the Platonic Representation Hypothesis. Whether this representational convergence extends to the reasoning processes that operate over shared representations remains untested. We evaluate representational similarity across 16 language models from 8 families (1.5B to 72B parameters) on 800 reasoning problems spanning mathematics, science, commonsense, and truthfulness, stratifying by problem difficulty, computational stage, and causal relevance. Our analysis reveals three dissociations: a difficulty inversion, where models converge more on problems they collectively fail (Centered Kernel Alignment [CKA] = 0.897) than on those they solve (CKA = 0.830); a generation gap, where pre-decision representations align (CKA = 0.875) while post-decision representations diverge (CKA = 0.274); and epiphenomenal correctness, where shared information is decodable across models (66% transfer accuracy) but exerts minimal causal influence on predictions (1.5% to 5.5% flip rate across ablation protocols). These results indicate that representational convergence in language models reflects shared input processing constraints rather than shared reasoning strategies, with direct implications for ensemble design, interpretability transfer, and evaluations of model similarity. Code is available at https://github.com/Usama1002/convergence-without-understanding.

Muhammad Usama, Dong Eui Chang

Control Laboratory, School of Electrical Engineering Korea Advanced Institute of Science and Technology (KAIST) Daejeon 34141, Republic of Korea · Control Laboratory, School of Electrical Engineering Korea Advanced Institute of Science and Technology (KAIST)2026 Daejeon 34141, Republic of Korea

Representational Similarity AnalysisLLM InterpretabilityReasoning Consistency in Language ModelsRepresentation Geometry in Language ModelsPlatonic Representation HypothesisLLM Reasoning
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May 13, 2026

Grounded Continuation: A Linear-Time Runtime Verifier for LLM Conversations

In a long conversation, an LLM may produce a fluent continuation that rests on premises the conversation has already abandoned. Context-manipulation attacks exploit precisely this weakness. We address this problem with a runtime verifier. An LLM Interpreter maps each utterance to one or more of eight epistemic operations, and then a symbolic engine applies these operations to a dependency map that records what every claim rests on and whether it still stands. Based on the dependency map, checking whether a continuation is grounded then reduces to a walk over the map, linear in its size and requiring no LLM call. Retraction propagates through the same map with a conflict-free guarantee and flags exactly the conclusions that lose support. Our experiments with five QA models demonstrate substantial improvements in QA accuracy at a low cost per query. On ReviseQA for belief revision and MemoryAgentBench's FactConsolidation split (MemAB-FC), the verifier outperforms a retrieval baseline and raises MemAB-FC single-hop accuracy from 0.460.46--0.950.95 to 0.940.94--0.980.98. With the verifier, even the small 7B model overtakes unaided GPT-4o. When a GPT-4o Interpreter extracts every update from raw text rather than taking the benchmarks' structured updates, the verifier still outperforms the retrieval baseline. Moreover, on MemAB-FC, QA prompts remain compact at 9797--174174 tokens while the full-context baseline reaches 114.5114.5K. Retraction queries take less than a microsecond at 20002000 turns.

Qisong He, Jinwei Hu, Xinmiao Huang +3

School of Computer Science & Informatics, University of Liverpool

Belief RevisionLLM GroundingLLM Answer VerificationReasoning Consistency in Language ModelsLLM ReliabilityLLM Context Management+1
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May 13, 2026

Controlling Logical Collapse in LLMs via Algebraic Ontology Projection over F2

Do large language models internally encode ontological relations in a formally verifiable algebraic structure? We introduce Algebraic Ontology Projection (AOP), which projects LLM hidden states into the Galois Field F2 under Liskov Substitution Principle constraints, using only 42 relational pairs as algebraic keys. AOP achieves up to 93.33% zero-shot inclusion accuracy on unseen concept pairs (Gemma-2 Instruct with optimized prompt), with consistent 86.67% accuracy observed across multiple model families -- with no model tuning, but through prompt alone. This algebraic structure is strongly layer-dependent. We introduce Semantic Crystallisation (SC), a metric that quantifies F2 constraint satisfaction relative to a random baseline and predicts zero-shot accuracy without held-out data. System prompts act as algebraic boundary conditions: only their combination with instruction tuning prevents Late-layer Collapse -- a systematic degradation of logical consistency in the final layers, observed in 7 of 10 conditions. These findings reframe forward computation as an iterative process of algebraic organisation, and open a path toward LLMs whose logical structure is not merely approximated, but formally accessible.

Hisashi Miyashita, Mgnite Inc

Mgnite Inc.

LLM InterpretabilityReasoning Consistency in Language ModelsLanguage Model Probing
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May 11, 2026

DGPO: Beyond Pairwise Preferences with Directional Consistent Groupwise Optimization

Although Large Language Models (LLMs) have made remarkable progress, current preference optimization methods still struggle to align directional consistency while preserving reasoning diversity. To address this limitation, we propose Directional-Groupwise Preference Optimization (DGPO), a lightweight framework that aggregates supervision signals at the group level and explicitly models direction-aware alignment through multi-candidate comparisons. DGPO organizes forward and reverse question-answer instances into structured sets and optimizes a margin-based likelihood objective that separates coherent reasoning paths from inconsistent alternatives. This group-wise formulation captures richer relative information than pairwise objectives and reinforces consistency across diverse reasoning pathways. Empirical results show that our constructed reverse data yields a 3.2% average improvement across five benchmarks, while DGPO further delivers consistent gains across multiple datasets and model families, achieving average accuracy improvements of up to 3.6%.

Mengyi Deng, Zhiwei Li, Xin Li +4

1Information Hub, The Hong Kong University of Science and Technology (Guangzhou), China · 2The Hong Kong University of Science and Technology, Hong Kong SAR

LLM AlignmentReasoning Consistency in Language ModelsPreference OptimizationPreference AlignmentLLM Reasoning
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May 8, 2026

Reliable Chain-of-Thought via Prefix Consistency

Large Language Models often improve accuracy on reasoning tasks by sampling multiple Chain-of-Thought (CoT) traces and aggregating them with majority voting (MV), a test-time technique called self-consistency. When we truncate a CoT partway through and regenerate the remainder, we observe that traces with correct answers reproduce their original answer more often than traces with wrong answers. We use this difference as a reliability signal, prefix consistency, that weights each candidate answer by how often it reappears under regeneration. It requires no access to token log-probabilities or self-rating prompts. Across five reasoning models and four math and science benchmarks, prefix consistency is the best correctness predictor in most settings, and reweighting votes by it reaches Standard MV plateau accuracy at up to 21x fewer tokens (median 4.6x). Our code is available at https://github.com/naoto-iwase/prefix-consistency.

Naoto Iwase, Yuki Ichihara, Mohammad Atif Quamar +1

Nagoya University · Nara Institute of Science and Technology · Mohamed bin Zayed University of Artificial Intelligence +1

Self-Consistency DecodingReasoning Consistency in Language ModelsLLM ReliabilityEfficient Language Model InferenceSelf-Consistency in Language ModelsLLM Reasoning+2
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May 7, 2026

Towards Annotation-Free Validation of MLLMs: A Vision-Language Logical Consistency Metric

Dominant accuracy evaluation might reward unwarranted guessing of Large Language Models, and it might not be applicable to novel tasks for model validation without ground-truth (gt) annotation. Based on basic logic principle, we propose a novel framework to evaluate the vision-language logical consistency of MLLMs on both sufficient and necessary cause-effect relations. We define Vision-Language Logical Consistency Metric (VL-LCM) on traditional MC-VQA tests, and recent NaturalBench tests without the need for gt annotation. Through systematic experiments on representative VL benchmark MMMU and recent VL challenges like NaturalBench, we evaluated 11 recent open-source MLLMs from 4 frontier families. Our findings reveal that, despite significant progress of recent MLLMs on accuracy, logical consistency lags behind significantly. Extensive evaluations on the correlations of VL-LCM with metrics on gt, the reliability of LCM, and the relation of VL-LCM with response distribution justify the validity and applicability of VL-LCM even without gt annotation. Our findings suggest that, beyond accuracy, logical consistency could be employed for both accuracy and reliability. VL-LCM can also be employed for MLLM selection, validation, and reliable answer justification in novel tasks without gt annotation.

Ying Gu, Mei Chee Leong, Hui Li Tan +3

Institute for Infocomm Research (I2R), Agency for Science, Technology and Research (A*STAR), Singapore

VLM EvaluationLarge Vision-Language ModelsReasoning Consistency in Language ModelsVLM Reasoning
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May 7, 2026

Logic-Regularized Verifier Elicits Reasoning from LLMs

Verifiers are crucial components for enhancing modern LLMs' reasoning capability. Typicalverifiers require resource-intensive superviseddataset construction, which is costly and faceslimitations in data diversity. In this paper, wepropose LOVER, an unsupervised verifier regularized by logical rules. LOVER treats theverifier as a binary latent variable, utilizinginternal activations and enforcing three logical constraints on multiple reasoning paths:negation consistency, intra-group consistency,and inter-group consistency (grouped by thefinal answer). By incorporating logical rulesas priors, LOVER can leverage unlabeled examples and is directly compatible with any offthe-shelf LLMs. Experiments on 10 datasetsdemonstrate that LOVER significantly outperforms unsupervised baselines, achieving performance comparable to the supervised verifier(reaching its 95% level on average). The sourcecode is publicly available at https://github.com/wangxinyufighting/llm-lover.

Xinyu Wang, Changzhi Sun, Lian Cheng +4

Department of Computer Science and Technology, East China Normal University · Institute of Artificial Intelligence (TeleAI), China Telecom

LLM EvaluationLLM Answer VerificationReasoning Consistency in Language ModelsLLM 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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Apr 17, 2026

Reasoning on the Manifold: Bidirectional Consistency for Self-Verification in Diffusion Language Models

While Diffusion Large Language Models (dLLMs) offer structural advantages for global planning, efficiently verifying that they arrive at correct answers via valid reasoning traces remains a critical challenge. In this work, we propose a geometric perspective: Reasoning on the Manifold. We hypothesize that valid generation trajectories reside as stable attractors on the high-density manifold of the learned distribution, whereas invalid paths exhibit off-manifold drift. To operationalize this, we introduce Bidirectional Manifold Consistency (BMC), a training-free, unsupervised metric that quantifies the stability of the generated sequence through a forward-masking and backward-reconstruction cycle. Empirically, we demonstrate BMC's versatility across the full reasoning lifecycle: (1) in Diagnosis, it serves as a robust discriminator of solution validity without ground truth answer; (2) in Inference, it enables rejection resampling to effectively concentrate computational resources on complex reasoning tasks; and (3) in Alignment, it functions as a dense geometric reward that transforms sparse outcome supervision into fine-grained guidance, empowering models to self-evolve beyond standard baselines. Our results establish intrinsic geometric stability as a robust indicator of correctness for dLLMs.

Jiaoyang Ruan, Xin Gao, Yinda Chen +5

Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, China · Shanghai Artificial Intelligence Laboratory, Shanghai, China · University of Science and Technology of China, Hefei, China +1

Diffusion Model AlignmentDiffusion Language Model InferenceReasoning Consistency in Language ModelsDiffusion Language ModelsReasoning Verification
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Apr 15, 2026

Empirical Evidence of Complexity-Induced Limits in Large Language Models on Finite Discrete State-Space Problems with Explicit Validity Constraints

Large Language Models (LLMs) are increasingly described as possessing strong reasoning capabilities, supported by high performance on mathematical, logical, and planning benchmarks. However, most existing evaluations rely on aggregate accuracy over fixed datasets, obscuring how reasoning behavior evolves as task complexity increases. In this work, we introduce a controlled benchmarking framework to systematically evaluate the robustness of reasoning in Large Reasoning Models (LRMs) under progressively increasing problem complexity. We construct a suite of nine classical reasoning tasks: Boolean Satisfiability, Cryptarithmetic, Graph Coloring, River Crossing, Tower of Hanoi, Water Jug, Checker Jumping, Sudoku, and Rubik's Cube, each parameterized to precisely control complexity while preserving underlying semantics. Using deterministic validators, we evaluate multiple open and proprietary LRMs across low, intermediate, and high complexity regimes, ensuring that only fully valid solutions are accepted. Our results reveal a consistent phase transition like behavior: models achieve high accuracy at low complexity but degrade sharply beyond task specific complexity thresholds. We formalize this phenomenon as reasoning collapse. Across tasks, we observe substantial accuracy declines, often exceeding 50%, accompanied by inconsistent reasoning traces, constraint violations, loss of state tracking, and confidently incorrect outputs. Increased reasoning length does not reliably improve correctness, and gains in one problem family do not generalize to others. These findings highlight the need for evaluation methodologies that move beyond static benchmarks and explicitly measure reasoning robustness under controlled complexity.

Md. Fahad Ullah Utsho, Mohd. Ruhul Ameen, Akif Islam +2

Department of Information and Communication Engineering, University of Rajshahi, Bangladesh · College of Engineering and Computer Sciences, Marshall University, Huntington, WV, USA · Department of Computer Science and Engineering, University of Rajshahi, Bangladesh

LLM EvaluationLarge Reasoning ModelsReasoning Consistency in Language ModelsConstraint Satisfaction
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Apr 12, 2026

FACT-E: Causality-Inspired Evaluation for Trustworthy Chain-of-Thought Reasoning

Chain-of-Thought (CoT) prompting has improved LLM reasoning, but models often generate explanations that appear coherent while containing unfaithful intermediate steps. Existing self-evaluation approaches are prone to inherent biases: the model may confidently endorse coherence even when the step-to-step implication is not valid, leading to unreliable faithfulness evaluation. We propose FACT-E, a causality-inspired framework for evaluating CoT quality. FACT-E uses controlled perturbations as an instrumental signal to separate genuine step-to-step dependence from bias-driven artifacts, producing more reliable faithfulness estimates (intra-chain faithfulness). To select trustworthy trajectories, FACT-E jointly considers intra-chain faithfulness and CoT-to-answer consistency, ensuring that selected chains are both faithful internally and supportive of the correct final answer. Experiments on GSM8K, MATH, and CommonsenseQA show that FACT-E improves reasoning-trajectory selection and yields stronger in-context learning exemplars. FACT-E also reliably detects flawed reasoning under noisy conditions, providing a robust metric for trustworthy LLM reasoning.

Yuxi Sun, Aoqi Zuo, Haotian Xie +3

Hong Kong Baptist University · The University of Melbourne · Singapore Management University

CoT EvaluationFaithfulness of Language Model ExplanationsReasoning Consistency in Language Models
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Apr 10, 2026

StaRPO: Stability-Augmented Reinforcement Policy Optimization

Reinforcement learning (RL) is effective in enhancing the accuracy of large language models in complex reasoning tasks. Existing RL policy optimization frameworks rely on final-answer correctness as feedback signals and rarely capture the internal logical structure of the reasoning process. Consequently, the models would generate fluent and semantically relevant responses but logically inconsistent, structurally erratic, or redundant. To this end, we propose StaRPO, a stability-augmented reinforcement learning framework that explicitly incorporates reasoning stability into the optimization objective. Our StaRPO decomposes stability into two computable lightweight metrics: the Autocorrelation Function (ACF) to evaluate local step-to-step coherence, and Path Efficiency (PE) to evaluate global goal-directedness of the reasoning trajectory. These stability rewards are combined with task rewards to provide complementary and process-aware feedback. We validate the effectiveness of using ACF and PE rewards by showing their correlation with logic errors on two backbone models. Experiments on four reasoning benchmarks show that StaRPO consistently outperforms compared baselines and can enhance both final-answer accuracy and logical stability.

Jinghan Zhang, Fengran Mo, Tharindu Cyril Weerasooriya +5

Clemson University · Université de Montréal · Accenture (United States) +2

RL for Language Model ReasoningReasoning Consistency in Language ModelsReward Shaping
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Apr 9, 2026

SeLaR: Selective Latent Reasoning in Large Language Models

Chain-of-Thought (CoT) has become a cornerstone of reasoning in large language models, yet its effectiveness is constrained by the limited expressiveness of discrete token sampling. Recent latent reasoning approaches attempt to alleviate this limitation by replacing discrete tokens with soft embeddings (probability-weighted mixtures of token embeddings) or hidden states, but they commonly suffer from two issues: (1) global activation injects perturbations into high-confidence steps, impairing reasoning stability; and (2) soft embeddings quickly collapse toward the highest-probability token, limiting exploration of alternative trajectories. To address these challenges, we propose SeLaR (Selective Latent Reasoning), a lightweight and training-free framework. SeLaR introduces an entropy-gated mechanism that activates soft embeddings only at low-confidence steps, while preserving discrete decoding at high-confidence steps. Additionally, we propose an entropy-aware contrastive regularization that pushes soft embeddings away from the dominant (highest-probability) token's direction, encouraging sustained exploration of multiple latent reasoning paths. Experiments on five reasoning benchmarks demonstrate that SeLaR consistently outperforms standard CoT and state-of-the-art training-free methods.

Renyu Fu, Guibo Luo

Guangdong Provincial Key Laboratory of Ultra High Definition Immersive Media Technology Shenzhen Graduate School, Peking University

CoT ReasoningContinuous Latent ReasoningReasoning Consistency in Language Models
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Apr 8, 2026

ROZA Graphs: Self-Improving Near-Deterministic RAG through Evidence-Centric Feedback

Language model agents reason from scratch on every query, discarding their chain of thought after each run. The result is lower accuracy and high run-to-run variance. We introduce reasoning graphs, which persist the per-evidence chain of thought as structured edges. Unlike prior memory that retrieves distilled strategies by query similarity, reasoning graphs enable evidence-centric feedback: for every candidate item, the system traverses all incoming evaluation edges across prior runs to surface how that specific item has been judged before. We further introduce retrieval graphs, which feed a planner that prunes consistently-rejected candidates over successive runs. Together they form a ROZA graph: a self-improving feedback loop in which accuracy gains scale with gold-passage reuse (reasoning graph) and efficiency gains scale with candidate-pool overlap (retrieval graph). The base model remains frozen; all gains come from context engineering via graph traversal. We evaluate on MuSiQue and HotpotQA, plus a high-reuse deployment subset. Four findings stand out. (1) Dose-response: accuracy improves monotonically with evidence-profile coverage, reaching +10.6pp over Vanilla RAG at 50%+ coverage on the same questions (47% error reduction, p<0.0001p<0.0001; per-question Spearman ρ=+0.144ρ=+0.144, p<10−6p<10^{-6}, n=1,100n=1{,}100). (2) Multi-hop scaling: 4-hop accuracy improves by +11.0pp (p=0.0001p=0.0001). (3) Cross-cluster prediction: the cluster-level gain is predicted by gold-passage reuse density (r=0.604r=0.604, p=0.001p=0.001, n=26n=26 clusters). (4) High-reuse Pareto dominance: highest or tied-for-highest accuracy alongside 46% lower cost and 46% lower latency. Per-passage decision consistency across repeated runs (N=73N=73 paired probes, K=10K=10 runs each, two model families, three temperatures) rises by +8 to +13pp on a fixed 20-passage context and by +12 to +21pp when the retrieval graph also prunes (all p<0.005p<0.005).

Matthew Penaroza

Retrieval-Augmented GenerationGraph Retrieval-Augmented GenerationLLM Reasoning with GraphsMemory-Augmented Language Model AgentsReasoning Consistency in Language Models
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Apr 7, 2026

Stress-Testing the Reasoning Competence of LLMs With Proofs Under Minimal Formalism

We introduce ProofGrid, a benchmark suite for evaluating LLM reasoning through machine-checkable proofs rather than final answers alone. ProofGrid contains 15 tasks spanning proof writing, proof checking, proof masking, and proof gap-filling. Tasks are expressed in minimal formal notation, especially NDL, a compact natural-deduction language that fits in short prompts and supports precise, auditable verification. This yields mechanical, reproducible, and fine-grained evaluation rather than judgments by humans or LLMs. ProofGrid covers a calibrated difficulty spectrum, from foundational reasoning tests to structurally rich challenge tasks that no current model solves, while minimizing reliance on domain knowledge, solver delegation, and long-context artifacts. We also develop a comparative framework for reasoning benchmarks and use it to situate ProofGrid relative to existing work in terms of representation, verification guarantees, and reasoning depth. Methodologically, we introduce an instrumented proof-checking pipeline that tolerates minor surface deviations while locating the first substantive reasoning failure, improving measurement resolution and separating proof planning from low-level execution noise. Using this pipeline, we evaluate a broad range of open and proprietary models. Results show rapid progress but substantial remaining limits: frontier models perform well on several foundational tasks, yet difficult tasks, especially those requiring global combinatorial reasoning or low-level proof synthesis, remain far from solved. We also identify epistemic instability, where models generate flawed proofs yet correctly reject those local inferences in isolation, and formalize this with an Epistemic Stability Index. Finally, we complement accuracy with 2PL IRT analyses, Wright maps, and a normalized task-discrimination measure based on Fisher information.

Konstantine Arkoudas, Serafim Batzoglou

LLM EvaluationReasoning Consistency in Language Models
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Apr 6, 2026

How Reasoning Evolves from Post-Training Data: An Empirical Study Using Chess

We study how reasoning evolves in a language model -- from supervised fine-tuning (SFT) to reinforcement learning (RL) -- by analyzing how a set of theoretically-inspired datasets influences language model performance in chess. We find that fine-tuning a model to directly predict the best move leads to effective RL and the strongest downstream performance -- however, the RL stage elicits unfaithful reasoning (reasoning inconsistent with the chosen move). Alternatively, training on multi-move trajectories yields comparable downstream performance with faithful reasoning and more stable RL. We analyze multiple qualitative and quantitative measures and highlight how these evolve from SFT through RL; we find several SFT-checkpoint metrics -- spanning evaluation performance, hallucination rates, and reasoning quality -- to be predictive of post-RL model performance. Finally, we ground our results with an experiment measuring chess information density in our custom datasets. We release models as well as training data, evaluations, and code that allowed us to surpass leading open-source reasoning models in chess with a 7B-parameter model. Code, models, and data are available at https://github.com/lucasdino/lang-chess.

Lucas Dionisopoulos, Nicklas Majamaki, Prithviraj Ammanabrolu

Department of Computer Science and Engineering, University of California San Diego, San Diego, United States.

Language Model Post-TrainingRL for Language Model ReasoningReasoning Consistency in Language Models
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Apr 6, 2026

This Treatment Works, Right? Evaluating LLM Sensitivity to Patient Question Framing in Medical QA

Patients are increasingly turning to large language models (LLMs) with medical questions that are complex and difficult to articulate clearly. However, LLMs are sensitive to prompt phrasings and can be influenced by the way questions are worded. Ideally, LLMs should respond consistently regardless of phrasing, particularly when grounded in the same underlying evidence. We investigate this through a systematic evaluation in a controlled retrieval-augmented generation (RAG) setting for medical question answering (QA), where expert-selected documents are used rather than retrieved automatically. We examine two dimensions of patient query variation: question framing (positive vs. negative) and language style (technical vs. plain language). We construct a dataset of 6,614 query pairs grounded in clinical trial abstracts and evaluate response consistency across eight LLMs. Our findings show that positively- and negatively-framed pairs are significantly more likely to produce contradictory conclusions than same-framing pairs. This framing effect is further amplified in multi-turn conversations, where sustained persuasion increases inconsistency. We find no significant interaction between framing and language style. Our results demonstrate that LLM responses in medical QA can be systematically influenced through query phrasing alone, even when grounded in the same evidence, highlighting the importance of phrasing robustness as an evaluation criterion for RAG-based systems in high-stakes settings.

Hye Sun Yun, Geetika Kapoor, Michael Mackert +4

Northeastern University · UC Berkeley · UT Austin +2

Framing Effects in Language ModelsMedical LLMsReasoning Consistency in Language ModelsClinical Language Model EvaluationRetrieval-Augmented Generation
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Apr 3, 2026

Correct Answers from Sound Reasoning: Verifiable Process Supervision for Language Models

Training language models to produce both correct answers and sound reasoning remains an open challenge. Reinforcement learning with verifiable rewards typically optimizes only final outcomes, which can improve task accuracy at the expense of reasoning quality, producing inaccurate, incomplete, or inconsistent traces. We propose verifiable process supervision (VPS), a post-training framework that jointly optimizes prediction accuracy and reasoning quality by supervising structured intermediate claims. We first apply supervised fine-tuning to induce a structured reasoning format, enabling deterministic extraction and verification of intermediate claims for process-level rewards. To address the heterogeneous difficulty of reasoning subtasks, we introduce adaptive weighting that prioritizes components with the largest remaining errors, creating an implicit curriculum. We evaluate VPS on chess as a controlled testbed where reasoning steps can be deterministically verified against engine signals. While outcome-only RL improves move accuracy, it sharply degrades reasoning quality, increasing win-rate error by up to 112% and reducing internal consistency by up to 69%. In contrast, VPS preserves accuracy while significantly improving reasoning quality, reducing win-rate error by up to 30% and restoring consistency to near saturation. A reasoning-space analysis further shows that, without a structured prior, outcome-only RL converges to budget-dependent shortcuts rather than sound multi-step reasoning. Beyond chess, we observe the same phenomenon on math reasoning, where outcome-only RL improves accuracy while degrading step-level arithmetic and consistency, whereas VPS maintains both. These results show that VPS enables language models to reason both accurately and reliably in verifiable domains.

Kyuyoung Kim, Kevin Wang, Yunfei Xie +7

KAIST AI · University of Texas, Austin · Rice University +3

Process SupervisionRL for Language Model ReasoningReasoning Consistency in Language ModelsReinforcement Learning with Verifiable Rewards
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Apr 3, 2026

FoE: Forest of Errors Makes the First Solution the Best in Large Reasoning Models

Recent Large Reasoning Models (LRMs) like DeepSeek-R1 have demonstrated remarkable success in complex reasoning tasks, exhibiting human-like patterns in exploring multiple alternative solutions. Upon closer inspection, however, we uncover a surprising phenomenon: The First is The Best, where alternative solutions are not merely suboptimal but potentially detrimental. This observation challenges widely accepted test-time scaling laws, leading us to hypothesize that errors within the reasoning path scale concurrently with test time. Through comprehensive empirical analysis, we characterize errors as a forest-structured Forest of Errors (FoE) and conclude that FoE makes the First the Best, which is underpinned by rigorous theoretical analysis. Leveraging these insights, we propose RED, a self-guided efficient reasoning framework comprising two components: I) Refining First, which suppresses FoE growth in the first solution; and II) Discarding Subs, which prunes subsequent FoE via dual-consistency. Extensive experiments across five benchmarks and six backbone models demonstrate that RED outperforms eight competitive baselines, achieving performance gains of up to 19.0% while reducing token consumption by 37.7% ~ 70.4%. Moreover, comparative experiments on FoE metrics shed light on how RED achieves effectiveness.

Kehan Jiang, Haonan Dong, Zhaolu Kang +2

School of Software and Microelectronics, Peking University · State Key Laboratory of General Artificial Intelligence, School of Intelligence Science and Technology, Peking University

Efficient Language Model ReasoningLarge Reasoning ModelsTest-Time ScalingReasoning Consistency in Language Models
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Apr 3, 2026

DeltaLogic: Minimal Premise Edits Reveal Belief-Revision Failures in Logical Reasoning Models

Reasoning benchmarks typically evaluate whether a model derives the correct answer from a fixed premise set, but they under-measure a closely related capability that matters in dynamic environments: belief revision under minimal evidence change. We introduce DeltaLogic, a benchmark transformation protocol that converts natural-language reasoning examples into short revision episodes. Each episode first asks for an initial conclusion under premises P, then applies a minimal edit δ(P), and finally asks whether the previous conclusion should remain stable or be revised. We instantiate DeltaLogic from FOLIO and ProofWriter and evaluate small causal language models with constrained label scoring. On a completed 30-episode Qwen evaluation subset, stronger initial reasoning still does not imply stronger revision behavior: Qwen3-1.7B reaches 0.667 initial accuracy but only 0.467 revision accuracy, with inertia rising to 0.600 on episodes where the gold label should change, while Qwen3-0.6B collapses into near universal abstention. There, Qwen3-4B preserves the same inertial failure pattern (0.650 initial, 0.450 revised, 0.600 inertia), whereas Phi-4-mini-instruct is substantially stronger (0.950 initial, 0.850 revised) but still exhibits non-trivial abstention and control instability. These results suggest that logical competence under fixed premises does not imply disciplined belief revision after local evidence edits. DeltaLogic therefore targets a distinct and practically important reasoning capability that complements existing logical inference and belief-updating benchmarks.

Amit Dhanda

Amazon

LLM ReasoningBelief Updating in LLMsReasoning Consistency in Language ModelsKnowledge Conflicts in Language Models
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