Reasoning Verification

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3 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

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Latest papers 32

Oct 5, 2026cs.CL

Can Language Models Learn to Reject Their Own Bad Reasoning Steps?

Verifier-guided decoding can prevent harmful reasoning steps from contaminating subsequent generation, but typically relies on an external learned verifier. We ask whether a language model can instead reject its own bad reasoning steps. We define a prefix's recoverability as the probability that the frozen generator can complete it correctly. Diagnostics show that adjacent recoverability changes are often difficult to resolve with practical Monte Carlo budgets, while same-prefix candidates exhibit a sparse low-recoverability tail. We introduce Self-Step Rejection (SSR), which trains a lightweight LoRA acceptance gate on the generator backbone while keeping the base model frozen. SSR uses confidence-qualified first-passage supervision: steps before the first resolved crossing of a root-relative recoverability barrier are accepted, the crossing step is rejected, and unresolved steps and suffixes are excluded. Training combines pointwise classification, same-prefix pairwise learning, and group-relative policy refinement using final-answer correctness. At inference, SSR accepts candidates or resamples from the unchanged prefix under rejection budgets, without an external learned verifier. Across three reasoning models and five mathematical reasoning benchmarks, SSR improves macro-average accuracy over single-pass decoding by 5.4--10.1 points using 1.21--1.40x as many generated tokens, and achieves the highest macro-average accuracy among evaluated step-level methods. Full-solution scaling methods require 4.47--8.27x the single-pass token cost for comparable performance.

Siheng Xiong, Xiaoze Liu, Yiqiao Jin +2

Georgia Institute of Technology · Purdue University

LLM Self-Correction Language Model Decoding Efficient Language Model Reasoning LLM Reasoning Reasoning Verification

Oct 4, 2026cs.AI

Hallucination Across the Reasoning Lifecycle: Interface Visibility, Causal Evidence, and Release Control in Large Reasoning Models

Reasoning errors can propagate into later decisions and memory. This survey synthesizes 312 papers and first-party reports on text-based reasoning hallucinations around three questions: what evidence is observable, what study designs establish, and which corrective actions the evidence supports. UIPCA records unsupported premises (U), invalid inferences (I), dependent reuse (P), visible answer-trace consistency (C), and action-policy failures (A). Across 58 reviewed sources, no comparison establishes that a specified intervention improves reasoning while reducing factual reliability under matched conditions. The synthesis connects diagnosis to verification, repair, selective release, and persistent-state control across memory, tools, and training feedback.

Zhe Yu, Mohan Li, Lei Yu +6

Zhejiang University, China · Binjiang Institute of Zhejiang University, China · Guangzhou University, China +5

LLM Hallucination Mitigation Hallucination in Language Models LLM Reliability Reasoning Verification

Sep 27, 2026cs.AI

The Error You See Is Not the Error You Made: Progression-aware Reasoning Origin for Reasoning Error Localization

Verifying multi-step LLM reasoning requires more than determining whether a trace is correct: a useful verifier should identify where the reasoning first goes wrong. However, existing holistic methods provide little positional evidence, while forward sequential verification often treats the first rejected step as the error source. Under error propagation, this assumption can fail, since an earlier mistake may remain locally plausible and become observable only through its downstream consequences. We therefore rethink reasoning verification as a progression-aware error-source localization problem: rather than asking only where a reasoning trace first appears inconsistent, we ask which earlier step best explains how that inconsistency emerges along the trajectory. Based on this view, we propose Progression-aware Reasoning Origin (PRO), a training-free framework for first-error localization. PRO jointly models incoming support from the preceding context and outgoing compatibility with subsequent reasoning, selectively refines regions where these signals disagree, and finally performs detector-conditioned source attribution with intervention-based evidence to distinguish the true error origin from its propagated manifestations. We further formalize the gap between forward rejection and structural exposure, showing why incoming-side evidence alone is insufficient for reliable localization under error propagation. Experiments across open-form, medical, and structured reasoning tasks demonstrate consistent improvements over strong verification baselines, supporting progression-aware source attribution as a more faithful formulation of reasoning verification.

Yiguo Wang, Ziyuan Yang, Yi Zou +3

Xiaopeng Honors College, Nanchang Hangkong University, China · School of Cyber Science and Engineering, Sichuan University, China · School of Software, Nanchang Hangkong University, China +1

Language Model Error Detection Reasoning Verification

Sep 8, 2026cs.AI

Deposon: An Auditable, Conservation-Guaranteed, Game-Theoretically Tested Scattering Layer over LLM Reasoning Paths

Multi-step LLM reasoning lacks a machine-recheckable ledger: discarded reasoning paths leave no auditable record. We propose the Deposon scattering layer, which binds each node of an LLM-generated concept-decomposition graph to a two-parameter Deposon state; paths undergo three-channel scattering -- transmission, reflection, irreversible dissipation -- obeying T+R+A=1 for arbitrary parameters, with a maximum per-path energy-audit deviation of 2.2E-16 (machine epsilon). We report all three evidence tiers honestly. On synthetic trap benchmarks the path-filtering gain is closed (pre-registered): unified reaches 100% versus a decoy-capture baseline at 7%/10%. On real benchmarks the layer is indistinguishable from a trivial six-keyword rule filter (GSM8K 0.87 >= 0.85, McNemar p=0.5; StrategyQA 0.899 = 0.899); no difference is detected here, so we sharpen the claim to "the differential value lies solely in machine verifiability." Fusion yields a second negative result: convex combinations with a semantic prior never improve (physics 0.484 -> 0.452), and the apparent lambda=2 gain is an anti-field artifact; any fusion gain must be nonlinear. Modeling the reverse dynamics as a potential game on the graph, we evidence an auditable scalar's monotonicity and near-gradientness and quantify the empirical coordination ratio (ECR). The three formalized dynamical-equivalence propositions (P1a/P1b/T-P1c) are falsified under the pre-registered kill protocol, and the potential-game claim is downgraded to approximate (cyclic-graph median residual 0.669): only consistency-level evidence survives at the dynamical level. Code: github.com/zeroandcat/Deposon.

Qihao Yuan

School of Chemistry and Life Resources, Renmin University of China

LLM Reasoning with Graphs LLM Auditing Reasoning Verification

Aug 13, 2026cs.AI

ReflectFact: Self-Reflective Agents for Improving Comprehension and Reasoning in Multi-Hop Fact Verification

Multi-hop fact verification, which verifies claims by reasoning over multiple pieces of evidence, is critical for combating misinformation on social media yet remains highly challenging. Recent methods primarily rely on multi-agent collaboration to decompose fact verification into specialized subtasks. However, these methods face two critical limitations: (1) agents may perform individual subtasks without sufficient awareness of the global verification objective, causing their reasoning to deviate from the intended direction; and (2) conflicts between parametric knowledge and the provided evidence may undermine evidence-grounded reasoning and lead to incorrect verdicts. To address these challenges, we propose ReflectFact, a novel self-reflective agent framework for multi-hop fact verification. ReflectFact introduces three key tasks. Explicit Reasoning Path Planning builds an evidence-grounded reasoning path by resolving implicit entities, decomposing the claim into sub-questions, and integrating the verified facts into a verdict. Evidence-Drift Verification makes the agent re-answer by quoting the supporting evidence when a grounded answer merely echoes its parametric prior, thereby calibrating evidence deviation to ensure grounded comprehension. Reasoning Reflection Verification re-examines each reasoning step and regenerates it once an inconsistency is detected, correcting reasoning flaws such as location bias and replacement bias through a global task perspective. Subsequently, the agent aggregates validated reasoning chains to yield reliable verdicts. Extensive experiments on HOVER and EX-FEVER demonstrate that ReflectFact effectively remedies the comprehension and reasoning defects of existing methods, achieving state-of-the-art performance and respectively outperforming the strongest baseline by 3.32% and 2.78% on the two datasets.

Runze Zhao, Zixin Tang, Xiaoshuai Hao +4

Institute of Information Engineering, Chinese Academy of Sciences · 1Zhongguancun Laboratory · 3Xiaomi EV

Automated Fact-Checking Agentic Reasoning Metacognition in Language Models Reasoning Verification

Aug 3, 2026cs.AI

A Human Audit of OpenAIs AI-Generated Mathematical Proofs

We assess 18 chapter-specific reviews of the ten mathematical results announced by OpenAI on 1 August 2026, alongside review standards, Lean formalizations, subsequent research, and mathematical references. The article audits this review record without claiming a complete reconstruction of all ten proofs. No confirmed substantive mathematical error in a principal result remains in the examined assessments, although review depth varies and some dependencies remain partly checked. Chapter 8 presents the strongest reservation: a specialist review requests major revision of compressed analytic arguments. In Chapter 6, an apparent polarity error was withdrawn after an overbar lost during PDF extraction was recovered from the typeset source. Subsequent research independently reuses the Chapter 3 proof mechanism and confirms that Connes's rigidity conjecture is false, without independently reproducing Chapter 4's stronger infinite-family result. Among the cited follow-ups, Chapter 7 receives the strongest direct theorem-level corroboration through a stronger hardness theorem. Related equality results in Chapter 8 do not verify the analytic inequality proof. Some follow-ups disclose material AI assistance. We argue that confidence should combine formal checking, human reconstruction, independent mathematical use, and a public record supporting correction of both proofs and reviews.

Mikołaj Sienicki, Krzysztof Sienicki

Polish-Japanese Academy of Information Technology ul. Koszykowa 86, 02-008 Warsaw, Poland, European Union · Chair of Theoretical Physics of Naturally Intelligent Systems (NIS)1 ul. Lipowa 2 / Topolowa 19, 05-807 Podkowa Leśna, Poland, European Union

LLM Auditing Human Oversight of AI LLM Mathematical Reasoning Reasoning Verification

Jul 16, 2026cs.CL

Answer-Conditioned Chains of Thought Degrade Verifiable-Reasoning Distillation in Large Language Models

A standard recipe for distilling the reasoning ability of large language models (LLMs) is to sample chains of thought from the model, keep those that reach the correct final answer, and fine-tune on the survivors. When sampling fails, a common fix shows the generator the gold answer and asks it to write a chain that reaches that answer. We show that this second step degrades the training data in a way that correctness filtering cannot catch. We run a controlled experiment that fixes the generator, the problem set, and the correctness filter, and varies only whether the chain is generated under answer-conditioning, the gold answer shown with a request to reach it. Training a strong instruction-tuned reasoning model on its own answer-conditioned chains sharply lowers its verifiable-reasoning accuracy. The loss grows with difficulty, reaching as much as about 27 points on the hardest competition problems. The mechanism is legible in the chains themselves, which rationalize backward from the shown answer instead of deriving it, with the early final-answer statement as the measurable symptom. The harm is a property of the data rather than the generator, read off unlabeled generations before any fine-tuning, ordering the penalty across eight thinking models from four families, and transferring across teacher families. A prompt ablation localizes it to the rationalize-toward instruction rather than the answer's bare visibility. The practical takeaway is to generate answer-blind, because no correctness filter can see this damage in the data.

Jungseob Lee, Seungyoon Lee, Suhyune Son +4

1Korea University · 2Zoom Communications · 3Yonsei University

CoT Distillation Language Model Distillation LLM Reasoning Reasoning Verification

Jul 14, 2026cs.LG

Evidence-Grounded Verified Agentic Reasoning: A Path Toward Eliminating LLM Hallucination in Empirical Inference via Tool-Attested Kernel Proofs

Tool access alone does not make LLM empirical reasoning governable: accepted outputs need not descend from attested evidence, and accepted deductions need not hold up under formal scrutiny. We present EG-VAR (Evidence-Grounded Verified Agentic Reasoning), a Lean 4-based tool-calling architecture in which the Lean kernel is the sole minter of Verified claims via tool-attestation axioms and declared source lifts. Every verified output structurally descends from an attested tool call (Thm. 3.1) and a kernel-checked chain of valid inference (Thm. 3.2); residual outputs are honest Abstain with a replayable audit trail. On a subcollection of TableBench numerical reasoning (n=120), EG-VAR attains 120/120 versus a 95% same-tool baseline; on counterfactual stress tests (5 domains x 2 models), EG-VAR stays 100% source-faithful while same-tool drops to 80-90% (no-tool 50-80%). With the LLM as deployment-time formalizer, residual semantic-formalization error is 3.3% on Sonnet and 1.7% on Opus. We position EG-VAR as a technical-governance interface for high-stakes empirical claims: a formal sidecar makes the target proposition, source scope, evidence boundary, proof obligation, and abstention condition auditable, eliminating unsupported Verified outputs today while turning formalization errors, lift and source-authority disputes, ambiguities, and abstentions into explicit audit targets. Over time, typed sidecars in datasets, APIs, public records, and AI-generated documents can amortize this formalization burden into reusable infrastructure.

Junyu Ren

Committee on Computational and Applied Mathematics, University of Chicago, Chicago, IL, USA.

LLM Hallucination Mitigation Evidence-Grounded Reasoning Formal Verification LLM Tool Use Reasoning Verification

Jul 1, 2026cs.AI

Theoria: Rewrite-Acceptability Verification over Informal Reasoning States

When should an AI system's answer be trusted? Formal proof assistants offer certainty but cannot reach most of the problem distribution; scalar LLM judges offer coverage but produce opaque scores that cannot be audited after the fact and are subject to the same coherence issues as any LLM. We present Theoria, a verification architecture that closes this gap. A candidate solution is rewritten into a sequence of typed state transitions, each licensed by an explicit justification, whether that be a citation, computation, or problem-given fact, and every transition is independently auditable. The foundational invariant is completeness of change: every difference between consecutive proof states must be accounted for, so hidden premises surface as unlicensed mutations rather than passing silently. On HLE-Verified Gold (185 text-only expert problems), Theoria certifies 105 at 91.4% strict precision (Wilson 95% CI [84.5%, 95.4%]). Every certification produces a human readable proof trace in which each step can be independently challenged. Holistic LLM judges achieve comparable precision at matched coverage but fail on different problems (Jaccard 0.14-0.36), making the approaches complementary. On 95 adversarial poisoned proofs across 15 domains, structured judges catch 94.7% versus 83.2% for holistic judging (p= 0.0017). The overall 11.5 pp gap concentrates in hidden premises (90.6% vs. 62.5%, a 28 pp difference) and fabricated citations (100% vs. 90%), the error classes where the formal analysis predicts an advantage; performance is identical on arithmetic and theorem-misapplication errors, where no advantage is predicted. On GPQA Diamond (n= 65), certified precision is 97.1% (Wilson CI [85.1%, 99.5%]).

Michael Saldivar, Ben Slivinski

Independent Researchers

LLM Answer Verification LLM Auditing Formal Verification Reasoning Verification

Jun 18, 2026cs.AI

Think Again or Think Longer? Selective Verification for Budget-Aware Reasoning

Test-time reasoning is increasingly used as a serving-time control knob, but extra reasoning is not uniformly valuable: it can repair failed attempts, waste compute on already-correct answers, or introduce harmful answer changes. We study this as a deployment allocation problem rather than a new-verifier problem. We introduce \sevra, Selective Verification for Reasoning Allocation, a serving-layer controller that decides whether to preserve a frozen solver's initial answer or invoke active verification. Using a frozen Qwen3-4B solver, we log intervention outcomes and train recoverability-aware gates from serving-visible attempt state. On \mathfive, selective verification reaches 76.3% accuracy, compared with 75.5% for always verifying, while reducing post-generation tokens by 26.8% and harmful flips from 2.2% to 1.0%. However, an 8,192-token initial solve reaches 76.0% accuracy with 28% fewer total model tokens, showing that selective recovery is useful but not the best tested cost frontier. In frozen transfer to \gsm, the selective policy verifies only 3.0% of examples, improves accuracy from 93.4% to 94.5%, and reduces verification tokens by 91.2% relative to always verifying; again, a longer initial solve matches its accuracy with fewer realized tokens. On CommonsenseQA, always-on verification hurts, while Self-Consistency@5 improves accuracy at about five times the realized token cost. The resulting deployment rule is: tune the initial budget first, then use selective recovery when explicit checks, bounded retries, auditability, or regression-risk control matter.

Sajib Acharjee Dip, Dawei Zhou, Liqing Zhang

Department of Computer Science, Virginia Tech · Fralin Biomedical Research Institute, Virginia Tech · FBRI Cancer Research Center, Washington, DC

LLM Inference Efficiency Cost-Aware Inference Reasoning Verification

Jun 15, 2026cs.AI

Scaling LLM Reasoning from Minimal Labels: A Semi-Supervised Framework with a Lightweight Verifier

For the development of Large language models (LLMs), recent approaches to generating pseudo intermediate reasoning have shown remarkable progress. But they typically rely on large numbers of correctly annotated answers to assess reasoning quality. This paper presents a semi-supervised framework that scales reasoning learning from minimal supervision, turning reasoning verification itself into a data creation mechanism. We train a lightweight reasoning-correctness classifier on only a few labeled samples, which judges whether intermediate reasoning traces generated by an LLM are valid. Furthermore, an entropy-based confidence threshold filters out unreliable samples, and the remaining high-confidence reasoning traces are used to fine-tune the model. Experiments on Verifiable Math Problems (Orca-Math subset) and Question Answering on Image Scene Graphs (GQA) with Visual Programming show that our method achieves accuracy comparable to using 10-15x more labeled data. Ablation analyses confirm that both the classifier and entropy filtering are essential for scalable and noise-resistant pseudo-labeling. By replacing expensive answer-level supervision with lightweight reasoning verification, our method provides a practical path toward constructing large-scale reasoning resources and paves the way for future autonomous reasoning systems that learn from minimal human input.

Keizo Kato, Chenhui Chu, Yugo Murawaki +1

Fujitsu Limited, Kawasaki, Japan · Kyoto University, Kyoto, Japan · National Institute of Informatics, Tokyo, Japan

Pseudo-Labeling LLM Reasoning Reasoning Verification

Jun 15, 2026cs.AI

VibeThinker-3B: Exploring the Frontier of Verifiable Reasoning in Small Language Models

This technical report introduces VibeThinker-3B, a compact dense model with 3B parameters developed to investigate how far verifiable reasoning can be pushed within a strictly small-model regime. Building upon the Spectrum-to-Signal post-training paradigm, we systematically enhance the model through an optimized pipeline that includes curriculum-based supervised fine-tuning, multi-domain reinforcement learning, and offline self-distillation. Experimental evaluations demonstrate that VibeThinker-3B achieves frontier-level performance on highly demanding verifiable tasks. Specifically, it attains a score of 94.3 on AIME26 (improving to 97.1 with claim-level test-time scaling), an 80.2 Pass@1 on LiveCodeBench v6, and exhibits strong out-of-distribution generalization with a 96.1% acceptance rate on recent unseen LeetCode contests. This effectively places it in the performance band of first-tier reasoning systems, matching or exceeding flagship models that are orders of magnitude larger, such as DeepSeek V3.2, GLM-5, and Gemini 3 Pro. Furthermore, a score of 93.4 on IFEval confirms that this extreme reasoning enhancement does not compromise strict instruction controllability. Extending our previous 1.5B work, these findings motivate the Parametric Compression-Coverage Hypothesis, which views verifiable reasoning as compressible into compact reasoning cores, while open-domain knowledge and general-purpose competence require broad parameter coverage over facts, concepts, and long-tail scenarios. This perspective suggests that compact models are not merely deployment-efficient substitutes, but a complementary path toward frontier-level performance in parameter-dense capability regimes.

Sen Xu, Shixi Liu, Wei Wang +6

Sina Weibo Inc.

Small Language Models Reasoning Verification

Jun 14, 2026cs.CR

Odds Law: The Decomposition Algebra On How Intelligence Organizes Itself to Solve Difficult Problems Reliably

We ask a structural question: given unreliable elementary problem-solvers, what organizations of them solve hard problems reliably, and what are the limits? We develop a

decomposition~algebra

: elementary solvers are morphisms in a stochastic category, and four combinators (sequential composition, parallel ensembling, verification gating, and recursive reduction) generate the space of compound solvers. We equip this algebra with two homomorphisms, a

reliability

valuation into the ordered monoid

([0,1],\le)

and a

cost

valuation into a commutative semiring, and we derive the composition laws that govern how reliability flows through structure. Our central results are (i) a

verification~odds~law

(the result that names this report), showing that a verification gate multiplies the odds of correctness by the verifier's likelihood ratio

Λ

, so that

k

conditionally independent gates yield geometric amplification; (ii) a

reliability~amplification~theorem

, giving target reliability

1-δ

at

O(\log 1/δ)

verification depth whenever

Λ>1

; and (iii) a

threshold~dichotomy

: above the critical parameters reliability can be driven arbitrarily close to one at logarithmic cost, while at or below them no amplification is possible. We then show that

self-organization

is the least fixed point of a monotone improvement operator on the complete lattice of strategies, and that this fixed point equalizes marginal log-odds gain per unit cost. Finally, we prove matching limits: an information ceiling bounds per-gate amplification by a divergence quantity; shared error causes create a strictly positive voting floor, so diversity is

necessary

for unbounded amplification. Reliability, in short, is neither free nor magical: it is bought with independent information, arranged by composition, and bounded by the verifier.

Hidayet Aksu

Agent Reliability Ensemble Learning Reasoning Verification

Jun 12, 2026cs.AI

VeriGeo: Controllable Geometry Question Generation with Numerical and Analytical Verification

Geometry problem generation is useful for AI-assisted education and multimodal mathematical reasoning, but reliable synthesis remains difficult because the problem statement, diagram, constraints, and solution should be mutually consistent. Existing methods often trade off controllability and reliability: seed-based rewriting is flexible but weakly verifiable, whereas diagram-first construction improves validity but is less suited to arbitrary user-specified constraints. We introduce VeriGeo, a controllable geometry generation framework grounded in executable reasoning traces. Given user constraints such as target concepts and difficulty, an Author agent generates a problem and diagram, and a Solver agent produces a proof-aligned solution. Both agents use a shared action sequence that connects natural language, diagrams, geometric constraints, and proof steps into a verifiable representation. A three-stage pipeline checks numerical consistency, analytical realizability, and global consistency, using verification-guided reflection to repair recoverable failures and reject unrecoverable ones. Across five LLM backbones, raw generations frequently fail these checks, while VeriGeo repairs a substantial fraction of the invalid attempts. Supervised fine-tuning on 8.7k examples generated by VeriGeo achieves the best reported GeoQA performance among end-to-end multimodal LLM-based solvers, and obtains strong results on PGPS9K and MathVista-GPS, demonstrating the effectiveness of verified synthetic data for improving multimodal geometry reasoning.

Xiaoxian Duan, Zequn Liu, Yingce Xia

Institute of Automation, Chinese Academy of Sciences, Beijing, China · Zhongguancun Academy, Beijing, China

Synthetic Data Generation Multimodal Reasoning Visually Grounded Reasoning Reasoning Verification

Jun 9, 2026cs.AI

Evaluating Research-Level Math Proofs via Strict Step-Level Verification

Large Language Models (LLMs) struggle to rigorously verify complex mathematical proofs. Standard global evaluation approaches suffer from "context poisoning," in which superficially plausible statements mask subtle logical flaws, leading to hallucination or over-skepticism. To address this, we shift from global evaluation to strict step-level verification: our framework maintains detailed context for each deduction step and strictly constrains the sources of applied theorems. We evaluate on a carefully curated adversarial diagnostic suite of research-level proofs drawn from the FirstProof challenge. A systematic ablation study demonstrates that these deductive constraints are indispensable, as unconstrained global prompting consistently fails to localize subtle logical errors. Beyond outperforming global evaluation, our approach fundamentally alters the failure taxonomy. Error analysis reveals that, rather than exhibiting severe logical hallucinations, remaining rejections are primarily instances of "pedantic hyper-rigor" stemming from unstated domain conventions, effectively exposing implicit ambiguities within the expert benchmark itself. Our findings suggest that prompting agents to organize their verification notes in a cautious, human-mathematician-like manner can substantially improve their ability to distinguish rigorous proofs from flawed ones, with the potential to strengthen agentic reasoning on frontier mathematical concepts that the base model does not already know well, and to lay a theoretical foundation for future automated proof-review systems. Code and prompts are available at GitHub.

Yifeng Sun

Independent Researcher

LLM Answer Verification Automated Theorem Proving LLM Mathematical Reasoning Reasoning Verification

May 31, 2026cs.AI

An Enigma of Artificial Reason: Investigating the Production-Evaluation Gap in Large Reasoning Models

Studies of human reasoning have shown that people are typically stronger at evaluating reasoning than producing it from scratch. In contrast, large reasoning models (LRMs) are trained to excel at producing long chains of reasoning to solve complex problems. How then do LRMs perform at evaluating reasons? We investigate this with the Valid-Answer-Invalid-Reasoning (VAIR) dataset: math problems and solutions with trivial reasoning flaws but valid answers, designed to isolate reasoning evaluation from the confound of reasoning production. Unlike humans, who we find are only 6% worse at grading than solving such problems, we find a substantial production-evaluation gap in LRMs: frontier models score as low as 48% when evaluating VAIR solutions, despite near-perfect solution production. Why this enigma? Through chain-of-thought (CoT) analysis, we find evidence of an answer confirmation bias: LRMs often produce then check for the correct answer instead of carefully verifying each step, fabricating rationalizations even when noticing anomalous reasoning. Linear probes corroborate this, showing that while LRM activations encode some representation of valid reasoning, they fail to robustly represent VAIR solutions as invalid. Causal patching of the final answer's representations causes LRM verdicts and activations to flip, demonstrating that answer validity is responsible for models' confirmation biases. These findings indicate an outstanding limitation in dominant approaches to reasoning training, which incentivize LRMs to produce and confirm reasoning towards correct answers, but not to robustly evaluate the underlying reasons.

Mingzhong Sun, Teresa Yeo, Armando Solar-Lezama +1

1NUS Department of Computer Science · 4Singapore-MIT Alliance for Research and Technology (SMART) · 2MIT EECS +1

Reasoning Evaluation LLM Interpretability Large Reasoning Models Reasoning Verification

May 28, 2026cs.LG

Self-Trained Verification for Training- and Test-Time Self-Improvement

Self-improvement at scale has been a longstanding goal for reasoning models, and there are two natural places to do it: at test time, through verification-refinement (V-R) loops; and at training time, through self-training methods. Both are gated by the same bottleneck: the verifier. V-R loops stall when verifier scores inflate while accuracy stagnates, and when feedback is too generic to act on; self-training fails similarly when bad self-generated data are added to training. Better verification would unlock both, but the capability we want to train, i.e., catching self-generated errors, lacks training signal. To address this challenge, we propose self-trained verification (STV). Our key observation is that, while a model cannot catch these errors alone, it can when shown the reference solution. We turn this asymmetry into a supervision target and train the verifier to imitate a more informed version of itself. At test time, STV substantially improves V-R loops on hard problems, while alternatives (e.g., SFT, RL on verifier scores, and even meta-verifiers) do not. STV roughly doubles accuracy on hard math and lifts it 14x on scientific reasoning tasks (1.5% to 21%). At training time, we additionally train the generator using RL with STV verifier's feedback inside the V-R loop - a procedure we call verifier-in-the-loop training (ViL). Starting from an RL-converged generator, ViL yields a further 33% gain in pass@1. More notably, the generator's standalone pass@1, with no verifier at test time, climbs 30% relative past where standard RL had converged. Hence, the next frontier in reasoning on hard problems may lie in how we train for and with verification. Website: https://ar-forum.github.io/stv-webpage

Chen Henry Wu, Aditi Raghunathan

Carnegie Mellon University

LLM Self-Refinement Language Model Self-Improvement Reasoning Verification

May 28, 2026cs.AI

Conformal Certification of Reasoning Trace Prefixes

Language model reasoning traces are rarely all-or-nothing; they frequently contain valid intermediate steps before a critical error occurs. Existing uncertainty quantification methods typically certify final answers or entire responses, failing to provide statistical guarantees for the proportion of a sequential trace that can be safely retained. To address this, we introduce CROP (Conformal Reasoning Output Prefixes), a verifier-agnostic calibration procedure for clean-prefix certification. Given any step-level risk proxy, CROP selects a calibrated threshold and returns the longest contiguous prefix whose step risk proxies remain below it, routing the uncertified suffix for downstream review or repair. Assuming exchangeability, CROP rigorously controls the marginal probability that the returned prefix contains an annotated error. Across six process-labeled reasoning datasets, we demonstrate that standard step-level metrics such as AUROC do not fully capture prefix utility, suggesting verifiers should instead be evaluated by certified prefix length. Furthermore, CROP balances over- and under-withholding, improving downstream repair accuracy by preserving valid intermediate reasoning while discarding misleading suffixes. Ultimately, this work positions prefix certification as a rigorous, practical bridge between process supervision, abstention, and repair.

Matt Y. Cheung, Ashok Veeraraghavan, Hanjie Chen +1

Department of Electrical & Computer Engineering, Rice University · Department of Computer Science, Rice University

Conformal Prediction Language Model Calibration Conformal Risk Control LLM Reasoning Reasoning Verification Reasoning Trace Analysis

May 26, 2026cs.CL

Debate Helps Weak Judges Reward Stronger Models

Despite theoretical promise, debate as a scalable oversight protocol has produced mixed empirical results: gains in some settings, and null effects in others, especially when the judge does not have information hidden from it. We study proposer-critic debate in a stronger-debater/weaker-judge setting on programmatically verifiable code and logic tasks. Debate helps the judge over a consultancy baseline when the critic provides a usable advantage: the critic's classification ability must exceed the judge's, and the judge must treat critic speeches as claims to verify rather than testimony to summarize. On the three of five pairings where the condition holds, proposer-critic debate's gains are statistically significant over consultancy, and these pairings are the most capable model pairings. On the two non-responder pairings in our set, debate produces null effects, and judge verification rates drop by tens of percentage points once a critic enters the transcript. In these cases the critic's binary-classification ability and the judge's are within noise of each other, and the critic's disagreement is parsed as testimony rather than a claim to check. Ablating rebuttal rounds from debate produces no measurable change in judge performance: a single independent critique recovers the bulk of debate's benefit at lower inference cost. These findings suggest a cheaper primitive for training-free scalable oversight in verifiable domains (answer, critique, judge) and a pre-deployment audit (does the critic beat the judge, and will the judge verify it?) that predicts when debate will help.

Ethan Elasky, Frank Nakasako, Naman Goyal

Palaestra Research · Independent

Scalable Oversight LLM-as-a-Judge Multi-Agent Debate Human Oversight of AI Reasoning Verification

May 20, 2026cs.LG

The Hidden Signal of Verifier Strictness: Controlling and Improving Step-Wise Verification via Selective Latent Steering

Generative verifiers have emerged as a promising paradigm for step-wise verification, but their verification behavior is often poorly calibrated: they may be under-critical and miss erroneous steps, or over-critical and reject correct reasoning. We refer to this tendency to be overly lenient or overly critical as verifier strictness. In this work, we study whether verifier strictness can be controlled through hidden-state intervention. We uncover a verification-specific hidden-state signal: in step-wise verification, a verifier's tendency to accept or reject a solution step is encoded near the boundary of the corresponding verification paragraph. Exploiting this signal, we show that hidden-state steering can directly modulate verifier strictness without fine-tuning. However, uniform steering induces a trade-off between error detection and correctness certification. To address this, we propose VerifySteer, which exploits latent correctness signals for sample-level routing and selectively intervenes on paragraph boundaries. Experiments on ProcessBench and Hard2Verify show that VerifySteer outperforms prompt optimization and activation steering baselines, and is competitive with self-consistency while requiring 4-7x less inference compute. VerifySteer is also complementary to verification fine-tuning, providing further gains on top of fine-tuned verifiers. The code is available at https://github.com/YefanZhou/VerifySteer.

Yefan Zhou, Yilun Zhou, Austin Xu +3

Dartmouth College · Datadog AI Research · Salesforce AI Research

Language Model Steering Activation Steering Reasoning Verification

May 19, 2026cs.AI

Using Aristotle API for AI-Assisted Theorem Proving in Lean 4: A Formalisation Case Study of the Grasshopper Problem

AI-assisted theorem proving can now generate substantial Lean developments for olympiad-level mathematics, but the evidential status of such developments depends on which declarations are actually verified. This paper reports a Lean 4 formalization case study of an Aristotle API proof attempt for the Grasshopper problem, originally posed as IMO 2009 Problem 6. The generated artifact states a generalized Lean version of the theorem, contains four verified helper lemmas for local components of a maximality and adjacent-swap exchange strategy, and leaves the main theorem grasshopper closed directly by one unresolved sorry. The verified components establish that the final partial sum equals the total sum, that an adjacent transposition can affect only the relevant intermediate partial sum, that the changed partial sum has the expected form, and that maximality at a position admitting an adjacent successor swap forces a corresponding forbidden-set membership fact. The Aristotle output summary identifies the intended remaining mathematical step as the global counting step needed to show that these membership facts produce at least n distinct forbidden values, contradicting the cardinality assumption |M| < n; the Lean source itself does not reduce the main theorem to a separately encoded counting lemma. This case study gives an inspectable example of a central limitation in AI-assisted formalization, namely that local proof search can succeed while the global combinatorial bookkeeping required for a theorem remains unresolved. The paper contributes a reproducible Lean artifact and a precise analysis of its verified and unverified proof content.

Gabriel Rongyang Lau

Nanyang Technological University, Singapore

Mathematical Reasoning Lean Theorem Proving Autoformalization Reasoning Verification

May 19, 2026cs.CV

A Nash Equilibrium Framework For Training-Free Multimodal Step Verification

Multimodal large language models often generate reasoning chains containing subtle errors that lead to incorrect answers. Current verification approaches have notable limitations. Learned critics need extensive labeled data and show inconsistent performance across different tasks. Meanwhile, existing training-free methods simply average scores from different sources, missing a key insight: when these scores disagree, that disagreement itself carries important information about whether a reasoning step is truly valid or not. We propose a training-free verification approach that treats step-wise verification as a coordination problem among specialized judges. We formalize these judges' interaction as a Nash equilibrium game where agreement signals valid steps while disagreement reveals instability. Our method computes equilibrium scores through a closed-form solution, enabling both disagreement-aware filtering and stability-conscious ranking of reasoning steps. Evaluated across six benchmarks, our approach achieves consistent improvements of 2.4% to 5.2% over baseline models and shows competitive performance against learned critics, demonstrating that cross-modal agreement (not just average confidence) provides robust verification signals without task-specific adaptation.

Rohit Sinha, Kunal Tilaganji, Tanuja Ganu +3

1Microsoft Research India · 2Indian Institute of Technology Hyderabad

Multi-View Consistency Game Theory Multimodal Large Language Models Multimodal Reasoning Reasoning Verification

May 18, 2026cs.CL

Knowledge-to-Verification: Exploring RLVR for LLMs in Knowledge-Intensive Domains

Reinforcement learning with verifiable rewards (RLVR) has demonstrated promising potential to enhance the reasoning capabilities of large language models (LLMs) in domains such as mathematics and coding. However, its applications on knowledge-intensive domains have not been effectively explored due to the scarcity of high-quality verifiable data. Furthermore, current RLVR focuses solely on the correctness of final answers, leading to the limitations of flawed reasoning and sparse reward signals. In this work, we propose Knowledge-to-Verification (K2V), a framework that extends RLVR to knowledge-intensive domains through automated verifiable data synthesis, while enabling verification of the LLM's reasoning process. Extensive experiments demonstrate that K2V enhances the reasoning of LLM in knowledge-intensive domains without significantly compromising the model's general capabilities. This study also suggests that integrating automated data synthesis with reasoning verification is a promising direction to enhance model capabilities in these broader domains. Code is available at https://github.com/SeedScientist/K2V.

Zhonghang Yuan, Zhefan Wang, Fang Hu +7

Shanghai Artificial Intelligence Laboratory · Shanghai Innovation Institute

RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards Reasoning Verification

May 11, 2026cs.LG

Unsupervised Process Reward Models

Process Reward Models (PRMs) are a powerful mechanism for steering large language model reasoning by providing fine-grained, step-level supervision. However, this effectiveness comes at a significant cost: PRMs require expert annotations for every reasoning step, making them costly and difficult to scale. Here, we propose a method for training unsupervised PRMs (uPRM) that requires no human supervision, neither at the level of step-by-step annotations nor through ground-truth verification of final answers. The key idea behind our approach is to define a scoring function, derived from LLM next-token probabilities, that jointly assesses candidate positions of first erroneous steps across a batch of reasoning trajectories. We demonstrate the effectiveness of uPRM across diverse scenarios: (i) uPRM achieves up to 15% absolute accuracy improvements over the LLM-as-a-Judge in identifying first erroneous steps on the ProcessBench dataset; (ii) as a verifier for test-time scaling, uPRM performs comparably to supervised PRMs and outperforms the majority voting baseline by up to 6.9%, and (iii) when used as a reward signal in reinforcement learning, uPRM enables more robust policy optimization throughout training compared to a supervised PRM trained using ground-truth labels. Overall, our results open a path toward scalable reward modeling for complex reasoning tasks.

Artyom Gadetsky, Maxim Kodryan, Siba Smarak Panigrahi +2

Swiss Federal Institute of Technology (EPFL)

Reward Modeling Process Reward Models Reasoning Verification

May 8, 2026cs.CL

LaTER: Efficient Test-Time Reasoning via Latent Exploration and Explicit Verification

Chain-of-thought (CoT) reasoning improves large language models (LLMs) on difficult tasks, but it also makes inference expensive because every intermediate step must be generated as a discrete token. Latent reasoning reduces visible token generation by propagating continuous states, yet replacing explicit derivations with latent computation can hurt tasks that require symbolic checking. We propose Latent-Then-Explicit Reasoning (LaTER), a two-stage paradigm that first performs bounded exploration in a continuous latent space and then switches to explicit CoT for verification and answer generation. In a training-free instantiation, LaTER projects final-layer hidden states back to the input embedding space, preserves the latent KV cache, and uses entropy and model-native stop-token probes to decide when to switch. We find that strong reasoning models already exhibit structured latent trajectories under this interface. On Qwen3-14B, training-free LaTER reduces total token usage by 16%-32% on several benchmarks while matching or improving accuracy on most of them; for example, it improves AIME 2025 from 70.0% to 73.3% while reducing tokens from 15,730 to 10,661. We further construct Latent-Switch-69K, a supervised corpus that pairs condensed solution intuitions with shortened explicit derivations. Fine-tuning with latent rollout and halting supervision yields additional gains: trained LaTER reaches 80.0% accuracy on AIME 2025, 10.0 points above the standard CoT baseline, while using 33% fewer tokens. Our code, data, and model are available at https://github.com/TioeAre/LaTER.

Xuan Li, Yining Wang, Yuchen Liu +7

University of Science and Technology of China · Unisound AI Technology Co., Ltd · MAIS, Institute of Automation, Chinese Academy of Sciences

CoT Reasoning Efficient Language Model Reasoning LLM Inference Acceleration Continuous Latent Reasoning LLM Reasoning Latent Reasoning+2

May 4, 2026cs.AI

Verifiable Counterfactual Supervision for Process Reward Models

Process reward models (PRMs) require supervision that identifies not only whether a reasoning trajectory is correct, but also where the reasoning process first becomes unsupported by its prefix. We frame this requirement as verifiable counterfactual process supervision with paired correct and erroneous trajectories in which the first invalid transition is known, the error mechanism is controlled, and the downstream continuation remains coherent under the corrupted state. Starting from a verified symbolic reasoning chain, our method injects a template-aware error at a selected intermediate step, recomputes all subsequent steps under the corrupted state, and verifies that the injected step is not derivable from its original prefix. The resulting trajectories provide prefix-valid first-error annotations and are translated into aligned natural-language processes for PRM training and evaluation. Experiments show that the synthesized data improve Best-of-8 reranking on logical reasoning benchmarks and show preliminary transfer to mathematical process evaluation.

Yinghui Chi, Yuanhong Wang

Jilin University

Process Reward Models Process Supervision Counterfactual Data Augmentation Reasoning Verification

May 2, 2026cs.AI

Grounding Multi-Hop Reasoning in Structural Causal Models via Group Relative Policy Optimization

Multi-Hop Fact Verification requires complex reasoning across disparate evidence, posing significant challenges for Large Language Models , which may suffer from hallucinations and fractured logical chains. Existing methods, while improving transparency via Chain-of-Thought , often lack explicit modeling of the structural dependencies between evidence and claims. In this work, we introduce an SCM-inspired framework that grounds reasoning in explicit directed dependency graphs, treating verification as a constructive structural reasoning process rather than full causal inference with interventions or counterfactual semantics. We empirically identify an "inverted U-shaped" correlation between reasoning-chain length and accuracy, revealing that excessive structural complexity can degrade performance. To address this, we propose a rule-based reinforcement learning strategy using Group Relative Policy Optimization. This approach dynamically optimizes the trade-off between structural depth and conciseness. Extensive experiments on HoVer and EX-FEVER demonstrate that our SCM-GRPO framework outperforms strong baselines while producing more traceable reasoning structures for complex fact verification.

Yunhan Bu, Quan Zhang, Huaping Zhang +9

Beijing Institute of Technology, Beijing, China · School of Computer Science and Technology, Xinjiang University, Urumqi, China · Military Science Information Research Center, Academy of Military Science, Beijing, China

Structural Causal Models RL for Language Model Reasoning Automated Fact-Checking Multi-Hop Reasoning Reasoning Verification

Apr 20, 2026cs.HC

Navigating the Conceptual Multiverse

When language models answer open-ended problems, they implicitly make hidden decisions that shape their outputs, leaving users with uncontextualized answers rather than a working map of the problem; drawing on multiverse analysis from statistics, we build and evaluate the conceptual multiverse, an interactive system that represents conceptual decisions such as how to frame a question or what to value as a space users can transparently inspect, intervenably change, and check against principled domain reasoning; for this structure to be worth navigating rather than misleading, it must be rigorous and checkable against domain reasoning norms, so we develop a general verification framework that enforces properties of good decision structures like unambiguity and completeness calibrated by expert-level reasoning; across three domains, the conceptual multiverse helped participants develop a working map of the problem, with philosophy students rewriting essays with sharper framings and reversed theses, alignment annotators moving from surface preferences to reasoning about user intent and harm, and poets identifying compositional patterns that clarified their taste.

Andre Ye, Jenny Y. Huang, Alicia Guo +3

MIT EECS · UW Allen School of CSE · UW Department of Philosophy

LLM Decision-Making Human-AI Decision Making Reasoning Verification

Apr 17, 2026cs.LG

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 Alignment Diffusion Language Model Inference Reasoning Consistency in Language Models Diffusion Language Models Reasoning Verification

Feb 10, 2026cs.AI

Auditing Multi-Agent LLM Reasoning Trees Outperforms Majority Vote and LLM-as-Judge

Multi-agent systems (MAS) can substantially extend the reasoning capacity of large language models (LLMs). Most MAS frameworks aggregate agent outputs via simple majority voting, discarding the evidential structure of reasoning traces. Majority voting is brittle under confabulation consensus, where agents share correlated biases and converge on the same incorrect rationale. We introduce AgentAuditor, which moves beyond frequency-based aggregation by organizing agent traces into a Reasoning Tree that explicitly represents agreements and divergences in their reasoning. AgentAuditor resolves conflicts by comparing branch-level evidence at critical divergence points, turning global adjudication into efficient, localized verification. We further propose Anti-Consensus Preference Optimization (ACPO), which trains the adjudicator with evidence-verified preference supervision to reduce conformity to misleading majority cues. Across four MAS frameworks and multiple reasoning benchmarks, AgentAuditor consistently improves aggregation performance over majority voting, with gains of up to 5% absolute accuracy while remaining token-efficient.

Wei Yang, Shixuan Li, Heng Ping +3

University of Southern California

LLM Auditing Preference Optimization Multi-Agent Systems Multi-Agent Consensus Multi-Agent Reasoning Reasoning Verification

Aug 3, 2025cs.CL

The Bidirectional Process Reward Model

Process Reward Models (PRMs), which assign fine-grained scores to intermediate reasoning steps within a solution trajectory, have emerged as a promising approach to enhance the reasoning quality of Large Language Models (LLMs). However, most existing PRMs rely on a unidirectional left-to-right (L2R) evaluation scheme, which restricts their utilization of global context. In light of this challenge, we propose a novel bidirectional evaluation paradigm, named Bidirectional Process Reward Model (BiPRM). BiPRM incorporates a parallel right-to-left (R2L) evaluation stream, implemented via prompt reversal, alongside the conventional L2R flow. Then a gating mechanism is introduced to adaptively fuse the reward scores from both streams to yield a holistic quality assessment. Remarkably, compared to the original PRM, BiPRM introduces only a 0.3% parameter increase for the gating module, and the parallel execution of two streams incurs merely 5% inference time latency. Our extensive empirical evaluations spanning diverse benchmarks, LLM backbones, PRM objectives and sampling policies demonstrate that BiPRM consistently surpasses unidirectional baselines, achieving an average relative gain of 10.6% over 54 solution-level configurations and 37.7% in 12 step-level error detection scenarios. Generally, our results highlight the effectiveness, robustness and general applicability of BiPRM, offering a promising new direction for process-based reward modeling.

Lingyin Zhang, Jun Gao, Xiaoxue Ren +1

School of Computer Science and Technology, Soochow University · Biomedical Basic Research Center of Jiangsu, Soochow University, Suzhou, Jiangsu 215123, China · School of Software Technology, Zhejiang University +1

Process Reward Models Reasoning Verification

Date pendingcs.LG

Measuring Progress in Reasoning Toward Mathematical Discovery with Automatic Verification

Can AI make progress on important, unsolved mathematical problems? Large language models are now capable of sophisticated mathematical and scientific reasoning, but whether they can perform novel research is still widely debated and underexplored. We introduce HorizonMath, a benchmark of 113 predominantly unsolved problems spanning eight domains in mathematics and the mathematical sciences, paired with an open-source evaluation framework for automated verification. Our benchmark targets the generator-verifier gap: problems where discovery is hard and requires meaningful mathematical insight, but verification is computationally straightforward. This contrasts with most existing research-level benchmarks, which instead rely on formal proof verification or manual review, both of which are expensive to scale. Because these solutions are unknown, HorizonMath is resistant to data contamination, and most state-of-the-art models score under 10%. Using this framework, we identify six novel solutions to research problems that either resolve previously open questions or improve on the best-known published results, with GPT-5.4 Pro and GPT-5.6 Sol each discovering three of these solutions. Across seven frontier model families, reasoning efficiency and behavior also vary substantially. We release HorizonMath as an open challenge and a growing community resource, where each verified solution is a candidate contribution to the mathematical literature.

Erik Y. Wang, Sumeet R. Motwani, James V. Roggeveen +9

Stanford University · Benchmark · University of Oxford +3

Mathematical Reasoning Benchmarks LLM Mathematical Reasoning Reasoning Verification