Reasoning Verification

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Overview

Reasoning verification studies how to detect flawed steps, assess proof validity, and determine whether answers follow from evidence rather than merely matching an answer key. Approaches include process reward models and step classifiers, self- or multi-agent checking, symbolic and formal proof checkers, and evidence-grounded tools for tasks such as mathematics, code, and multi-hop fact verification. Benchmarks increasingly test first-error localization, robustness to valid but non-canonical solutions, and whether a verifier depends on the evidence it is given. A central challenge is balancing reliable detection against false rejection, reward hacking, and the token or human-review costs of stronger checks.

Latest papers

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57 papers9 papers in the last four weeks, up 80% on the four weeks before. 0.1% of all new papers.

May 31, 2026

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 EvaluationLLM InterpretabilityLarge Reasoning ModelsReasoning Verification
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May 28, 2026

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-RefinementLanguage Model Self-ImprovementReasoning Verification
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May 28, 2026

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 and improves 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. Code available at https://github.com/matthewyccheung/crop.

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

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

Conformal PredictionLanguage Model CalibrationConformal Risk ControlLLM ReasoningReasoning VerificationReasoning Trace Analysis
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May 26, 2026

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 OversightLLM-as-a-JudgeMulti-Agent DebateHuman Oversight of AIReasoning Verification
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May 20, 2026

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 SteeringActivation SteeringReasoning Verification
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May 19, 2026

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 ReasoningLean Theorem ProvingAutoformalizationReasoning Verification
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May 19, 2026

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 ConsistencyGame TheoryMultimodal Large Language ModelsMultimodal ReasoningReasoning Verification
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May 18, 2026

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 ReasoningReinforcement Learning with Verifiable RewardsReasoning Verification
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May 11, 2026

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 ModelingProcess Reward ModelsReasoning Verification
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May 8, 2026

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 ReasoningEfficient Language Model ReasoningLLM Inference AccelerationContinuous Latent ReasoningLLM ReasoningLatent Reasoning+2
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May 4, 2026

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 ModelsProcess SupervisionCounterfactual Data AugmentationReasoning Verification
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May 2, 2026

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 ModelsRL for Language Model ReasoningAutomated Fact-CheckingMulti-Hop ReasoningReasoning Verification
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Apr 20, 2026

Navigating the Conceptual Multiverse

When language models answer open-ended questions, they implicitly make decisions that shape their answers. However, the models do not show these decisions to the user, so users cannot contextualize answers: they cannot see the assumptions an answer rests on or the alternatives to it. Drawing on multiverse analysis from statistics, we introduce the conceptual multiverse, a representation in which language models express answers as the result of intermediate conceptual decisions. We build a system that generates such decisions explicitly, organizes them into a space of answers that users can see and change, and checks them against the norms of a specific domain. In a user study across three domains - philosophy, AI alignment annotation, and poetry - participants say that our system helps them see the decisions leading to an answer, explore the space of answers, and understand the decisions structuring this space.

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

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

LLM Decision-MakingHuman-AI Decision MakingReasoning Verification
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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 10, 2026

Toward Explanatory Equilibrium: Verifiable Reasoning as a Coordination Mechanism under Asymmetric Information

LLM-based agents increasingly coordinate decisions in multi-agent systems, often attaching natural-language reasoning to actions. However, reasoning is neither free nor automatically reliable: it incurs computational cost and, without verification, may degenerate into persuasive cheap talk. We introduce Explanatory Equilibrium as a design principle for explanation-aware multi-agent systems and study a regime in which agents exchange structured reasoning artifacts-auditable claims paired with concise text-while receivers apply bounded verification through probabilistic audits under explicit resource constraints. We contribute (i) a minimal mechanism-level exchange-audit model linking audit intensity, misreporting incentives, and reasoning costs, and (ii) empirical evidence from a finance-inspired LLM setting involving a Trader and a Risk Manager. In ambiguous, borderline proposals, auditable artifacts prevent the cost of silence driven by conservative validation under asymmetric information: without structured claims, approval and welfare collapse. By contrast, structured reasoning unlocks coordination while maintaining consistently low bad-approval rates across audit intensities, audit budgets, and incentive regimes. Our results suggest that scalable, safety-preserving coordination in LLM-based multi-agent systems depends not only on audit strength, but more fundamentally on disciplined externalization of reasoning into partially verifiable artifacts.

Feliks Bańka, Jarosław A. Chudziak

The Faculty of Electronics and Information Technology, Warsaw University of Technology, Warsaw, Poland

Multi-Agent LLM SystemsMulti-Agent CoordinationReasoning VerificationMechanism DesignAI Agent Auditing
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Apr 10, 2026

Case-Grounded Evidence Verification: A Framework for Constructing Evidence-Sensitive Supervision

Evidence-grounded reasoning requires more than attaching retrieved text to a prediction: a model should make decisions that depend on whether the provided evidence supports the target claim. In practice, this often fails because supervision is weak, evidence is only loosely tied to the claim, and evaluation does not test evidence dependence directly. We introduce case-grounded evidence verification, a general framework in which a model receives a local case context, external evidence, and a structured claim, and must decide whether the evidence supports the claim for that case. Our key contribution is a supervision construction procedure that generates explicit support examples together with semantically controlled non-support examples, including counterfactual wrong-state and topic-related negatives, without manual evidence annotation. We instantiate the framework in radiology and train a standard verifier on the resulting support task. The learned verifier substantially outperforms both case-only and evidence-only baselines, remains strong under correct evidence, and collapses when evidence is removed or swapped, indicating genuine evidence dependence. This behavior transfers across unseen evidence articles and an external case distribution, though performance degrades under evidence-source shift and remains sensitive to backbone choice. Overall, the results suggest that a major bottleneck in evidence grounding is not only model capacity, but the lack of supervision that encodes the causal role of evidence.

Soroosh Tayebi Arasteh, Mehdi Joodaki, Mahshad Lotfinia +2

RWTH Aachen University, Aachen, Germany

Evidence-Grounded ReasoningReasoning Verification
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Apr 7, 2026

ProofSketcher: Hybrid LLM + Lightweight Proof Checker for Reliable Math/Logic Reasoning

The large language models (LLMs) might produce a persuasive argument within mathematical and logical fields, although such argument often includes some minor missteps, including the entire omission of side conditions, invalid inference patterns, or appeals to a lemma that cannot be derived logically out of the context being discussed. These omissions are infamously hard to notice solely out of the text, as even the misconstrued construction still may seem mostly accurate. Conversely, interactive theorem provers like Lean and Coq have rigorous reliability by ensuring that syntactic and semantic statements only accept statements that can pass all the syntactic and semantic steps in the program which is a small trusted kernel of the language type-checks with. Despite the fact that this technique provides strong guarantees, it comes at quite a heavy price: the evidence must be completely formalized, and the evidence user or a auxiliary search program must provide an avalanche of low-level information. This paper presents a hybrid pipeline where an LLM generates a typed proof sketch in a compact DSL and a lightweight trusted kernel expands the sketch into explicit proof obligations.

Kranthi Kommuru, Kunal Khanvilkar, Gaurav Parekh

Automatic Data Processing, Inc Atlanta, USA · Amazon Web Services, Inc Banglore, India

Large Language Model-Guided Theorem ProvingAutomated Theorem ProvingLLM Mathematical ReasoningReasoning VerificationFormal Verification
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Apr 2, 2026

Do We Need Frontier Models to Verify Mathematical Proofs?

Advances in training, post-training, and inference-time methods have enabled frontier reasoning models to win gold medals in math competitions and settle challenging open problems. Gaining trust in the responses of these models requires that natural language proofs be checked for errors. LLM judges are increasingly being adopted to meet the growing demand for evaluating such proofs. While verification is considered easier than generation, what model capability does reliable verification actually require? We systematically evaluate four open-source and two frontier LLMs on datasets of human-graded natural language proofs of competition-level problems. We consider two key metrics: verifier accuracy and self-consistency (the rate of agreement across repeated judgments on the same proof). We observe that smaller open-source models are only up to ~10% behind frontier models in accuracy but they are up to ~25% more inconsistent. Furthermore, we see that verifier accuracy is sensitive to prompt choice across all models. We then demonstrate that the smaller models, in fact, do possess the mathematical capabilities to verify proofs at the level of frontier models, but they struggle to reliably elicit these capabilities with general judging prompts. Through an LLM-guided prompt search, we synthesize an ensemble of specialized prompts that overcome the specific failure modes of smaller models, boosting their performance by up to 9.1% in accuracy and 15.9% in self-consistency. These gains are realized across models and datasets, allowing models like Qwen3.5-35B to perform on par with frontier models such as Gemini 3.1 Pro for proof verification.

Aaditya Naik, Guruprerana Shabadi, Rajeev Alur +1

University of Pennsylvania, U.S.A.

LLM Input OptimizationReasoning VerificationLLM ReasoningLLM EvaluationLLM PromptingSelf-Consistency in Language Models
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Mar 22, 2026

ORACLE: Optimizing Reasoning Abilities of Large Language Models via Constraint-Led Synthetic Data Elicitation

Training large language models (LLMs) with synthetic reasoning data has become a popular approach to enhancing their reasoning capabilities, while a key factor influencing the effectiveness of this paradigm is the quality of the generated multi-step reasoning data. To generate high-quality reasoning data, many recent methods generate synthetic reasoning paths and filter them based on final answer correctness, often overlooking flaws in intermediate reasoning steps. To enhance the verification of intermediate reasoning steps, prior work primarily resorts to code execution or symbolic reasoning engines. However, code-based validation is restricted to code or mathematical tasks, and reasoning engines require a well-structured and complete context. As a result, existing methods fail to function effectively in natural language reasoning tasks that involve ambiguous or incomplete contexts. In these tasks, synthetic data still lack reliable checks for verifying each reasoning step. To address this challenge, we introduce ORACLE, a structured data generation framework inspired by syllogistic reasoning. ORACLE integrates the generative strengths of LLMs with symbolic supervision: the LLM produces step-wise reasoning contexts, while a symbolic reasoning engine verifies the validity of each intermediate step. By employing a unified prompting template to elicit modular reasoning chains, ORACLE enables fine-grained, step-level validation, facilitating the construction of high-quality multi-step reasoning data. Across six logical, factual, and commonsense reasoning benchmarks, our ORACLE consistently outperforms strong baselines on multiple models.

Zhuojie Yang, Wentao Wan, Keze Wang

School of Computer Science and Engineering, Sun Yat-sen University

Synthetic Data Generation for Language ModelsLLM ReasoningReasoning Verification
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Mar 19, 2026

Towards Verifiable AI with Lightweight Cryptographic Proofs of Inference

When large AI models are deployed as cloud-based services, clients have no guarantee that responses are correct or were produced by the intended model. Rerunning inference locally is infeasible for large models, and existing cryptographic proof systems -- while providing strong correctness guarantees -- introduce prohibitive prover overhead (e.g., hundreds of seconds per query for billion-parameter models). We present a verification framework and protocol that replaces full cryptographic proofs with a lightweight, sampling-based approach grounded in statistical properties of neural networks. We formalize the conditions under which trace separation between functionally dissimilar models can be leveraged to argue the security of verifiable inference protocols. The prover commits to the execution trace of inference via Merkle-tree-based vector commitments and opens only a small number of entries along randomly sampled paths from output to input. This yields a protocol that trades soundness for efficiency, a tradeoff well-suited to auditing, large-scale deployment settings where repeated queries amplify detection probability, and scenarios with rationally incentivized provers who face penalties upon detection. Our approach reduces proving times by several orders of magnitude compared to state-of-the-art cryptographic proof systems, going from the order of minutes to the order of milliseconds, with moderately larger proofs. Experiments on ResNet-18 classifiers and Llama-2-7B confirm that common architectures exhibit the statistical properties our protocol requires, and that natural adversarial strategies (gradient-descent reconstruction, inverse transforms, logit swapping) fail to produce traces that evade detection. We additionally present a protocol in the refereed delegation model, where two competing servers enable correct output identification in a logarithmic number of rounds.

Pranay Anchuri, Matteo Campanelli, Paul Cesaretti +4

Offchain Labs · University of Tartu, Estonia · CUNY Graduate Center +1

Verifiable Outsourced ComputationNeural Network VerificationReasoning Verification
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Mar 16, 2026

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 BenchmarksLLM Mathematical ReasoningReasoning VerificationAI-Assisted Mathematical Discovery
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Mar 16, 2026

MiroThinker-1.7 & H1: Towards Heavy-Duty Research Agents via Verification

We present MiroThinker-1.7, a new research agent designed for complex long-horizon reasoning tasks. Building on this foundation, we further introduce MiroThinker-H1, which extends the agent with heavy-duty reasoning capabilities for more reliable multi-step problem solving. In particular, MiroThinker-1.7 improves the reliability of each interaction step through an agentic mid-training stage that emphasizes structured planning, contextual reasoning, and tool interaction. This enables more effective multi-step interaction and sustained reasoning across complex tasks. MiroThinker-H1 further incorporates verification directly into the reasoning process at both local and global levels. Intermediate reasoning decisions can be evaluated and refined during inference, while the overall reasoning trajectory is audited to ensure that final answers are supported by coherent chains of evidence. Across benchmarks covering open-web research, scientific reasoning, and financial analysis, MiroThinker-H1 achieves state-of-the-art performance on deep research tasks while maintaining strong results on specialized domains. We also release MiroThinker-1.7 and MiroThinker-1.7-mini as open-source models, providing competitive research-agent capabilities with significantly improved efficiency.

MiroMind Team, S. Bai, L. Bing +41

Autonomous Research AgentsLong-Horizon LLM AgentsAgentic ReasoningLLM Agent ReliabilityReasoning Verification
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Mar 1, 2026

One-Token Verification for Reasoning Correctness Estimation

Recent breakthroughs in large language models (LLMs) have led to notable successes in complex reasoning tasks, such as mathematical problem solving. A common strategy for improving performance is parallel thinking, in which multiple reasoning traces are generated and the final prediction is made using aggregation schemes like majority voting or best-of-NN decoding. However, two key challenges persist. First, multi-sample decoding incurs substantial inference latency, especially for long-form outputs. Second, effective mechanisms for reliably assessing the correctness of individual reasoning traces are still limited. To address these challenges, we introduce One-Token Verification (OTV), a computational method that estimates reasoning correctness in a single forward pass during generation. OTV is activated by a learnable token and integrated into the LLM via low-rank adaptation to probe internal reasoning signals through the key-value cache, supporting token-level correctness estimation at any stage of generation without disrupting primary reasoning. Experiments on mathematical reasoning benchmarks demonstrate that OTV consistently surpasses existing verifiers. Additionally, OTV reduces token usage by up to 90%90\% through correctness-guided early termination, prioritizing shorter, more reliable solutions.

Zhan Zhuang, Xiequn Wang, Zebin Chen +4

Southern University of Science and Technology, Shenzhen, China · City University of Hong Kong, Hong Kong SAR · Zhejiang University, Hangzhou, China

Reasoning VerificationLLM ReasoningEfficient Language Model ReasoningConfidence Estimation in Language ModelsNumerical Reasoning in Language Models
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Feb 20, 2026

Reward Under Attack: Analyzing the Robustness and Hackability of Process Reward Models

Process Reward Models (PRMs) are rapidly becoming the backbone of LLM reasoning pipelines, yet we demonstrate that state-of-the-art PRMs are systematically exploitable under adversarial optimization pressure. To address this, we introduce a three-tiered diagnostic framework that applies increasing adversarial pressure to quantify these vulnerabilities. Static perturbation analysis uncovers a fluency-logic dissociation: high invariance to surface-level style changes reward changes <<0.1, yet inconsistent detection of logically-corrupted reasoning, with different models failing on different attack types. Adversarial optimization demonstrates that gradient-based attacks inflate rewards on invalid trajectories, with reward landscapes exhibiting wide, exploitable peaks. RL-induced reward hacking exposes the critical failure mode: policies trained on AIME problems achieve near-perfect PRM rewards (>>0.9), while ground-truth accuracy remains low (below 4%), with 43% of reward gains attributable to stylistic shortcuts. These findings reveal that current PRMs function as fluency detectors rather than reasoning verifiers, creating systematic blind spots that undermine their use as training signals. We release PRM-BiasBench and a diagnostic toolkit to enable robustness evaluation before deployment. The code and dataset are available at https://github.com/SqueezeAILab/reward-under-attack.

Rishabh Tiwari, Aditya Tomar, Udbhav Bamba +5

UC Berkeley · Transmute AI · ICSI +1

Process Reward ModelsReward HackingAdversarial AttacksReasoning VerificationRL for Language Model Reasoning
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Feb 19, 2026

When to Trust the Cheap Check: Weak and Strong Verification for Reasoning

Reasoning with LLMs increasingly unfolds inside a broader verification loop. Internally, systems use cheap checks, such as self-consistency or proxy rewards, which we call weak verification. Externally, users inspect outputs and steer the model through feedback until results are trustworthy, which we call strong verification. These signals differ sharply in cost and reliability: strong verification can establish trust but is resource-intensive, while weak verification is fast and scalable but noisy and imperfect. We formalize this tension through weak--strong verification policies, which decide when to accept or reject based on weak verification and when to defer to strong verification. We introduce metrics capturing incorrect acceptance, incorrect rejection, and strong-verification frequency. Over population, we show that optimal policies admit a two-threshold structure and that calibration and sharpness govern the value of weak verifiers. Building on this, we develop an online algorithm that provably controls acceptance and rejection errors without assumptions on the query stream, the language model, or the weak verifier.

Shayan Kiyani, Sima Noorani, George Pappas +1

University of Pennsylvania

LLM Answer VerificationReasoning Verification
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Feb 10, 2026

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 AuditingPreference OptimizationMulti-Agent SystemsMulti-Agent ConsensusMulti-Agent ReasoningReasoning Verification
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Aug 3, 2025

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 ModelsReasoning Verification
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