Daily Papers

Large language models (LLMs) exhibit remarkable reasoning capabilities across diverse downstream tasks. However, their autoregressive nature leads to substantial inference latency, posing challenges for real-time applications. Speculative sampling mitigates this issue by introducing a drafting phase followed by a parallel validation phase, enabling faster token generation and verification. Existing approaches, however, overlook the inherent coherence in text generation, limiting their efficiency. To address this gap, we propose a Speculative Sampling with Syntactic and Semantic Coherence (S^4C) framework, which extends speculative sampling by leveraging multi-head drafting for rapid token generation and a continuous verification tree for efficient candidate validation and feature reuse. Experimental results demonstrate that S^4C surpasses baseline methods across mainstream tasks, offering enhanced efficiency, parallelism, and the ability to generate more valid tokens with fewer computational resources. On Spec-bench benchmarks, S^4C achieves an acceleration ratio of 2.26x-2.60x, outperforming state-of-the-art methods.

Verifying the reliability of complex, multi-step reasoning in Large Language Models (LLMs) remains a fundamental challenge, as existing methods often lack both faithfulness and precision. To address this issue, we propose the Graph of Verification (GoV) framework. GoV offers three key contributions: First, it explicitly models the underlying deductive process as a directed acyclic graph (DAG), whether this structure is implicit or explicitly constructed. Second, it enforces a topological order over the DAG to guide stepwise verification. Third, GoV introduces the notion of customizable node blocks, which flexibly define the verification granularity, from atomic propositions to full paragraphs, while ensuring that all requisite premises derived from the graph are provided as contextual input for each verification unit. We evaluate GoV on the Number Triangle Summation task and the ProcessBench benchmark with varying levels of reasoning complexity. Experimental results show that GoV substantially improves verification accuracy, faithfulness, and error localization when compared to conventional end-to-end verification approaches. Our code and data are available at https://github.com/Frevor/Graph-of-Verification.

Recent advancements in large language models (LLMs) suggest great promises in code and proof generations. However, scaling automated formal verification to real-world projects requires resolving cross-module dependencies and global contexts, which are crucial challenges overlooked by existing LLM-based methods with a special focus on targeting isolated, function-level verification tasks. To systematically explore and address the significant challenges of verifying entire software repositories, we introduce RVBench, the first verification benchmark explicitly designed for repository-level evaluation, constructed from four diverse and complex open-source Verus projects. We further introduce RagVerus, an extensible framework that synergizes retrieval-augmented generation with context-aware prompting to automate proof synthesis for multi-module repositories. RagVerus triples proof pass rates on existing benchmarks under constrained model inference budgets, and achieves a 27% relative improvement on the more challenging RVBench benchmark, demonstrating a scalable and sample-efficient verification solution.

Large language models demonstrate remarkable reasoning capabilities but often produce unreliable or incorrect responses. Existing verification methods are typically model-specific or domain-restricted, requiring significant computational resources and lacking scalability across diverse reasoning tasks. To address these limitations, we propose VerifiAgent, a unified verification agent that integrates two levels of verification: meta-verification, which assesses completeness and consistency in model responses, and tool-based adaptive verification, where VerifiAgent autonomously selects appropriate verification tools based on the reasoning type, including mathematical, logical, or commonsense reasoning. This adaptive approach ensures both efficiency and robustness across different verification scenarios. Experimental results show that VerifiAgent outperforms baseline verification methods (e.g., deductive verifier, backward verifier) among all reasoning tasks. Additionally, it can further enhance reasoning accuracy by leveraging feedback from verification results. VerifiAgent can also be effectively applied to inference scaling, achieving better results with fewer generated samples and costs compared to existing process reward models in the mathematical reasoning domain. Code is available at https://github.com/Jiuzhouh/VerifiAgent

Recent advancements in tree search algorithms guided by verifiers have significantly enhanced the reasoning capabilities of large language models (LLMs), but at the cost of increased computational resources. In this work, we identify two key challenges contributing to this inefficiency: over-exploration due to redundant states with semantically equivalent content, and under-exploration caused by high variance in verifier scoring leading to frequent trajectory switching. To address these issues, we propose FETCH, an efficient tree search framework, which is a flexible, plug-and-play system compatible with various tree search algorithms. Our framework mitigates over-exploration by merging semantically similar states using agglomerative clustering of text embeddings obtained from a fine-tuned SimCSE model. To tackle under-exploration, we enhance verifiers by incorporating temporal difference learning with adjusted lambda-returns during training to reduce variance, and employing a verifier ensemble to aggregate scores during inference. Experiments on GSM8K, GSM-Plus, and MATH datasets demonstrate that our methods significantly improve reasoning accuracy and computational efficiency across four different tree search algorithms, paving the way for more practical applications of LLM-based reasoning. The code is available at https://github.com/Soistesimmer/Fetch.

State-of-the-art neural network (NN) verifiers demonstrate that applying the branch-and-bound (BaB) procedure with fast bounding techniques plays a key role in tackling many challenging verification properties. In this work, we introduce the linear constraint-driven clipping framework, a class of scalable and efficient methods designed to enhance the efficacy of NN verifiers. Under this framework, we develop two novel algorithms that efficiently utilize linear constraints to 1) reduce portions of the input space that are either verified or irrelevant to a subproblem in the context of branch-and-bound, and 2) directly improve intermediate bounds throughout the network. The process novelly leverages linear constraints that often arise from bound propagation methods and is general enough to also incorporate constraints from other sources. It efficiently handles linear constraints using a specialized GPU procedure that can scale to large neural networks without the use of expensive external solvers. Our verification procedure, Clip-and-Verify, consistently tightens bounds across multiple benchmarks and can significantly reduce the number of subproblems handled during BaB. We show that our clipping algorithms can be integrated with BaB-based verifiers such as α,β-CROWN, utilizing either the split constraints in activation-space BaB or the output constraints that denote the unverified input space. We demonstrate the effectiveness of our procedure on a broad range of benchmarks where, in some instances, we witness a 96% reduction in the number of subproblems during branch-and-bound, and also achieve state-of-the-art verified accuracy across multiple benchmarks. Clip-and-Verify is part of the α,β-CROWN verifier (http://abcrown.org), the VNN-COMP 2025 winner. Code available at https://github.com/Verified-Intelligence/Clip_and_Verify.

The main issue with most evaluation schemes today is their "static" nature: the same problems are reused repeatedly, allowing for memorization, format exploitation, and eventual saturation. To measure genuine AI progress, we need evaluation that is robust by construction, not by post-hoc detection. In response, we propose VeRA (Verified Reasoning Data Augmentation), a framework that converts benchmark problems into executable specifications, comprising (i) a natural language template with placeholder slots, (ii) a coherent generator that samples valid configurations, and (iii) a deterministic verifier that validates parameters and calculates the corresponding correct answers for each configuration. From a single seed problem, VeRA automatically creates unlimited verified variants with reliable labels at near-zero marginal cost without human involvement. VeRA operates in two complementary modes. VeRA-E (equivalent) rewrites problems while keeping the underlying logic intact, useful for detecting memorization versus genuine reasoning. VeRA-H (hardened) systematically increases complexity while remaining verifiable, enabling reliable creation and labelling of fresh difficult tasks at the boundary of intelligence. Evaluating 16 frontier models with VeRA, we find: (i) VeRA-E improves evaluation quality and reveals contamination patterns. (ii) VeRA-H enables human-free generation of hard tasks with reliable labels. (iii) VeRA establishes verified benchmarks as a general paradigm. VeRA reconceptualizes benchmarks from static objects used until exhausted, to executable specifications generating fresh, verified instances on demand, enhancing robustness and cost-effectiveness for evaluation. With VeRA, we envision that evaluation in any verifiable domain can scale indefinitely without sacrificing label integrity. To stimulate future research, we have open-sourced all code and datasets.

Large Language Models (LLMs) have demonstrated remarkable potential in handling complex reasoning tasks by generating step-by-step rationales.Some methods have proven effective in boosting accuracy by introducing extra verifiers to assess these paths. However, existing verifiers, typically trained on binary-labeled reasoning paths, fail to fully utilize the relative merits of intermediate steps, thereby limiting the effectiveness of the feedback provided. To overcome this limitation, we propose Tree-based Preference Learning Verifier (Tree-PLV), a novel approach that constructs reasoning trees via a best-first search algorithm and collects step-level paired data for preference training. Compared to traditional binary classification, step-level preferences more finely capture the nuances between reasoning steps, allowing for a more precise evaluation of the complete reasoning path. We empirically evaluate Tree-PLV across a range of arithmetic and commonsense reasoning tasks, where it significantly outperforms existing benchmarks. For instance, Tree-PLV achieved substantial performance gains over the Mistral-7B self-consistency baseline on GSM8K (67.55% to 82.79%), MATH (17.00% to 26.80%), CSQA (68.14% to 72.97%), and StrategyQA (82.86% to 83.25%).Additionally, our study explores the appropriate granularity for applying preference learning, revealing that step-level guidance provides feedback that better aligns with the evaluation of the reasoning process.

Large language models (LLMs) can generate plausible code but offer limited guarantees of correctness. Formally verifying that implementations satisfy specifications requires constructing machine-checkable proofs, a task that remains beyond current automation. We propose a hierarchical proof search framework for automated code verification in Lean~4 that decomposes complex verification goals into structurally simpler subgoals before attempting tactic-level proving. Central to our approach is a principled decomposition score that combines constructive justification with structural effectiveness. Crucially, this score serves as both the training reward and the inference-time ranking criterion, ensuring strict alignment between optimization and deployment. We train Goedel-Code-Prover-8B, a single unified policy for both decomposition and completion, via supervised initialization followed by hybrid reinforcement learning, where a continuous decomposition reward drives planning exploration while supervised replay stabilizes proof generation. On three Lean-based code verification benchmarks comprising 427 tasks, our 8B-parameter model achieves a 62.0\% prove success rate, a 2.6times improvement over the strongest baseline, surpassing neural provers up to 84times larger. We further observe consistent inference-time scaling: success rates improve monotonically with search iterations and sampling budget, with our trained model achieving greater efficiency than frontier off-the-shelf models of comparable scale.

The proliferation of Large Language Models (LLMs) accessed via black-box APIs introduces a significant trust challenge: users pay for services based on advertised model capabilities (e.g., size, performance), but providers may covertly substitute the specified model with a cheaper, lower-quality alternative to reduce operational costs. This lack of transparency undermines fairness, erodes trust, and complicates reliable benchmarking. Detecting such substitutions is difficult due to the black-box nature, typically limiting interaction to input-output queries. This paper formalizes the problem of model substitution detection in LLM APIs. We systematically evaluate existing verification techniques, including output-based statistical tests, benchmark evaluations, and log probability analysis, under various realistic attack scenarios like model quantization, randomized substitution, and benchmark evasion. Our findings reveal the limitations of methods relying solely on text outputs, especially against subtle or adaptive attacks. While log probability analysis offers stronger guarantees when available, its accessibility is often limited. We conclude by discussing the potential of hardware-based solutions like Trusted Execution Environments (TEEs) as a pathway towards provable model integrity, highlighting the trade-offs between security, performance, and provider adoption. Code is available at https://github.com/sunblaze-ucb/llm-api-audit

This paper presents a quantitative program verification infrastructure for discrete probabilistic programs. Our infrastructure can be viewed as the probabilistic analogue of Boogie: its central components are an intermediate verification language (IVL) together with a real-valued logic. Our IVL provides a programming-language-style for expressing verification conditions whose validity implies the correctness of a program under investigation. As our focus is on verifying quantitative properties such as bounds on expected outcomes, expected run-times, or termination probabilities, off-the-shelf IVLs based on Boolean first-order logic do not suffice. Instead, a paradigm shift from the standard Boolean to a real-valued domain is required. Our IVL features quantitative generalizations of standard verification constructs such as assume- and assert-statements. Verification conditions are generated by a weakest-precondition-style semantics, based on our real-valued logic. We show that our verification infrastructure supports natural encodings of numerous verification techniques from the literature. With our SMT-based implementation, we automatically verify a variety of benchmarks. To the best of our knowledge, this establishes the first deductive verification infrastructure for expectation-based reasoning about probabilistic programs.

Despite substantial progress in fact-verification benchmarks, claims grounded in large-scale structured data remain underexplored. In this work, we introduce ClaimDB, the first fact-verification benchmark where the evidence for claims is derived from compositions of millions of records and multiple tables. ClaimDB consists of 80 unique real-life databases covering a wide range of domains, from governance and healthcare to media, education and the natural sciences. At this scale, verification approaches that rely on "reading" the evidence break down, forcing a timely shift toward reasoning in executable programs. We conduct extensive experiments with 30 state-of-the-art proprietary and open-source (below 70B) LLMs and find that none exceed 83% accuracy, with more than half below 55%. Our analysis also reveals that both closed- and open-source models struggle with abstention -- the ability to admit that there is no evidence to decide -- raising doubts about their reliability in high-stakes data analysis. We release the benchmark, code, and the LLM leaderboard at https://claimdb.github.io .

Claim verification is essential in combating misinformation, and large language models (LLMs) have recently emerged in this area as powerful tools for assessing the veracity of claims using external knowledge. Existing LLM-based methods for claim verification typically adopt a Decompose-Then-Verify paradigm, which involves decomposing complex claims into several independent sub-claims and verifying each sub-claim separately. However, this paradigm often introduces errors during the claim decomposition process. To mitigate these errors, we propose to develop the Chain-of-Thought (CoT)-Verify paradigm, which leverages LLM reasoning methods to generate CoT-verification paths for the original complex claim without requiring decompositions into sub-claims and separate verification stages. The CoT-Verify paradigm allows us to propose a natural fine-tuning method called Reasoning-CV to enhance the verification capabilities in LLMs. Reasoning-CV includes a supervised fine-tuning (SFT) stage and a self-improvement direct preference optimization (DPO) stage. Utilizing only an 8B pre-trained LLM, Reasoning-CV demonstrates superior knowledge-assisted claim verification performances compared to existing Decompose-Then-Verify methods, as well as powerful black-box LLMs such as GPT-4o+CoT and o1-preview. Our code is available.

Automated code generation with large language models has gained significant traction, but there remains no guarantee on the correctness of generated code. We aim to use formal verification to provide mathematical guarantees that the generated code is correct. However, generating formally verified code with LLMs is hindered by the scarcity of training data and the complexity of formal proofs. To tackle this challenge, we introduce AlphaVerus, a self-improving framework that bootstraps formally verified code generation by iteratively translating programs from a higher-resource language and leveraging feedback from a verifier. AlphaVerus operates in three phases: exploration of candidate translations, Treefinement -- a novel tree search algorithm for program refinement using verifier feedback, and filtering misaligned specifications and programs to prevent reward hacking. Through this iterative process, AlphaVerus enables a LLaMA-3.1-70B model to generate verified code without human intervention or model finetuning. AlphaVerus shows an ability to generate formally verified solutions for HumanEval and MBPP, laying the groundwork for truly trustworthy code-generation agents.

Humanity's Last Exam (HLE) has become a widely used benchmark for evaluating frontier large language models on challenging, multi-domain questions. However, community-led analyses have raised concerns that HLE contains a non-trivial number of noisy items, which can bias evaluation results and distort cross-model comparisons. To address this challenge, we introduce HLE-Verified, a verified and revised version of HLE with a transparent verification protocol and fine-grained error taxonomy. Our construction follows a two-stage validation-and-repair workflow resulting in a certified benchmark. In Stage I, each item undergoes binary validation of the problem and final answer through domain-expert review and model-based cross-checks, yielding 641 verified items. In Stage II, flawed but fixable items are revised under strict constraints preserving the original evaluation intent, through dual independent expert repairs, model-assisted auditing, and final adjudication, resulting in 1,170 revised-and-certified items. The remaining 689 items are released as a documented uncertain set with explicit uncertainty sources and expertise tags for future refinement. We evaluate seven state-of-the-art language models on HLE and HLE-Verified, observing an average absolute accuracy gain of 7--10 percentage points on HLE-Verified. The improvement is particularly pronounced on items where the original problem statement and/or reference answer is erroneous, with gains of 30--40 percentage points. Our analyses further reveal a strong association between model confidence and the presence of errors in the problem statement or reference answer, supporting the effectiveness of our revisions. Overall, HLE-Verified improves HLE-style evaluations by reducing annotation noise and enabling more faithful measurement of model capabilities. Data is available at: https://github.com/SKYLENAGE-AI/HLE-Verified

Large language models (LLMs) increasingly rely on reinforcement learning (RL) to enhance their reasoning capabilities through feedback. A critical challenge is verifying the consistency of model-generated responses and reference answers, since these responses are often lengthy, diverse, and nuanced. Rule-based verifiers struggle with complexity, prompting the use of model-based verifiers. However, specialized verifiers lack flexibility, while general LLM judges can be inconsistent. Existing research primarily focuses on building better verifiers, yet a systematic evaluation of different types of verifiers' performance across domains remains lacking, severely constraining the reliable development of Reinforcement Learning with Verifiable Reward (RLVR). To address this, we propose VerifyBench--a cross-domain comprehensive benchmark for systematically evaluating verifiers. We construct 4,000 expert-level questions covering mathematics, physics, chemistry, and biology. Each question is equipped with reference answers and diverse responses. The reliability of the evaluation is ensured through a rigorous annotation process conducted by a multidisciplinary expert team. We design a four-dimensional experimental framework to comprehensively compare the performance boundaries of specialized verifiers and general LLMs under combined conditions of extracted answers vs. complete responses, and short vs. long outputs. Our evaluation uncovers fundamental trade-offs in verifiers: while specialized verifiers achieve leading accuracy, they exhibit deficiencies in recall; general models show stronger inclusivity but unstable precision. More importantly, we discover verifiers' high sensitivity to input structure and inherent limitations in cross-domain generalization, providing critical insights into the bottlenecks of current verifier technology.

Large Language Models (LLMs) have achieved significant advances in reasoning tasks. A key approach is tree-based search with verifiers, which expand candidate reasoning paths and use reward models to guide pruning and selection. Although effective in improving accuracy, these methods are not optimal in terms of efficiency: they perform simple decomposition on the reasoning process, but ignore the planning-execution nature of tasks such as math reasoning or code generation. This results in inefficient exploration of reasoning process. To address this, we propose a dual-phase test-time scaling framework that explicitly separates reasoning into planning and execution, and performs search over the two phases individually. Specifically, we decompose reasoning trajectories and develop reward models for each phase, enabling the search to explore and prune plans and executions separately. We further introduce a dynamic budget allocation mechanism that adaptively redistributes sampling effort based on reward feedback, allowing early stopping on confident steps and reallocation of computation to more challenging parts of the reasoning process. Experiments on both mathematical reasoning and code generation benchmarks demonstrate that our approach consistently improves accuracy while reducing redundant computation.

Answer verification methods are widely employed in language model training pipelines spanning data curation, evaluation, and reinforcement learning with verifiable rewards (RLVR). While prior work focus on developing unified verifiers applicable across multiple reasoning scenarios, significant challenges remain in computation-oriented scientific domains, such as algebraic equivalence checking and physical constant substitution. In this paper, we introduce \model, a tool-augmented verifier that leverages external executors to perform precise computations and symbolic simplifications. \model enables robust verification that goes beyond simple semantic matching. We propose a novel two-stage pipeline, which begin with cold-start fine-tuning and followed by multi-turn reinforcement learning with tool integration. Extensive experiments conducted on STEM subjects, general QA, and long-form reasoning tasks demonstrates strong generalization of \model. The results shows that the \model achieves state-of-the-art performance on VerifyBench-Hard and SCI-Bench. And we also employ our \model in RLVR as a reward model, the results show that it consistently outperforms both rubric-based and model-based verifiers on AIME'24 and AIME'25, demonstrating strong potential to enhance reasoning capabilities of LLM. Our model is released at https://huggingface.co/Nanbeige/CoSineVerifier-Tool-4B{https://huggingface.co/Nanbeige/CoSineVerifier-Tool-4B}.

For humans to trust the fluent generations of large language models (LLMs), they must be able to verify their correctness against trusted, external sources. Recent efforts aim to increase verifiability through citations of retrieved documents or post-hoc provenance. However, such citations are prone to mistakes that further complicate their verifiability. To address these limitations, we tackle the verifiability goal with a different philosophy: we trivialize the verification process by developing models that quote verbatim statements from trusted sources in pre-training data. We propose Quote-Tuning, which demonstrates the feasibility of aligning LLMs to leverage memorized information and quote from pre-training data. Quote-Tuning quantifies quoting against large corpora with efficient membership inference tools, and uses the amount of quotes as an implicit reward signal to construct a synthetic preference dataset for quoting, without any human annotation. Next, the target model is aligned to quote using preference optimization algorithms. Experimental results show that Quote-Tuning significantly increases the percentage of LLM generation quoted verbatim from high-quality pre-training documents by 55% to 130% relative to untuned models while maintaining response quality. Further experiments demonstrate that Quote-Tuning generalizes quoting to out-of-domain data, is applicable in different tasks, and provides additional benefits to truthfulness. Quote-Tuning not only serves as a hassle-free method to increase quoting but also opens up avenues for improving LLM trustworthiness through better verifiability.

Large Language Models (LLMs) are accelerating scientific idea generation, but rigorously evaluating these numerous, often superficial, AI-generated propositions for novelty and factual accuracy is a critical bottleneck; manual verification is too slow. Existing validation methods are inadequate: LLMs as standalone verifiers may hallucinate and lack domain knowledge (our findings show 60% unawareness of relevant papers in specific domains), while traditional citation networks lack explicit causality and narrative surveys are unstructured. This underscores a core challenge: the absence of structured, verifiable, and causally-linked historical data of scientific evolution.To address this,we introduce THE-Tree (Technology History Evolution Tree), a computational framework that constructs such domain-specific evolution trees from scientific literature. THE-Tree employs a search algorithm to explore evolutionary paths. During its node expansion, it utilizes a novel "Think-Verbalize-Cite-Verify" process: an LLM proposes potential advancements and cites supporting literature. Critically, each proposed evolutionary link is then validated for logical coherence and evidential support by a recovered natural language inference mechanism that interrogates the cited literature, ensuring that each step is grounded. We construct and validate 88 THE-Trees across diverse domains and release a benchmark dataset including up to 71k fact verifications covering 27k papers to foster further research. Experiments demonstrate that i) in graph completion, our THE-Tree improves hit@1 by 8% to 14% across multiple models compared to traditional citation networks; ii) for predicting future scientific developments, it improves hit@1 metric by nearly 10%; and iii) when combined with other methods, it boosts the performance of evaluating important scientific papers by almost 100%.

Semi-structured tables, widely used in real-world applications (e.g., financial reports, medical records, transactional orders), often involve flexible and complex layouts (e.g., hierarchical headers and merged cells). These tables generally rely on human analysts to interpret table layouts and answer relevant natural language questions, which is costly and inefficient. To automate the procedure, existing methods face significant challenges. First, methods like NL2SQL require converting semi-structured tables into structured ones, which often causes substantial information loss. Second, methods like NL2Code and multi-modal LLM QA struggle to understand the complex layouts of semi-structured tables and cannot accurately answer corresponding questions. To this end, we propose ST-Raptor, a tree-based framework for semi-structured table question answering using large language models. First, we introduce the Hierarchical Orthogonal Tree (HO-Tree), a structural model that captures complex semi-structured table layouts, along with an effective algorithm for constructing the tree. Second, we define a set of basic tree operations to guide LLMs in executing common QA tasks. Given a user question, ST-Raptor decomposes it into simpler sub-questions, generates corresponding tree operation pipelines, and conducts operation-table alignment for accurate pipeline execution. Third, we incorporate a two-stage verification mechanism: forward validation checks the correctness of execution steps, while backward validation evaluates answer reliability by reconstructing queries from predicted answers. To benchmark the performance, we present SSTQA, a dataset of 764 questions over 102 real-world semi-structured tables. Experiments show that ST-Raptor outperforms nine baselines by up to 20% in answer accuracy. The code is available at https://github.com/weAIDB/ST-Raptor.

Code verification has recently found great success as a critical component in training large scale reasoning models for coding. Synthetic techniques such as self-generated test cases and reward models provide a way to enhance code capabilities beyond predefined tests. Building on these advancements, we propose new benchmarks designed to systematically evaluate the impact of synthetic verification methods on assessing solution correctness. We introduce HE-R, HE-R+, MBPP-R, and MBPP-R+, which transform existing coding benchmarks into scoring and ranking datasets to evaluate the effectiveness of synthetic verifiers. Using these benchmarks, we analyze synthetic verification methods in standard, reasoning-based, and reward-based LLMs. Our results show that recent reasoning models significantly improve test case generation and that scaling test cases enhances verification accuracy.

Verification is crucial for effective mathematical reasoning. We present a new temporal consistency method where verifiers iteratively refine their judgments based on the previous assessment. Unlike one-round verification or multi-model debate approaches, our method leverages consistency in a sequence of self-reflection actions to improve verification accuracy. Empirical evaluations across diverse mathematical process error identification benchmarks (Mathcheck, ProcessBench, and PRM800K) show consistent performance improvements over baseline methods. When applied to the recent DeepSeek R1 distilled models, our method demonstrates strong performance, enabling 7B/8B distilled models to outperform all 70B/72B models and GPT-4o on ProcessBench. Notably, the distilled 14B model with our method achieves performance comparable to Deepseek-R1. Our codes are available at https://github.com/jcguo123/Temporal-Consistency

Test-time scaling (TTS) has proven effective in enhancing the reasoning capabilities of large language models (LLMs). Verification plays a key role in TTS, simultaneously influencing (1) reasoning performance and (2) compute efficiency, due to the quality and computational cost of verification. In this work, we challenge the conventional paradigms of verification, and make the first attempt toward systematically investigating the impact of verification granularity-that is, how frequently the verifier is invoked during generation, beyond verifying only the final output or individual generation steps. To this end, we introduce Variable Granularity Search (VG-Search), a unified algorithm that generalizes beam search and Best-of-N sampling via a tunable granularity parameter g. Extensive experiments with VG-Search under varying compute budgets, generator-verifier configurations, and task attributes reveal that dynamically selecting g can improve the compute efficiency and scaling behavior. Building on these findings, we propose adaptive VG-Search strategies that achieve accuracy gains of up to 3.1\% over Beam Search and 3.6\% over Best-of-N, while reducing FLOPs by over 52\%. We will open-source the code to support future research.

Chain-of-Thought (CoT) prompting has become the de facto method to elicit reasoning capabilities from large language models (LLMs). However, to mitigate hallucinations in CoT that are notoriously difficult to detect, current methods such as process reward models (PRMs) or self-consistency operate as opaque boxes and do not provide checkable evidence for their judgments, possibly limiting their effectiveness. To address this issue, we draw inspiration from the idea that "the gold standard for supporting a mathematical claim is to provide a proof". We propose a retrospective, step-aware formal verification framework Safe. Rather than assigning arbitrary scores, we strive to articulate mathematical claims in formal mathematical language Lean 4 at each reasoning step and provide formal proofs to identify hallucinations. We evaluate our framework Safe across multiple language models and various mathematical datasets, demonstrating a significant performance improvement while offering interpretable and verifiable evidence. We also propose FormalStep as a benchmark for step correctness theorem proving with 30,809 formal statements. To the best of our knowledge, our work represents the first endeavor to utilize formal mathematical language Lean 4 for verifying natural language content generated by LLMs, aligning with the reason why formal mathematical languages were created in the first place: to provide a robust foundation for hallucination-prone human-written proofs.

Large language model (LLM)-based reasoning systems have recently achieved gold medal-level performance in the IMO 2025 competition, writing mathematical proofs where, to receive full credit, each step must be not only correct but also sufficiently supported. To train LLM-based reasoners in such challenging, open-ended settings, strong verifiers capable of catching step-level mistakes are necessary prerequisites. We introduce Hard2Verify, a human-annotated, step-level verification benchmark produced with over 500 hours of human labor. Hard2Verify is designed to rigorously assess step-level verifiers at the frontier: Verifiers must provide step-level annotations or identify the first error in responses generated by frontier LLMs for very recent, challenging, and open-ended math questions. We evaluate 29 generative critics and process reward models, demonstrating that, beyond a few standouts, open-source verifiers lag closed source models. We subsequently analyze what drives poor performance in step-level verification, the impacts of scaling verifier compute, as well as fundamental questions such as self-verification and verification-generation dynamics.

Scaling automated formal verification to real-world projects requires resolving cross-module dependencies and global contexts, which are challenges overlooked by existing function-centric methods. We introduce RagVerus, a framework that synergizes retrieval-augmented generation with context-aware prompting to automate proof synthesis for multi-module repositories, achieving a 27% relative improvement on our novel RepoVBench benchmark -- the first repository-level dataset for Verus with 383 proof completion tasks. RagVerus triples proof pass rates on existing benchmarks under constrained language model budgets, demonstrating a scalable and sample-efficient verification.

Large Reasoning Models (LRMs) achieve strong performance by generating long reasoning traces with reflection. Through a large-scale empirical analysis, we find that a substantial fraction of reflective steps consist of self-verification (recheck) that repeatedly confirm intermediate results. These rechecks occur frequently across models and benchmarks, yet the vast majority are confirmatory rather than corrective, rarely identifying errors and altering reasoning outcomes. This reveals a mismatch between how often self-verification is activated and how often it is actually useful. Motivated by this, we propose a novel, experience-driven test-time framework that reduces the overused verification. Our method detects the activation of recheck behavior, consults an offline experience pool of past verification outcomes, and estimates whether a recheck is likely unnecessary via efficient retrieval. When historical experience suggests unnecessary, a suppression signal redirects the model to proceed. Across multiple model and benchmarks, our approach reduces token usage up to 20.3% while maintaining the accuracy, and in some datasets even yields accuracy improvements.

Due to the expanding capabilities and pre-training data, Large Language Models (LLMs) are facing increasingly serious evaluation challenges. On one hand, the data leakage issue cause over-estimation on existing benchmarks. On the other hand, periodically curating datasets manually is costly. In this paper, we propose to automate dataset updates for reliable and timely evaluation. The basic idea is to generate unseen and high-quality testing samples based on existing ones to mitigate leakage issues. In specific, we propose two strategies with systematically verification. First, the mimicking strategy employs LLMs to create new samples resembling existing ones, to the maximum extent preserving the stylistic of the original dataset. Our experiments demonstrate its evaluation stability across multiple instantiations and its effectiveness in dealing with data leakage issues in most cases. Second, for the cases that mimicking dataset works poorly, we design an extending strategy that adjusts the difficulty of the generated samples according to varying cognitive levels. This not only makes our evaluation more systematic, but also, with a balanced difficulty, even discern model capabilities better at fine-grained levels.

Loop invariants are fundamental to reasoning about programs with loops. They establish properties about a given loop's behavior. When they additionally are inductive, they become useful for the task of formal verification that seeks to establish strong mathematical guarantees about program's runtime behavior. The inductiveness ensures that the invariants can be checked locally without consulting the entire program, thus are indispensable artifacts in a formal proof of correctness. Finding inductive loop invariants is an undecidable problem, and despite a long history of research towards practical solutions, it remains far from a solved problem. This paper investigates the capabilities of the Large Language Models (LLMs) in offering a new solution towards this old, yet important problem. To that end, we first curate a dataset of verification problems on programs with loops. Next, we design a prompt for exploiting LLMs, obtaining inductive loop invariants, that are checked for correctness using sound symbolic tools. Finally, we explore the effectiveness of using an efficient combination of a symbolic tool and an LLM on our dataset and compare it against a purely symbolic baseline. Our results demonstrate that LLMs can help improve the state-of-the-art in automated program verification.

Synthesizing inductive loop invariants is fundamental to automating program verification. In this work, we observe that Large Language Models (such as gpt-3.5 or gpt-4) are capable of synthesizing loop invariants for a class of programs in a 0-shot setting, yet require several samples to generate the correct invariants. This can lead to a large number of calls to a program verifier to establish an invariant. To address this issue, we propose a {\it re-ranking} approach for the generated results of LLMs. We have designed a ranker that can distinguish between correct inductive invariants and incorrect attempts based on the problem definition. The ranker is optimized as a contrastive ranker. Experimental results demonstrate that this re-ranking mechanism significantly improves the ranking of correct invariants among the generated candidates, leading to a notable reduction in the number of calls to a verifier.

We propose an online training procedure for a transformer-based automated theorem prover. Our approach leverages a new search algorithm, HyperTree Proof Search (HTPS), inspired by the recent success of AlphaZero. Our model learns from previous proof searches through online training, allowing it to generalize to domains far from the training distribution. We report detailed ablations of our pipeline's main components by studying performance on three environments of increasing complexity. In particular, we show that with HTPS alone, a model trained on annotated proofs manages to prove 65.4% of a held-out set of Metamath theorems, significantly outperforming the previous state of the art of 56.5% by GPT-f. Online training on these unproved theorems increases accuracy to 82.6%. With a similar computational budget, we improve the state of the art on the Lean-based miniF2F-curriculum dataset from 31% to 42% proving accuracy.

Formally verifying properties of software code has been a highly desirable task, especially with the emergence of LLM-generated code. In the same vein, they provide an interesting avenue for the exploration of formal verification and mechanistic interpretability. Since the introduction of code-specific models, despite their successes in generating code in Lean4 and Isabelle, the task of generalized theorem proving still remains far from being fully solved and will be a benchmark for reasoning capability in LLMs. In this work, we introduce a framework that generates whole proofs in a formal language to be used within systems that utilize the power of built-in tactics and off-the-shelf automated theorem provers. Our framework includes 3 components: generating natural language statements of the code to be verified, an LLM that generates formal proofs for the given statement, and a module employing heuristics for building the final proof. To train the LLM, we employ a 2-stage fine-tuning process, where we first use SFT-based training to enable the model to generate syntactically correct Isabelle code and then RL-based training that encourages the model to generate proofs verified by a theorem prover. We validate our framework using the miniF2F-test benchmark and the Isabelle proof assistant and design a use case to verify the correctness of the AWS S3 bucket access policy code. We also curate a dataset based on the FVEL\textnormal{ER} dataset for future training tasks.

Large Language Models (LLMs) have exploded a new heatwave of AI, for their ability to engage end-users in human-level conversations with detailed and articulate answers across many knowledge domains. In response to their fast adoption in many industrial applications, this survey concerns their safety and trustworthiness. First, we review known vulnerabilities of the LLMs, categorising them into inherent issues, intended attacks, and unintended bugs. Then, we consider if and how the Verification and Validation (V&V) techniques, which have been widely developed for traditional software and deep learning models such as convolutional neural networks, can be integrated and further extended throughout the lifecycle of the LLMs to provide rigorous analysis to the safety and trustworthiness of LLMs and their applications. Specifically, we consider four complementary techniques: falsification and evaluation, verification, runtime monitoring, and ethical use. Considering the fast development of LLMs, this survey does not intend to be complete (although it includes 300 references), especially when it comes to the applications of LLMs in various domains, but rather a collection of organised literature reviews and discussions to support the quick understanding of the safety and trustworthiness issues from the perspective of V&V.

Formal verification is the next frontier for ensuring the correctness of code generated by Large Language Models (LLMs). While methods that co-generate code and formal specifications in formal languages, like Dafny, can, in principle, prove alignment with user intent, progress is bottlenecked by specification quality evaluation. Current benchmarks rely on matching against ground-truth specifications, a manual and expertise-intensive process that has limited existing datasets to a few hundred simple problems and also suffers from a reliability issue. To address this, we introduce VeriEquivBench, a new benchmark with 2,389 complex algorithmic problems that probe the limitations of current models in both code generation and formal reasoning. Our evaluation framework replaces ground-truth matching with a formally grounded metric, the equivalence score, and rigorously verifies the quality of generated specifications and code. Our results show that generating formally verifiable code remains a profound challenge for state-of-the-art LLMs. This underscores both the difficulty of the task and the need for benchmarks like VeriEquivBench to drive progress toward scalable and reliable coding agents.

Code LLMs still struggle with code execution reasoning, especially in smaller models. Existing methods rely on supervised fine-tuning (SFT) with teacher-generated explanations, primarily in two forms: (1) input-output (I/O) prediction chains and (2) natural-language descriptions of execution traces. However, intermediate execution steps cannot be explicitly verified during SFT, so the training objective can reduce to merely matching teacher explanations. Moreover, training data is typically collected without explicit control over task difficulty. We introduce ExecVerify, which goes beyond text imitation by incorporating verifiable white-box rewards derived from execution traces, including next-statement prediction and variable value/type prediction. Our work first builds a dataset with multiple difficulty levels via constraint-based program synthesis. Then, we apply reinforcement learning (RL) to reward correct answers about both intermediate execution steps and final outputs, aligning the training objective with semantic correctness at each execution step. Finally, we adopt a two-stage training pipeline that first enhances execution reasoning and then transfers to code generation. Experiments demonstrate that a 7B model trained with ExecVerify achieves performance comparable to 32B models on code reasoning benchmarks and improves pass@1 by up to 5.9\% on code generation tasks over strong post-training baselines.

Formal verification can provably guarantee the correctness of critical system software, but the high proof burden has long hindered its wide adoption. Recently, Large Language Models (LLMs) have shown success in code analysis and synthesis. In this paper, we present a combination of LLMs and static analysis to synthesize invariants, assertions, and other proof structures for a Rust-based formal verification framework called Verus. In a few-shot setting, LLMs demonstrate impressive logical ability in generating postconditions and loop invariants, especially when analyzing short code snippets. However, LLMs lack the ability to retain and propagate context information, a strength of traditional static analysis. Based on these observations, we developed a prototype based on OpenAI's GPT-4 model. Our prototype decomposes the verification task into multiple smaller ones, iteratively queries GPT-4, and combines its output with lightweight static analysis. We evaluated the prototype with a developer in the automation loop on 20 vector-manipulating programs. The results demonstrate that it significantly reduces human effort in writing entry-level proof code.

Recent advances have shown that scaling test-time computation enables large language models (LLMs) to solve increasingly complex problems across diverse domains. One effective paradigm for test-time scaling (TTS) involves LLM generators producing multiple solution candidates, with LLM verifiers assessing the correctness of these candidates without reference answers. In this paper, we study generative verifiers, which perform verification by generating chain-of-thought (CoT) reasoning followed by a binary verdict. We systematically analyze verification dynamics across three dimensions - problem difficulty, generator capability, and verifier generation capability - with empirical studies on 12 benchmarks across mathematical reasoning, knowledge, and natural language reasoning tasks using 14 open-source models (2B to 72B parameter range) and GPT-4o. Our experiments reveal three key findings about verification effectiveness: (1) Easy problems allow verifiers to more reliably certify correct responses; (2) Weak generators produce errors that are easier to detect than strong generators; (3) Verification ability is generally correlated with the verifier's own problem-solving capability, but this relationship varies with problem difficulty. These findings reveal opportunities to optimize basic verification strategies in TTS applications. First, given the same verifier, some weak generators can nearly match stronger ones in post-verification TTS performance (e.g., the Gemma2-9B to Gemma2-27B performance gap shrinks by 75.5%). Second, we identify cases where strong verifiers offer limited advantage over weak ones, as both fail to provide meaningful verification gains, suggesting that verifier scaling alone cannot overcome fundamental verification challenges.

Large language models for code generation increasingly rely on synthetic data, where both problem solutions and verification tests are generated by models. While this enables scalable data creation, it introduces a previously unexplored bottleneck: the verification ceiling, in which the quality and diversity of training data are fundamentally constrained by the capabilities of synthetic verifiers. In this work, we systematically study how verification design and strategies influence model performance. We investigate (i) what we verify by analyzing the impact of test complexity and quantity: richer test suites improve code generation capabilities (on average +3 pass@1), while quantity alone yields diminishing returns, (ii) how we verify by exploring relaxed pass thresholds: rigid 100% pass criteria can be overly restrictive. By allowing for relaxed thresholds or incorporating LLM-based soft verification, we can recover valuable training data, leading to a 2-4 point improvement in pass@1 performance. However, this benefit is contingent upon the strength and diversity of the test cases used, and (iii) why verification remains necessary through controlled comparisons of formally correct versus incorrect solutions and human evaluation: retaining diverse correct solutions per problem yields consistent generalization gains. Our results show that Verification as currently practiced is too rigid, filtering out valuable diversity. But it cannot be discarded, only recalibrated. By combining calibrated verification with diverse, challenging problem-solution pairs, we outline a path to break the verification ceiling and unlock stronger code generation models.

We introduce HunyuanProver, an language model finetuned from the Hunyuan 7B for interactive automatic theorem proving with LEAN4. To alleviate the data sparsity issue, we design a scalable framework to iterative synthesize data with low cost. Besides, guided tree search algorithms are designed to enable effective ``system 2 thinking`` of the prover. HunyuanProver achieves state-of-the-art (SOTA) performances on major benchmarks. Specifically, it achieves a pass of 68.4% on the miniF2F-test compared to 65.9%, the current SOTA results. It proves 4 IMO statements (imo_1960_p2, imo_1962_p2}, imo_1964_p2 and imo_1983_p6) in miniF2F-test. To benefit the community, we will open-source a dataset of 30k synthesized instances, where each instance contains the original question in natural language, the converted statement by autoformalization, and the proof by HunyuanProver.

Assurance cases can be used to argue for the safety of products in safety engineering. In safety-critical areas, the construction of assurance cases is indispensable. Trustworthiness Derivation Trees (TDTs) enhance assurance cases by incorporating formal methods, rendering it possible for automatic reasoning about assurance cases. We present Trustworthiness Derivation Tree Analyzer (Trusta), a desktop application designed to automatically construct and verify TDTs. The tool has a built-in Prolog interpreter in its backend, and is supported by the constraint solvers Z3 and MONA. Therefore, it can solve constraints about logical formulas involving arithmetic, sets, Horn clauses etc. Trusta also utilizes large language models to make the creation and evaluation of assurance cases more convenient. It allows for interactive human examination and modification. We evaluated top language models like ChatGPT-3.5, ChatGPT-4, and PaLM 2 for generating assurance cases. Our tests showed a 50%-80% similarity between machine-generated and human-created cases. In addition, Trusta can extract formal constraints from text in natural languages, facilitating an easier interpretation and validation process. This extraction is subject to human review and correction, blending the best of automated efficiency with human insight. To our knowledge, this marks the first integration of large language models in automatic creating and reasoning about assurance cases, bringing a novel approach to a traditional challenge. Through several industrial case studies, Trusta has proven to quickly find some subtle issues that are typically missed in manual inspection, demonstrating its practical value in enhancing the assurance case development process.

In this paper we present a novel solution that combines the capabilities of Large Language Models (LLMs) with Formal Verification strategies to verify and automatically repair software vulnerabilities. Initially, we employ Bounded Model Checking (BMC) to locate the software vulnerability and derive a counterexample. The counterexample provides evidence that the system behaves incorrectly or contains a vulnerability. The counterexample that has been detected, along with the source code, are provided to the LLM engine. Our approach involves establishing a specialized prompt language for conducting code debugging and generation to understand the vulnerability's root cause and repair the code. Finally, we use BMC to verify the corrected version of the code generated by the LLM. As a proof of concept, we create ESBMC-AI based on the Efficient SMT-based Context-Bounded Model Checker (ESBMC) and a pre-trained Transformer model, specifically gpt-3.5-turbo, to detect and fix errors in C programs. Our experimentation involved generating a dataset comprising 1000 C code samples, each consisting of 20 to 50 lines of code. Notably, our proposed method achieved an impressive success rate of up to 80% in repairing vulnerable code encompassing buffer overflow and pointer dereference failures. We assert that this automated approach can effectively incorporate into the software development lifecycle's continuous integration and deployment (CI/CD) process.

One core capability of Large Language Models (LLMs) is to follow natural language instructions. However, the evaluation of such abilities is not standardized: Human evaluations are expensive, slow, and not objectively reproducible, while LLM-based auto-evaluation is potentially biased or limited by the ability of the evaluator LLM. To overcome these issues, we introduce Instruction-Following Eval (IFEval) for large language models. IFEval is a straightforward and easy-to-reproduce evaluation benchmark. It focuses on a set of "verifiable instructions" such as "write in more than 400 words" and "mention the keyword of AI at least 3 times". We identified 25 types of those verifiable instructions and constructed around 500 prompts, with each prompt containing one or more verifiable instructions. We show evaluation results of two widely available LLMs on the market. Our code and data can be found at https://github.com/google-research/google-research/tree/master/instruction_following_eval

JSON Schema is an important, evolving standard schema language for families of JSON documents. It is based on a complex combination of structural and Boolean assertions, and features negation and recursion. The static analysis of JSON Schema documents comprises practically relevant problems, including schema satisfiability, inclusion, and equivalence. These three problems can be reduced to witness generation: given a schema, generate an element of the schema, if it exists, and report failure otherwise. Schema satisfiability, inclusion, and equivalence have been shown to be decidable, by reduction to reachability in alternating tree automata. However, no witness generation algorithm has yet been formally described. We contribute a first, direct algorithm for JSON Schema witness generation. We study its effectiveness and efficiency, in experiments over several schema collections, including thousands of real-world schemas. Our focus is on the completeness of the language, where we only exclude the uniqueItems operator, and on the ability of the algorithm to run in a reasonable time on a large set of real-world examples, despite the exponential complexity of the underlying problem.

Reasoning methods such as chain-of-thought prompting and self-consistency have shown immense potential to improve the accuracy of large language models across various reasoning tasks. However such methods involve generation of lengthy reasoning chains, which substantially increases token consumption, computational cost, and latency. To address this inefficiency, we propose ProofSketch, a verification-guided reasoning framework that integrates symbolic closure computation, lexicographic verification and adaptive sketch generation. Our experiments show that ProofSketch consistently reduces token usage while improving accuracy, demonstrating that this approach offers a promising path for efficient and trustworthy reasoning.

The performance of autonomous Web GUI agents heavily relies on the quality and quantity of their training data. However, a fundamental bottleneck persists: collecting interaction trajectories from real-world websites is expensive and difficult to verify. The underlying state transitions are hidden, leading to reliance on inconsistent and costly external verifiers to evaluate step-level correctness. To address this, we propose AutoWebWorld, a novel framework for synthesizing controllable and verifiable web environments by modeling them as Finite State Machines (FSMs) and use coding agents to translate FSMs into interactive websites. Unlike real websites, where state transitions are implicit, AutoWebWorld explicitly defines all states, actions, and transition rules. This enables programmatic verification: action correctness is checked against predefined rules, and task success is confirmed by reaching a goal state in the FSM graph. AutoWebWorld enables a fully automated search-and-verify pipeline, generating over 11,663 verified trajectories from 29 diverse web environments at only $0.04 per trajectory. Training on this synthetic data significantly boosts real-world performance. Our 7B Web GUI agent outperforms all baselines within 15 steps on WebVoyager. Furthermore, we observe a clear scaling law: as the synthetic data volume increases, performance on WebVoyager and Online-Mind2Web consistently improves.

As large language models (LLMs) transition from research prototypes to production systems, practitioners often need reliable methods to verify that model outputs satisfy required constraints. While sampling-based estimates provide an intuition of model behavior, they offer no sound guarantees. We present BEAVER, the first practical framework for computing deterministic, sound probability bounds on LLM constraint satisfaction. Given any prefix-closed semantic constraint, BEAVER systematically explores the generation space using novel token trie and frontier data structures, maintaining provably sound bounds at every iteration. We formalize the verification problem, prove soundness of our approach, and evaluate BEAVER on correctness verification, privacy verification and secure code generation tasks across multiple state of the art LLMs. BEAVER achieves 6 to 8 times tighter probability bounds and identifies 3 to 4 times more high risk instances compared to baseline methods under identical computational budgets, enabling precise characterization and risk assessment that loose bounds or empirical evaluation cannot provide.

As Large Language Models (LLMs) have made significant advancements across various tasks, such as question answering, translation, text summarization, and dialogue systems, the need for accuracy in information becomes crucial, especially for serious financial products serving billions of users like Alipay. To address this, Alipay has developed a Retrieval-Augmented Generation (RAG) system that grounds LLMs on the most accurate and up-to-date information. However, for a real-world product serving millions of users, the inference speed of LLMs becomes a critical factor compared to a mere experimental model. Hence, this paper presents a generic framework for accelerating the inference process, resulting in a substantial increase in speed and cost reduction for our RAG system, with lossless generation accuracy. In the traditional inference process, each token is generated sequentially by the LLM, leading to a time consumption proportional to the number of generated tokens. To enhance this process, our framework, named lookahead, introduces a multi-branch strategy. Instead of generating a single token at a time, we propose a Trie-based Retrieval (TR) process that enables the generation of multiple branches simultaneously, each of which is a sequence of tokens. Subsequently, for each branch, a Verification and Accept (VA) process is performed to identify the longest correct sub-sequence as the final output. Our strategy offers two distinct advantages: (1) it guarantees absolute correctness of the output, avoiding any approximation algorithms, and (2) the worst-case performance of our approach is equivalent to the conventional process. We conduct extensive experiments to demonstrate the significant improvements achieved by applying our inference acceleration framework. Code is avaliable: https://github.com/alipay/PainlessInferenceAcceleration.

Verifying the success of computer use agent (CUA) trajectories is a critical challenge: without reliable verification, neither evaluation nor training signal can be trusted. In this paper, we present lessons learned from building a best-in-class verifier for web tasks we call the Universal Verifier. We design the Universal Verifier around four key principles: 1) constructing rubrics with meaningful, non-overlapping criteria to reduce noise; 2) separating process and outcome rewards that yield complementary signals, capturing cases where an agent follows the right steps but gets blocked or succeeds through an unexpected path; 3) distinguishing between controllable and uncontrollable failures scored via a cascading-error-free strategy for finer-grained failure understanding; and 4) a divide-and-conquer context management scheme that attends to all screenshots in a trajectory, improving reliability on longer task horizons. We validate these findings on CUAVerifierBench, a new set of CUA trajectories with both process and outcome human labels, showing that our Universal Verifier agrees with humans as often as humans agree with each other. We report a reduction in false positive rates to near zero compared to baselines like WebVoyager (geq 45\%) and WebJudge (geq 22\%). We emphasize that these gains stem from the cumulative effect of the design choices above. We also find that an auto-research agent achieves 70\% of expert quality in 5\% of the time, but fails to discover all strategies required to replicate the Universal Verifier. We open-source our Universal Verifier system along with CUAVerifierBench; available at https://github.com/microsoft/fara.

Large Language Models (LLMs) augmented with external tools have demonstrated remarkable capabilities in complex reasoning tasks. However, existing frameworks rely heavily on natural language reasoning to determine when tools can be invoked and whether their results should be committed, lacking formal guarantees for logical safety and verifiability. We present ToolGate, a forward execution framework that provides logical safety guarantees and verifiable state evolution for LLM tool calling. ToolGate maintains an explicit symbolic state space as a typed key-value mapping representing trusted world information throughout the reasoning process. Each tool is formalized as a Hoare-style contract consisting of a precondition and a postcondition, where the precondition gates tool invocation by checking whether the current state satisfies the required conditions, and the postcondition determines whether the tool's result can be committed to update the state through runtime verification. Our approach guarantees that the symbolic state evolves only through verified tool executions, preventing invalid or hallucinated results from corrupting the world representation. Experimental validation demonstrates that ToolGate significantly improves the reliability and verifiability of tool-augmented LLM systems while maintaining competitive performance on complex multi-step reasoning tasks. This work establishes a foundation for building more trustworthy and debuggable AI systems that integrate language models with external tools.

The Massive Text Embedding Benchmark (MTEB) has become a standard evaluation platform for text embedding models. While previous work has established the core benchmark methodology, this paper focuses on the engineering aspects that ensure MTEB's continued reproducibility and extensibility. We present our approach to maintaining robust continuous integration pipelines that validate dataset integrity, automate test execution, and assess benchmark results' generalizability. We detail the design choices that collectively enhance reproducibility and usability. Furthermore, we discuss our strategies for handling community contributions and extending the benchmark with new tasks and datasets. These engineering practices have been instrumental in scaling MTEB to become more comprehensive while maintaining quality and, ultimately, relevance to the field. Our experiences offer valuable insights for benchmark maintainers facing similar challenges in ensuring reproducibility and usability in machine learning evaluation frameworks. The MTEB repository is available at: https://github.com/embeddings-benchmark/mteb

The evolution of machine learning has increasingly prioritized the development of powerful models and more scalable supervision signals. However, the emergence of foundation models presents significant challenges in providing effective supervision signals necessary for further enhancing their capabilities. Consequently, there is an urgent need to explore novel supervision signals and technical approaches. In this paper, we propose verifier engineering, a novel post-training paradigm specifically designed for the era of foundation models. The core of verifier engineering involves leveraging a suite of automated verifiers to perform verification tasks and deliver meaningful feedback to foundation models. We systematically categorize the verifier engineering process into three essential stages: search, verify, and feedback, and provide a comprehensive review of state-of-the-art research developments within each stage. We believe that verifier engineering constitutes a fundamental pathway toward achieving Artificial General Intelligence.

Software testing and verification are critical for ensuring the reliability and security of modern software systems. Traditionally, formal verification techniques, such as model checking and theorem proving, have provided rigorous frameworks for detecting bugs and vulnerabilities. However, these methods often face scalability challenges when applied to complex, real-world programs. Recently, the advent of Large Language Models (LLMs) has introduced a new paradigm for software analysis, leveraging their ability to understand insecure coding practices. Although LLMs demonstrate promising capabilities in tasks such as bug prediction and invariant generation, they lack the formal guarantees of classical methods. This paper presents a comprehensive study of state-of-the-art software testing and verification, focusing on three key approaches: classical formal methods, LLM-based analysis, and emerging hybrid techniques, which combine their strengths. We explore each approach's strengths, limitations, and practical applications, highlighting the potential of hybrid systems to address the weaknesses of standalone methods. We analyze whether integrating formal rigor with LLM-driven insights can enhance the effectiveness and scalability of software verification, exploring their viability as a pathway toward more robust and adaptive testing frameworks.

Reinforcement learning with verifiable rewards (RLVR) has become a key technique for enhancing large language models (LLMs), with verification engineering playing a central role. However, best practices for RL in instruction following remain underexplored. In this work, we explore the verification challenge in RL for instruction following and propose VerIF, a verification method that combines rule-based code verification with LLM-based verification from a large reasoning model (e.g., QwQ-32B). To support this approach, we construct a high-quality instruction-following dataset, VerInstruct, containing approximately 22,000 instances with associated verification signals. We apply RL training with VerIF to two models, achieving significant improvements across several representative instruction-following benchmarks. The trained models reach state-of-the-art performance among models of comparable size and generalize well to unseen constraints. We further observe that their general capabilities remain unaffected, suggesting that RL with VerIF can be integrated into existing RL recipes to enhance overall model performance. We have released our datasets, codes, and models to facilitate future research at https://github.com/THU-KEG/VerIF.

As large language models (LLMs) are increasingly applied to scientific reasoning, the complexity of answer formats and the diversity of equivalent expressions make answer verification a critical yet challenging task. Existing verification studies in scientific domains suffer from two major limitations: (a) the absence of systematic evaluation standards and insufficient disciplinary coverage, which hinders their comprehensive assessment; and (b) heavy reliance on cumbersome rule design or prompt engineering, which reduces their effectiveness in complex reasoning scenarios or limits their cross-disciplinary generalization. To address these challenges, we propose solutions at both the data and model levels. On the data side, we construct SCI-VerifyBench, a cross-disciplinary benchmark covering mathematics, physics, biology, chemistry, and general scientific QA. The benchmark is built from real LLM responses and enhanced with domain-specific equivalence transformations that generate challenging and realistic data. Model-based and expert annotations ensure both quality and diversity, enabling rigorous evaluation of verification ability. On the model side, we emphasize the importance of reasoning for verification and introduce SCI-Verifier, a unified reasoning-augmented verifier for scientific domains. Through post-training, SCI-Verifier demonstrates strong logical reasoning and equivalence judgment capabilities while maintaining concise and stable outputs. Together, SCI-VerifyBench and SCI-Verifier provide a principled framework for scientific verification, offering both systematic evaluation and practical pathways to enhance the reliability and applicability of LLMs in scientific domains.

Error detection (ED), which aims to identify incorrect or inconsistent cell values in tabular data, is important for ensuring data quality. Recent state-of-the-art ED methods leverage the pre-trained knowledge and semantic capability embedded in large language models (LLMs) to directly label whether a cell is erroneous. However, this LLM-as-a-labeler pipeline (1) relies on the black box, implicit decision process, thus failing to provide explainability for the detection results, and (2) is highly sensitive to prompts, yielding inconsistent outputs due to inherent model stochasticity, therefore lacking robustness. To address these limitations, we propose an LLM-as-an-inducer framework that adopts LLM to induce the decision tree for ED (termed TreeED) and further ensembles multiple such trees for consensus detection (termed ForestED), thereby improving explainability and robustness. Specifically, based on prompts derived from data context, decision tree specifications and output requirements, TreeED queries the LLM to induce the decision tree skeleton, whose root-to-leaf decision paths specify the stepwise procedure for evaluating a given sample. Each tree contains three types of nodes: (1) rule nodes that perform simple validation checks (e.g., format or range), (2) Graph Neural Network (GNN) nodes that capture complex patterns (e.g., functional dependencies), and (3) leaf nodes that output the final decision types (error or clean). Furthermore, ForestED employs uncertainty-based sampling to obtain multiple row subsets, constructing a decision tree for each subset using TreeED. It then leverages an Expectation-Maximization-based algorithm that jointly estimates tree reliability and optimizes the consensus ED prediction. Extensive xperiments demonstrate that our methods are accurate, explainable and robust, achieving an average F1-score improvement of 16.1% over the best baseline.

Code verifiers play a critical role in post-verification for LLM-based code generation, yet existing supervised fine-tuning methods suffer from data scarcity, high failure rates, and poor inference efficiency. While reinforcement learning (RL) offers a promising alternative by optimizing models through execution-driven rewards without labeled supervision, our preliminary results show that naive RL with only functionality rewards fails to generate effective unit tests for difficult branches and samples. We first theoretically analyze showing that branch coverage, sample difficulty, syntactic and functional correctness can be jointly modeled as RL rewards, where optimizing these signals can improve the reliability of unit-test-based verification. Guided by this analysis, we design syntax- and functionality-aware rewards and further propose branch- and sample-difficulty--aware RL using exponential reward shaping and static analysis metrics. With this formulation, CVeDRL achieves state-of-the-art performance with only 0.6B parameters, yielding up to 28.97% higher pass rate and 15.08% higher branch coverage than GPT-3.5, while delivering over 20times faster inference than competitive baselines. Code is available at https://github.com/LIGHTCHASER1/CVeDRL.git

Deep research agents autonomously conduct open-ended investigations, integrating complex information retrieval with multi-step reasoning across diverse sources to solve real-world problems. To sustain this capability on long-horizon tasks, reliable verification is critical during both training and inference. A major bottleneck in existing paradigms stems from the lack of explicit verification mechanisms in QA data synthesis, trajectory construction, and test-time scaling. Errors introduced at each stage propagate downstream and degrade the overall agent performance. To address this, we present Marco DeepResearch, a deep research agent optimized with a verification-centric framework design at three levels: (1)~QA Data Synthesis: We introduce verification mechanisms to graph-based and agent-based QA synthesis to control question difficulty while ensuring answers are unique and correct; (2)~Trajectory Construction: We design a verification-driven trajectory synthesis method that injects explicit verification patterns into training trajectories; and (3)~Test-time scaling: We use Marco DeepResearch itself as a verifier at inference time and effectively improve performance on challenging questions. Extensive experimental results demonstrate that our proposed Marco DeepResearch agent significantly outperforms 8B-scale deep research agents on most challenging benchmarks, such as BrowseComp and BrowseComp-ZH. Crucially, under a maximum budget of 600 tool calls, Marco DeepResearch even surpasses or approaches several 30B-scale agents, like Tongyi DeepResearch-30B.

Sampling-based search, a simple paradigm for utilizing test-time compute, involves generating multiple candidate responses and selecting the best one -- typically by verifying each response for correctness. In this paper, we study the scaling trends governing sampling-based search. Among our findings is that simply scaling up a minimalist implementation that uses only random sampling and direct self-verification results in sustained performance improvements that, for example, elevate the Gemini v1.5 Pro model's reasoning capabilities past that of o1-Preview on popular benchmarks. We partially attribute the scalability of sampling-based search to a phenomenon of implicit scaling, where sampling a larger pool of responses in turn improves verification accuracy. We further identify two useful principles for improving self-verification capabilities with test-time compute: (1) comparing across responses provides helpful signals about the locations of errors and hallucinations, and (2) different model output styles are useful for different contexts -- chains of thought are useful for reasoning but harder to verify. We also find that, though accurate verification can be elicited, frontier models demonstrate remarkably weak out-of-box verification capabilities and introduce a benchmark to measure progress on these deficiencies.

Large language models (LLMs) struggle with multi-step reasoning, where inference-time scaling has emerged as a promising strategy for performance improvement. Verifier-guided search outperforms repeated sampling when sample size is limited by selecting and prioritizing valid reasoning paths. However, we identify a critical limitation: scaling flaws, prevalent across different models (Mistral 7B and DeepSeekMath 7B), benchmarks (GSM8K and MATH), and verifiers (outcome value models and process reward models). As sample size increases, verifier-guided search exhibits diminishing advantages and eventually underperforms repeated sampling. Our analysis attributes this to verifier failures, where imperfect verifiers misrank candidates and erroneously prune all valid paths. These issues are further exacerbated in challenging and out-of-distribution problems, restricting search effectiveness. To mitigate verifier failures, we explore reducing reliance on verifiers and conduct preliminary investigations using two simple methods. Our findings reveal fundamental limitations in verifier-guided search and suggest future directions.

In the realm of formal theorem proving, the Coq proof assistant stands out for its rigorous approach to verifying mathematical assertions and software correctness. Despite the advances in artificial intelligence and machine learning, the specialized nature of Coq syntax and semantics poses unique challenges for Large Language Models (LLMs). Addressing this gap, we present a comprehensive dataset specifically designed to enhance LLMs' proficiency in interpreting and generating Coq code. This dataset, derived from a collection of over 10,000 Coq source files, encompasses a wide array of propositions, proofs, and definitions, enriched with metadata including source references and licensing information. Our primary aim is to facilitate the development of LLMs capable of generating syntactically correct and semantically meaningful Coq constructs, thereby advancing the frontier of automated theorem proving. Initial experiments with this dataset have showcased its significant potential; models trained on this data exhibited enhanced accuracy in Coq code generation. Notably, a particular experiment revealed that a fine-tuned LLM was capable of generating 141 valid proofs for a basic lemma, highlighting the dataset's utility in facilitating the discovery of diverse and valid proof strategies. This paper discusses the dataset's composition, the methodology behind its creation, and the implications of our findings for the future of machine learning in formal verification. The dataset is accessible for further research and exploration: https://huggingface.co/datasets/florath/coq-facts-props-proofs-gen0-v1

As autonomous AI agents are used in regulated and safety-critical settings, organizations need effective ways to turn policy into enforceable controls. We introduce a regulatory machine learning framework that converts unstructured design artifacts (like PRDs, TDDs, and code) into verifiable runtime guardrails. Our Policy as Prompt method reads these documents and risk controls to build a source-linked policy tree. This tree is then compiled into lightweight, prompt-based classifiers for real-time runtime monitoring. The system is built to enforce least privilege and data minimization. For conformity assessment, it provides complete provenance, traceability, and audit logging, all integrated with a human-in-the-loop review process. Evaluations show our system reduces prompt-injection risk, blocks out-of-scope requests, and limits toxic outputs. It also generates auditable rationales aligned with AI governance frameworks. By treating policies as executable prompts (a policy-as-code for agents), this approach enables secure-by-design deployment, continuous compliance, and scalable AI safety and AI security assurance for regulatable ML.

Large language models (LLMs) have demonstrated remarkable code generation capabilities, but the correctness of the generated code cannot be inherently trusted. This paper explores the feasibility of using formal software verification, specifically the SPARK framework for Ada, to ensure the reliability of LLM-generated code. We present Marmaragan, a tool that leverages an LLM in order to generate SPARK annotations for existing programs, enabling formal verification of the code. The tool is benchmarked on a curated set of SPARK programs, with annotations selectively removed to test specific capabilities. The performance of Marmaragan with GPT-4o on the benchmark is promising, with correct annotations having been generated for 50.7% of the benchmark cases. The results establish a foundation for future work on combining the power of LLMs with the reliability of formal software verification.

Large Language Models (LLMs) significantly benefit from Chain-of-Thought (CoT) prompting in performing various reasoning tasks. While CoT allows models to produce more comprehensive reasoning processes, its emphasis on intermediate reasoning steps can inadvertently introduce hallucinations and accumulated errors, thereby limiting models' ability to solve complex reasoning tasks. Inspired by how humans engage in careful and meticulous deductive logical reasoning processes to solve tasks, we seek to enable language models to perform explicit and rigorous deductive reasoning, and also ensure the trustworthiness of their reasoning process through self-verification. However, directly verifying the validity of an entire deductive reasoning process is challenging, even with advanced models like ChatGPT. In light of this, we propose to decompose a reasoning verification process into a series of step-by-step subprocesses, each only receiving their necessary context and premises. To facilitate this procedure, we propose Natural Program, a natural language-based deductive reasoning format. Our approach enables models to generate precise reasoning steps where subsequent steps are more rigorously grounded on prior steps. It also empowers language models to carry out reasoning self-verification in a step-by-step manner. By integrating this verification process into each deductive reasoning stage, we significantly enhance the rigor and trustfulness of generated reasoning steps. Along this process, we also improve the answer correctness on complex reasoning tasks. Code will be released at https://github.com/lz1oceani/verify_cot.

Language models (LMs) are widely used by an increasing number of users, underscoring the challenge of maintaining factuality across a broad range of topics. We first present VERIFY (Verification and Evidence RetrIeval for FactualitY evaluation), a pipeline to evaluate LMs' factuality in real-world user interactions. VERIFY considers the verifiability of LM-generated content and categorizes content units as supported, unsupported, or undecidable based on the retrieved evidence from the Web. Importantly, factuality judgment by VERIFY correlates better with human evaluations than existing methods. Using VERIFY, we identify "hallucination prompts" across diverse topics, i.e., those eliciting the highest rates of incorrect and inconclusive LM responses. These prompts form FactBench, a dataset of 1K prompts across 150 fine-grained topics. Our dataset captures emerging factuality challenges in real-world LM interactions and can be regularly updated with new prompts. We benchmark widely-used LMs from GPT, Gemini, and Llama3.1 family on FactBench, yielding the following key findings: (i) Proprietary models exhibit better factuality, with performance declining from Easy to Hard hallucination prompts. (ii) Llama3.1-405B-Instruct shows comparable or lower factual accuracy than Llama3.1-70B-Instruct across all evaluation methods due to its higher subjectivity that leads to more content labeled as undecidable. (iii) Gemini1.5-Pro shows a significantly higher refusal rate, with over-refusal in 25% of cases. Our code and data are publicly available at https://huggingface.co/spaces/launch/factbench.

Robustness of reasoning remains a significant challenge for large language models, and addressing it is essential for the practical applicability of AI-driven reasoning systems. We introduce Semantic Self-Verification (SSV), a novel approach that addresses the key challenge in combining language models with the rigor of logical solvers: to accurately formulate the reasoning problem from natural language to the formal language of the solver. SSV uses a consistency-based approach to produce strong abstract formalizations of problems using concrete instantiations that are generated by the model and verified by the solver. In addition to significantly advancing the overall reasoning accuracy over the state-of-the-art, a key novelty that this approach presents is a feature of verification that has near-perfect precision over a significant coverage of cases, as we demonstrate on open reasoning benchmarks. We propose such *near-certain reasoning* as a new approach to reduce the need for manual verification in many cases, taking us closer to more dependable and autonomous AI reasoning systems.

Large Language Model (LLM) reasoning for complex tasks inherently involves a trade-off between solution accuracy and computational efficiency. The subsequent step of verification, while intended to improve performance, further complicates this landscape by introducing its own challenging trade-off: sophisticated Generative Reward Models (GenRMs) can be computationally prohibitive if naively integrated with LLMs at test-time, while simpler, faster methods may lack reliability. To overcome these challenges, we introduce FlexiVe, a novel generative verifier that flexibly balances computational resources between rapid, reliable fast thinking and meticulous slow thinking using a Flexible Allocation of Verification Budget strategy. We further propose the Solve-Detect-Verify pipeline, an efficient inference-time scaling framework that intelligently integrates FlexiVe, proactively identifying solution completion points to trigger targeted verification and provide focused solver feedback. Experiments show FlexiVe achieves superior accuracy in pinpointing errors within reasoning traces on ProcessBench. Furthermore, on challenging mathematical reasoning benchmarks (AIME 2024, AIME 2025, and CNMO), our full approach outperforms baselines like self-consistency in reasoning accuracy and inference efficiency. Our system offers a scalable and effective solution to enhance LLM reasoning at test time.

The increasing complexity of large language models (LLMs) raises concerns about their ability to "cheat" on standard Question Answering (QA) benchmarks by memorizing task-specific data. This undermines the validity of benchmark evaluations, as they no longer reflect genuine model capabilities but instead the effects of data leakage. While prior work has focused on detecting such leakage, little attention has been given to mitigating its impact and preserving the long-term utility of benchmarks. In this paper, we introduce LastingBench, a novel framework designed to continuously reinforce and safeguard existing benchmarks against knowledge leakage. LastingBench identifies leakage points in the context through perturbation, then rewrites the leakage points to counterfactual ones-disrupting memorization while preserving the benchmark's original evaluative intent. Evaluations of state-of-the-art QA benchmarks show significant performance gaps, highlighting the efficacy of LastingBench in reducing memorization effects. LastingBench offers a practical and scalable solution to ensure benchmark robustness over time, promoting fairer and more interpretable evaluations of LLMs.

Test-time scaling (TTS) has emerged as a new frontier for scaling the performance of Large Language Models. In test-time scaling, by using more computational resources during inference, LLMs can improve their reasoning process and task performance. Several approaches have emerged for TTS such as distilling reasoning traces from another model or exploring the vast decoding search space by employing a verifier. The verifiers serve as reward models that help score the candidate outputs from the decoding process to diligently explore the vast solution space and select the best outcome. This paradigm commonly termed has emerged as a superior approach owing to parameter free scaling at inference time and high performance gains. The verifiers could be prompt-based, fine-tuned as a discriminative or generative model to verify process paths, outcomes or both. Despite their widespread adoption, there is no detailed collection, clear categorization and discussion of diverse verification approaches and their training mechanisms. In this survey, we cover the diverse approaches in the literature and present a unified view of verifier training, types and their utility in test-time scaling. Our repository can be found at https://github.com/elixir-research-group/Verifierstesttimescaling.github.io.

In this paper we introduce a new publicly available dataset for verification against textual sources, FEVER: Fact Extraction and VERification. It consists of 185,445 claims generated by altering sentences extracted from Wikipedia and subsequently verified without knowledge of the sentence they were derived from. The claims are classified as Supported, Refuted or NotEnoughInfo by annotators achieving 0.6841 in Fleiss kappa. For the first two classes, the annotators also recorded the sentence(s) forming the necessary evidence for their judgment. To characterize the challenge of the dataset presented, we develop a pipeline approach and compare it to suitably designed oracles. The best accuracy we achieve on labeling a claim accompanied by the correct evidence is 31.87%, while if we ignore the evidence we achieve 50.91%. Thus we believe that FEVER is a challenging testbed that will help stimulate progress on claim verification against textual sources.

Fact verification is essential for ensuring the reliability of LLM applications. In this study, we evaluate 12 pre-trained LLMs and one specialized fact-verifier, including frontier LLMs and open-weight reasoning LLMs, using a collection of examples from 14 fact-checking benchmarks. We share three findings intended to guide future development of more robust fact verifiers. First, we highlight the importance of addressing annotation errors and ambiguity in datasets, demonstrating that approximately 16\% of ambiguous or incorrectly labeled data substantially influences model rankings. Neglecting this issue may result in misleading conclusions during comparative evaluations, and we suggest using a systematic pipeline utilizing LLM-as-a-judge to help identify these issues at scale. Second, we discover that frontier LLMs with few-shot in-context examples, often overlooked in previous works, achieve top-tier performance. We therefore recommend future studies include comparisons with these simple yet highly effective baselines. Lastly, despite their effectiveness, frontier LLMs incur substantial costs, motivating the development of small, fine-tuned fact verifiers. We show that these small models still have room for improvement, particularly on instances that require complex reasoning. Encouragingly, we demonstrate that augmenting training with synthetic multi-hop reasoning data significantly enhances their capabilities in such instances. We release our code, model, and dataset at https://github.com/just1nseo/verifying-the-verifiers

The application of machine learning algorithms to source code has grown in the past years. Since these algorithms are quite sensitive to input data, it is not surprising that researchers experiment with input representations. Nowadays, a popular starting point to represent code is abstract syntax trees (ASTs). Abstract syntax trees have been used for a long time in various software engineering domains, and in particular in IDEs. The API of modern IDEs allows to manipulate and traverse ASTs, resolve references between code elements, etc. Such algorithms can enrich ASTs with new data and therefore may be useful in ML-based code analysis. In this work, we present PSIMiner - a tool for processing PSI trees from the IntelliJ Platform. PSI trees contain code syntax trees as well as functions to work with them, and therefore can be used to enrich code representation using static analysis algorithms of modern IDEs. To showcase this idea, we use our tool to infer types of identifiers in Java ASTs and extend the code2seq model for the method name prediction problem.

Large language models (LLMs) are increasingly integrated in software development, but ensuring correctness in LLM-generated code remains challenging and often requires costly manual review. Verifiable code generation -- jointly generating code, specifications, and proofs of code-specification alignment -- offers a promising path to address this limitation and further unleash LLMs' benefits in coding. Yet, there exists a significant gap in evaluation: current benchmarks often lack support for end-to-end verifiable code generation. In this paper, we introduce Verina (Verifiable Code Generation Arena), a high-quality benchmark enabling a comprehensive and modular evaluation of code, specification, and proof generation as well as their compositions. Verina consists of 189 manually curated coding tasks in Lean, with detailed problem descriptions, reference implementations, formal specifications, and extensive test suites. Our extensive evaluation of state-of-the-art LLMs reveals significant challenges in verifiable code generation, especially in proof generation, underscoring the need for improving LLM-based theorem provers in verification domains. The best model, OpenAI o4-mini, generates only 61.4% correct code, 51.0% sound and complete specifications, and 3.6% successful proofs, with one trial per task. We hope Verina will catalyze progress in verifiable code generation by providing a rigorous and comprehensive benchmark. We release our dataset on https://huggingface.co/datasets/sunblaze-ucb/verina and our evaluation code on https://github.com/sunblaze-ucb/verina.

Fact-checking long-form text is challenging, and it is therefore common practice to break it down into multiple atomic claims. The typical approach to fact-checking these atomic claims involves retrieving a fixed number of pieces of evidence, followed by a verification step. However, this method is usually not cost-effective, as it underutilizes the verification model's internal knowledge of the claim and fails to replicate the iterative reasoning process in human search strategies. To address these limitations, we propose FIRE, a novel agent-based framework that integrates evidence retrieval and claim verification in an iterative manner. Specifically, FIRE employs a unified mechanism to decide whether to provide a final answer or generate a subsequent search query, based on its confidence in the current judgment. We compare FIRE with other strong fact-checking frameworks and find that it achieves slightly better performance while reducing large language model (LLM) costs by an average of 7.6 times and search costs by 16.5 times. These results indicate that FIRE holds promise for application in large-scale fact-checking operations. Our code is available at https://github.com/mbzuai-nlp/fire.git.

We consider the task of mapping pseudocode to long programs that are functionally correct. Given test cases as a mechanism to validate programs, we search over the space of possible translations of the pseudocode to find a program that passes the validation. However, without proper credit assignment to localize the sources of program failures, it is difficult to guide search toward more promising programs. We propose to perform credit assignment based on signals from compilation errors, which constitute 88.7% of program failures. Concretely, we treat the translation of each pseudocode line as a discrete portion of the program, and whenever a synthesized program fails to compile, an error localization method tries to identify the portion of the program responsible for the failure. We then focus search over alternative translations of the pseudocode for those portions. For evaluation, we collected the SPoC dataset (Search-based Pseudocode to Code) containing 18,356 programs with human-authored pseudocode and test cases. Under a budget of 100 program compilations, performing search improves the synthesis success rate over using the top-one translation of the pseudocode from 25.6% to 44.7%.

Factual hallucination remains a central challenge for large language models (LLMs). Existing mitigation approaches primarily rely on either external post-hoc verification or mapping uncertainty directly to abstention during fine-tuning, often resulting in overly conservative behavior. We propose VeriFY, a training-time framework that teaches LLMs to reason about factual uncertainty through consistency-based self-verification. VeriFY augments training with structured verification traces that guide the model to produce an initial answer, generate and answer a probing verification query, issue a consistency judgment, and then decide whether to answer or abstain. To address the risk of reinforcing hallucinated content when training on augmented traces, we introduce a stage-level loss masking approach that excludes hallucinated answer stages from the training objective while preserving supervision over verification behavior. Across multiple model families and scales, VeriFY reduces factual hallucination rates by 9.7 to 53.3 percent, with only modest reductions in recall (0.4 to 5.7 percent), and generalizes across datasets when trained on a single source. The source code, training data, and trained model checkpoints will be released upon acceptance.

We present DafnyPro, an inference-time framework that enhances LLMs for generating verification annotations in Dafny. DafnyPro comprises three key components: a diff-checker that prevents modifications to base program logic, a pruner that removes unnecessary invariants, and a hint-augmentation system that retrieves and applies predefined, problem-independent proof strategies. We evaluate DafnyPro using Claude Sonnet 3.5 and 3.7 on four benchmarks: Clover, MBPP-Dafny, HumanEval-Dafny, and DafnyBench, achieving consistent performance gains in all cases. Notably, on DafnyBench, the most challenging benchmark, Claude Sonnet 3.5 enhanced with DafnyPro achieves 86% correct proofs, a 16 pp improvement over the base model. We also fine-tune two Qwen models on training data derived from verification attempts by larger models enhanced with DafnyPro. Our 7B and 14B models achieve 68% and 70% correct proofs on DafnyBench, respectively, demonstrating that smaller models can maintain high verification accuracy.

We present IBR, an Iterative Backward Reasoning model to solve the proof generation tasks on rule-based Question Answering (QA), where models are required to reason over a series of textual rules and facts to find out the related proof path and derive the final answer. We handle the limitations of existed works in two folds: 1) enhance the interpretability of reasoning procedures with detailed tracking, by predicting nodes and edges in the proof path iteratively backward from the question; 2) promote the efficiency and accuracy via reasoning on the elaborate representations of nodes and history paths, without any intermediate texts that may introduce external noise during proof generation. There are three main modules in IBR, QA and proof strategy prediction to obtain the answer and offer guidance for the following procedure; parent node prediction to determine a node in the existing proof that a new child node will link to; child node prediction to find out which new node will be added to the proof. Experiments on both synthetic and paraphrased datasets demonstrate that IBR has better in-domain performance as well as cross-domain transferability than several strong baselines. Our code and models are available at https://github.com/find-knowledge/IBR .

In this work, we propose a novel method named Automated Process-Supervised Verifier (\textsc{AutoPSV}) to enhance the reasoning capabilities of large language models (LLMs) by automatically annotating the reasoning steps. AutoPSV begins by training a verification model on the correctness of final answers, enabling it to generate automatic process annotations. This verification model assigns a confidence score to each reasoning step, indicating the probability of arriving at the correct final answer from that point onward. We detect relative changes in the verification's confidence scores across reasoning steps to automatically annotate the reasoning process, enabling error detection even in scenarios where ground truth answers are unavailable. This alleviates the need for numerous manual annotations or the high computational costs associated with model-induced annotation approaches. We experimentally validate that the step-level confidence changes learned by the verification model trained on the final answer correctness can effectively identify errors in the reasoning steps. We demonstrate that the verification model, when trained on process annotations generated by AutoPSV, exhibits improved performance in selecting correct answers from multiple LLM-generated outputs. Notably, we achieve substantial improvements across five datasets in mathematics and commonsense reasoning. The source code of AutoPSV is available at https://github.com/rookie-joe/AutoPSV.

QDNA-ID is a trust-chain framework that links physical quantum behavior to digitally verified records. The system first executes standard quantum circuits with random shot patterns across different devices to generate entropy profiles and measurement data that reveal device-specific behavior. A Bell or CHSH test is then used to confirm that correlations originate from genuine non classical processes rather than classical simulation. The verified outcomes are converted into statistical fingerprints using entropy, divergence, and bias features to characterize each device. These features and metadata for device, session, and random seed parameters are digitally signed and time stamped to ensure integrity and traceability. Authenticated artifacts are stored in a hierarchical index for reproducible retrieval and long term auditing. A visualization and analytics interface monitors drift, policy enforcement, and device behavior logs. A machine learning engine tracks entropy drift, detects anomalies, and classifies devices based on evolving patterns. An external verification API supports independent recomputation of hashes, signatures, and CHSH evidence. QDNA-ID operates as a continuous feedback loop that maintains a persistent chain of trust for quantum computing environments.

Operationalizing large language models (LLMs) for custom, repetitive data pipelines is challenging, particularly due to their unpredictable and potentially catastrophic failures. Acknowledging the inevitability of these errors, we focus on identifying when LLMs may be generating incorrect responses when used repeatedly as part of data generation pipelines. We present SPADE, a method for automatically synthesizing assertions that identify bad LLM outputs. SPADE analyzes prompt version histories to create candidate assertion functions and then selects a minimal set that fulfills both coverage and accuracy requirements. In testing across nine different real-world LLM pipelines, SPADE efficiently reduces the number of assertions by 14% and decreases false failures by 21% when compared to simpler baselines.

We tackle the challenge of training reliable code-fixing agents in real repositories, where complex builds and shifting dependencies make evaluation unstable. We developed a verifiable pipeline with success defined as post-fix build validation and improved reproducibility across ~1K real issues by pinning dependencies and disabling automatic upgrades. Building on this, we introduced a scalable simplified pipeline for large-scale reinforcement learning (RL). Using this setup, we supervised fine-tuned Qwen3-32B in the full pipeline and applied RL on top of the SFT model in the simplified environment. The SFT model distilled from GPT-4.1 trajectories performs on par while being 56x smaller, and RL added 7-20% absolute gains under matched train-test conditions. "Thinking mode" was on par or worse in our experiments. Both SFT and RL models failed to generalize across environments, highlighting the importance of matching train-test environments for building reliable real-world code-fixing agents.

We introduce {rm C{small LEVER}}, a high-quality, curated benchmark of 161 problems for end-to-end verified code generation in Lean. Each problem consists of (1) the task of generating a specification that matches a held-out ground-truth specification, and (2) the task of generating a Lean implementation that provably satisfies this specification. Unlike prior benchmarks, {rm C{small LEVER}} avoids test-case supervision, LLM-generated annotations, and specifications that leak implementation logic or allow vacuous solutions. All outputs are verified post-hoc using Lean's type checker to ensure machine-checkable correctness. We use {rm C{small LEVER}} to evaluate several few-shot and agentic approaches based on state-of-the-art language models. These methods all struggle to achieve full verification, establishing it as a challenging frontier benchmark for program synthesis and formal reasoning. Our benchmark can be found on GitHub(https://github.com/trishullab/clever) as well as HuggingFace(https://huggingface.co/datasets/amitayusht/clever). All our evaluation code is also available online(https://github.com/trishullab/clever-prover).

Prompting language models to provide step-by-step answers (e.g., "Chain-of-Thought") is the prominent approach for complex reasoning tasks, where more accurate reasoning chains typically improve downstream task performance. Recent literature discusses automatic methods to verify reasoning steps to evaluate and improve their correctness. However, no fine-grained step-level datasets are available to enable thorough evaluation of such verification methods, hindering progress in this direction. We introduce Reveal: Reasoning Verification Evaluation, a new dataset to benchmark automatic verifiers of complex Chain-of-Thought reasoning in open-domain question answering settings. Reveal includes comprehensive labels for the relevance, attribution to evidence passages, and logical correctness of each reasoning step in a language model's answer, across a wide variety of datasets and state-of-the-art language models.

Large Language Models (LLMs) show remarkable capabilities, yet their stochastic next-token prediction creates logical inconsistencies and reward hacking that formal symbolic systems avoid. To bridge this gap, we introduce a formal logic verification-guided framework that dynamically interleaves formal symbolic verification with the natural language generation process, providing real-time feedback to detect and rectify errors as they occur. Distinguished from previous neuro-symbolic methods limited by passive post-hoc validation, our approach actively penalizes intermediate fallacies during the reasoning chain. We operationalize this framework via a novel two-stage training pipeline that synergizes formal logic verification-guided supervised fine-tuning and policy optimization. Extensive evaluation on six benchmarks spanning mathematical, logical, and general reasoning demonstrates that our 7B and 14B models outperform state-of-the-art baselines by average margins of 10.4% and 14.2%, respectively. These results validate that formal verification can serve as a scalable mechanism to significantly push the performance boundaries of advanced LLM reasoning.

Recent advancements have significantly augmented the reasoning capabilities of Large Language Models (LLMs) through various methodologies, especially chain-of-thought (CoT) reasoning. However, previous methods fail to address reasoning errors in intermediate steps, leading to accumulative errors. In this paper, we propose Deductive Beam Search (DBS), which seamlessly integrates CoT and deductive reasoning with step-wise beam search for LLMs. Our approach deploys a verifier, verifying the deducibility of a reasoning step and its premises, thus alleviating the error accumulation. Furthermore, we introduce a scalable and labor-free data construction method to amplify our model's verification capabilities. Extensive experiments demonstrate that our approach significantly enhances the base performance of LLMs of various scales (7B, 13B, 70B, and ChatGPT) across 8 reasoning datasets from 3 diverse reasoning genres, including arithmetic, commonsense, and symbolic. Moreover, our analysis proves DBS's capability of detecting diverse and subtle reasoning errors and robustness on different model scales.

Recent Retrieval Augmented Generation (RAG) aims to enhance Large Language Models (LLMs) by incorporating extensive knowledge retrieved from external sources. However, such approach encounters some challenges: Firstly, the original queries may not be suitable for precise retrieval, resulting in erroneous contextual knowledge; Secondly, the language model can easily generate inconsistent answer with external references due to their knowledge boundary limitation. To address these issues, we propose the chain-of-verification (CoV-RAG) to enhance the external retrieval correctness and internal generation consistency. Specifically, we integrate the verification module into the RAG, engaging in scoring, judgment, and rewriting. To correct external retrieval errors, CoV-RAG retrieves new knowledge using a revised query. To correct internal generation errors, we unify QA and verification tasks with a Chain-of-Thought (CoT) reasoning during training. Our comprehensive experiments across various LLMs demonstrate the effectiveness and adaptability compared with other strong baselines. Especially, our CoV-RAG can significantly surpass the state-of-the-art baselines using different LLM backbones.

Scientific research relies on accurate citation for attribution and integrity, yet large language models (LLMs) introduce a new risk: fabricated references that appear plausible but correspond to no real publications. Such hallucinated citations have already been observed in submissions and accepted papers at major machine learning venues, exposing vulnerabilities in peer review. Meanwhile, rapidly growing reference lists make manual verification impractical, and existing automated tools remain fragile to noisy and heterogeneous citation formats and lack standardized evaluation. We present the first comprehensive benchmark and detection framework for hallucinated citations in scientific writing. Our multi-agent verification pipeline decomposes citation checking into claim extraction, evidence retrieval, passage matching, reasoning, and calibrated judgment to assess whether a cited source truly supports its claim. We construct a large-scale human-validated dataset across domains and define unified metrics for citation faithfulness and evidence alignment. Experiments with state-of-the-art LLMs reveal substantial citation errors and show that our framework significantly outperforms prior methods in both accuracy and interpretability. This work provides the first scalable infrastructure for auditing citations in the LLM era and practical tools to improve the trustworthiness of scientific references.

Large Language Models (LLMs) are evolving beyond their classical role of providing information within dialogue systems to actively engaging with tools and performing actions on real-world applications and services. Today, humans verify the correctness and appropriateness of the LLM-generated outputs (e.g., code, functions, or actions) before putting them into real-world execution. This poses significant challenges as code comprehension is well known to be notoriously difficult. In this paper, we study how humans can efficiently collaborate with, delegate to, and supervise autonomous LLMs in the future. We argue that in many cases, "post-facto validation" - verifying the correctness of a proposed action after seeing the output - is much easier than the aforementioned "pre-facto validation" setting. The core concept behind enabling a post-facto validation system is the integration of an intuitive undo feature, and establishing a damage confinement for the LLM-generated actions as effective strategies to mitigate the associated risks. Using this, a human can now either revert the effect of an LLM-generated output or be confident that the potential risk is bounded. We believe this is critical to unlock the potential for LLM agents to interact with applications and services with limited (post-facto) human involvement. We describe the design and implementation of our open-source runtime for executing LLM actions, Gorilla Execution Engine (GoEX), and present open research questions towards realizing the goal of LLMs and applications interacting with each other with minimal human supervision. We release GoEX at https://github.com/ShishirPatil/gorilla/.

Claim verification with large language models (LLMs) has recently attracted growing attention, due to their strong reasoning capabilities and transparent verification processes compared to traditional answer-only judgments. However, existing approaches to online claim verification, which requires iterative evidence retrieval and reasoning, still mainly rely on prompt engineering or pre-designed reasoning workflows, without unified training to improve necessary skills. Therefore, we introduce Veri-R1, an online reinforcement learning (RL) framework that enables an LLM to interact with a search engine and to receive reward signals that explicitly shape its planning, retrieval, and reasoning behaviors. This dynamic interaction of LLM with retrieval systems more accurately reflects real-world verification scenarios and fosters comprehensive verification skills. Empirical results show that Veri-R1 improves joint accuracy by up to 30% and doubles the evidence score, often surpassing its larger-scale model counterparts. Ablation studies further reveal the impact of reward components, and the link between output logits and label accuracy. Our results highlight the effectiveness of online RL for precise and faithful claim verification, providing an important foundation for future research. We release our code to support community progress in LLM empowered claim verification.

Formal reasoning and automated theorem proving constitute a challenging subfield of machine learning, in which machines are tasked with proving mathematical theorems using formal languages like Lean. A formal verification system can check whether a formal proof is correct or not almost instantaneously, but generating a completely correct formal proof with large language models (LLMs) remains a formidable task. The usual approach in the literature is to prompt the LLM many times (up to several thousands) until one of the generated proofs passes the verification system. In this work, we present APOLLO (Automated PrOof repair via LLM and Lean cOllaboration), a modular, model-agnostic pipeline that combines the strengths of the Lean compiler with an LLM's reasoning abilities to achieve better proof-generation results at a low sampling budget. Apollo directs a fully automated process in which the LLM generates proofs for theorems, a set of agents analyze the proofs, fix the syntax errors, identify the mistakes in the proofs using Lean, isolate failing sub-lemmas, utilize automated solvers, and invoke an LLM on each remaining goal with a low top-K budget. The repaired sub-proofs are recombined and reverified, iterating up to a user-controlled maximum number of attempts. On the miniF2F benchmark, we establish a new state-of-the-art accuracy of 75.0% among 7B-parameter models while keeping the sampling budget below one thousand. Moreover, Apollo raises the state-of-the-art accuracy for Goedel-Prover-SFT to 65.6% while cutting sample complexity from 25,600 to a few hundred. General-purpose models (o3-mini, o4-mini) jump from 3-7% to over 40% accuracy. Our results demonstrate that targeted, compiler-guided repair of LLM outputs yields dramatic gains in both efficiency and correctness, suggesting a general paradigm for scalable automated theorem proving.

Large language models have shown impressive capabilities across a variety of NLP tasks, yet their generating text autoregressively is time-consuming. One way to speed them up is speculative decoding, which generates candidate segments (a sequence of tokens) from a fast draft model that is then verified in parallel by the target model. However, the acceptance rate of candidate tokens receives limitations from several factors, such as the model, the dataset, and the decoding setup. This paper proposes sampling multiple candidates from a draft model and then organising them in batches for verification. We design algorithms for efficient multi-candidate verification while maintaining the distribution of the target model. Our approach shows significant improvements in acceptance rates on multiple datasets and models, consistently outperforming standard speculative decoding.

Recent work has shown that integrating large language models (LLMs) with theorem provers (TPs) in neuro-symbolic pipelines helps with entailment verification and proof-guided refinement of explanations for natural language inference (NLI). However, scaling such refinement to naturalistic NLI remains difficult: long, syntactically rich inputs and deep multi-step arguments amplify autoformalisation errors, where a single local mismatch can invalidate the proof. Moreover, current methods often handle failures via costly global regeneration due to the difficulty of localising the responsible span or step from prover diagnostics. Aiming to address these problems, we propose a decompose-and-formalise framework that (i) decomposes premise-hypothesis pairs into an entailment tree of atomic steps, (ii) verifies the tree bottom-up to isolate failures to specific nodes, and (iii) performs local diagnostic-guided refinement instead of regenerating the whole explanation. Moreover, to improve faithfulness of autoformalisation, we introduce θ-substitution in an event-based logical form to enforce consistent argument-role bindings. Across a range of reasoning tasks using five LLM backbones, our method achieves the highest explanation verification rates, improving over the state-of-the-art by 26.2%, 21.7%, 21.6% and 48.9%, while reducing refinement iterations and runtime and preserving strong NLI accuracy.

The standard paradigm for solving coding tasks via large language models (LLMs) is to generate-then-rank programs, where the latter step uses a verifier in the ranking process. The growing consensus is that a comprehensive verifier (e.g., a full test suite) should be prioritized over an outcome reward model (ORM) whenever possible, with little consideration given to the trade-offs involved. We aim to challenge this assumption by systematically exploring the tradeoff between speed and accuracy. We find that ORMs play a crucial role in scaling verification through trading accuracy for speed, even when a comprehensive verifier is available. Their value becomes especially apparent when used in a generate-prune-then-rank approach, where a faster but less accurate verifier removes incorrect solutions prior to ranking -- leading to a system that is 11.65x faster while only being 8.33% less accurate than the full test suite. We analyze the generate-prune-then-rank approach and show that it works by filtering out incorrect but highly ranked solutions. These findings enable the design of scalable and accurate program ranking systems.

Formal theorem proving with TLA+ provides rigorous guarantees for system specifications, but constructing proofs requires substantial expertise and effort. While large language models have shown promise in automating proofs for tactic-based theorem provers like Lean, applying these approaches directly to TLA+ faces significant challenges due to the hierarchical proof structure of the TLA+ proof system. We present a prompt-based approach that leverages LLMs to guide hierarchical decomposition of complex proof obligations into simpler sub-claims, while relying on symbolic provers for verification. Our key insight is to constrain LLMs to generate normalized claim decompositions rather than complete proofs, significantly reducing syntax errors. We also introduce a benchmark suite of 119 theorems adapted from (1) established mathematical collections and (2) inductive proofs of distributed protocols. Our approach consistently outperforms baseline methods across the benchmark suite.

Using large language models (LLMs) to generate source code from natural language prompts is a popular and promising idea with a wide range of applications. One of its limitations is that the generated code can be faulty at times, often in a subtle way, despite being presented to the user as correct. In this paper, we explore ways in which formal methods can assist with increasing the quality of code generated by an LLM. Instead of emitting code in a target language directly, we propose that the user guides the LLM to first generate an opaque intermediate representation, in the verification-aware language Dafny, that can be automatically validated for correctness against agreed on specifications. The correct Dafny program is then compiled to the target language and returned to the user. All user-system interactions throughout the procedure occur via natural language; Dafny code is never exposed. We describe our current prototype and report on its performance on the HumanEval Python code generation benchmarks.

Competition-level code generation tasks pose significant challenges for current state-of-the-art large language models (LLMs). For example, on the LiveCodeBench-Hard dataset, models such as O1-Mini and O1-Preview achieve pass@1 rates of only 0.366 and 0.143, respectively. While tree search techniques have proven effective in domains like mathematics and general coding, their potential in competition-level code generation remains under-explored. In this work, we propose a novel token-level tree search method specifically designed for code generation. Leveraging Qwen2.5-Coder-32B-Instruct, our approach achieves a pass rate of 0.305 on LiveCodeBench-Hard, surpassing the pass@100 performance of GPT4o-0513 (0.245). Furthermore, by integrating Chain-of-Thought (CoT) prompting, we improve our method's performance to 0.351, approaching O1-Mini's pass@1 rate. To ensure reproducibility, we report the average number of generations required per problem by our tree search method on the test set. Our findings underscore the potential of tree search to significantly enhance performance on competition-level code generation tasks. This opens up new possibilities for large-scale synthesis of challenging code problems supervised fine-tuning (SFT) data, advancing competition-level code generation tasks.

Despite their outstanding capabilities, large language models (LLMs) are prone to hallucination and producing factually incorrect information. This challenge has spurred efforts in attributed text generation, which prompts LLMs to generate content with supporting evidence. In this paper, we propose a novel framework, called Think&Cite, and formulate attributed text generation as a multi-step reasoning problem integrated with search. Specifically, we propose Self-Guided Monte Carlo Tree Search (SG-MCTS), which capitalizes on the self-reflection capability of LLMs to reflect on the intermediate states of MCTS for guiding the tree expansion process. To provide reliable and comprehensive feedback, we introduce Progress Reward Models to measure the progress of tree search from the root to the current state from two aspects, i.e., generation and attribution progress. We conduct extensive experiments on three datasets and the results show that our approach significantly outperforms baseline approaches.

Large language models are trained on vast amounts of internet data, prompting concerns and speculation that they have memorized public benchmarks. Going from speculation to proof of contamination is challenging, as the pretraining data used by proprietary models are often not publicly accessible. We show that it is possible to provide provable guarantees of test set contamination in language models without access to pretraining data or model weights. Our approach leverages the fact that when there is no data contamination, all orderings of an exchangeable benchmark should be equally likely. In contrast, the tendency for language models to memorize example order means that a contaminated language model will find certain canonical orderings to be much more likely than others. Our test flags potential contamination whenever the likelihood of a canonically ordered benchmark dataset is significantly higher than the likelihood after shuffling the examples. We demonstrate that our procedure is sensitive enough to reliably prove test set contamination in challenging situations, including models as small as 1.4 billion parameters, on small test sets of only 1000 examples, and datasets that appear only a few times in the pretraining corpus. Using our test, we audit five popular publicly accessible language models for test set contamination and find little evidence for pervasive contamination.

Large language models have achieved strong performance on medical reasoning benchmarks, yet their deployment in clinical settings demands rigorous verification to ensure factual accuracy. While reward models offer a scalable approach for reasoning trace verification, existing methods face two limitations: they produce only scalar reward values without explicit justification, and they rely on single-pass retrieval that precludes adaptive knowledge access as verification unfolds. We introduce method, an agentic framework that addresses these limitations by training medical reasoning verifiers to iteratively query external medical corpora during evaluation. Our approach combines tool-augmented verification with an iterative reinforcement learning paradigm that requires only trace-level supervision, alongside an adaptive curriculum mechanism that dynamically adjusts training data distribution. Across four medical reasoning benchmarks, method achieves substantial gains over existing methods, improving MedQA accuracy by 23.5% and MedXpertQA by 32.0% relative to the base generator in particular. Crucially, method demonstrates an 8times reduction in sampling budget requirement compared to prior reward model baselines. These findings establish that grounding verification in dynamically retrieved evidence offers a principled path toward more reliable medical reasoning systems.

Verification is a key bottleneck in improving inference speed while maintaining distribution fidelity in Speculative Decoding. Recent work has shown that sequence-level verification leads to a higher number of accepted tokens compared to token-wise verification. However, existing solutions often rely on surrogate approximations or are constrained by partial information, struggling with joint intractability. In this work, we propose Hierarchical Speculative Decoding (HSD), a provably lossless verification method that significantly boosts the expected number of accepted tokens and overcomes joint intractability by balancing excess and deficient probability mass across accessible branches. Our extensive large-scale experiments demonstrate that HSD yields consistent improvements in acceptance rates across diverse model families and benchmarks. Moreover, its strong explainability and generality make it readily integrable into a wide range of speculative decoding frameworks. Notably, integrating HSD into EAGLE-3 yields over a 12% performance gain, establishing state-of-the-art decoding efficiency without compromising distribution fidelity. Code is available at https://github.com/ZhouYuxuanYX/Hierarchical-Speculative-Decoding.

In order to properly train a machine learning model, data must be properly collected. To guarantee a proper data collection, verifying that the collected data set holds certain properties is a possible solution. For example, guaranteeing that the data set contains samples across the whole input space, or that the data set is balanced w.r.t. different classes. We present a formal approach for verifying a set of arbitrarily stated properties over a data set. The proposed approach relies on the transformation of the data set into a first order logic formula, which can be later verified w.r.t. the different properties also stated in the same logic. A prototype tool, which uses the z3 solver, has been developed; the prototype can take as an input a set of properties stated in a formal language and formally verify a given data set w.r.t. to the given set of properties. Preliminary experimental results show the feasibility and performance of the proposed approach, and furthermore the flexibility for expressing properties of interest.

Random forests and, more generally, (decision\nobreakdash-)tree ensembles are widely used methods for classification and regression. Recent algorithmic advances allow to compute decision trees that are optimal for various measures such as their size or depth. We are not aware of such research for tree ensembles and aim to contribute to this area. Mainly, we provide two novel algorithms and corresponding lower bounds. First, we are able to carry over and substantially improve on tractability results for decision trees, obtaining a (6delta D S)^S cdot poly-time algorithm, where S is the number of cuts in the tree ensemble, D the largest domain size, and delta is the largest number of features in which two examples differ. To achieve this, we introduce the witness-tree technique which also seems promising for practice. Second, we show that dynamic programming, which has been successful for decision trees, may also be viable for tree ensembles, providing an ell^n cdot poly-time algorithm, where ell is the number of trees and n the number of examples. Finally, we compare the number of cuts necessary to classify training data sets for decision trees and tree ensembles, showing that ensembles may need exponentially fewer cuts for increasing number of trees.

Test-time scaling is a powerful strategy for boosting the performance of large language models on complex reasoning tasks. While state-of-the-art approaches often employ generative verifiers to select the best solution from a pool of candidates, this method incurs prohibitive computational costs, limiting its practicality. In this work, we shift the focus to a more budget-aware paradigm: discriminative verification. We conduct a thorough empirical analysis and demonstrate that while discriminative verifiers may underperform in isolation, combining them with self-consistency in a hybrid approach creates a powerful and efficient test-time scaling mechanism. Notably, under a fixed compute budget, this hybrid approach surpasses state-of-the-art generative verification by a significant margin: achieving up to 15.3\% higher accuracy on AIME2025. Our findings establish that for practical, real-world applications, budget-aware scaling with discriminative verifiers is not only a "free" upgrade over self-consistency, but also a more effective and efficient alternative to costly generative techniques. Code is available at https://github.com/wang-research-lab/verification.

Large Language Models (LLMs) are powerful candidates for complex decision-making, leveraging vast encoded knowledge and remarkable zero-shot abilities. However, their adoption in high-stakes environments is hindered by their opacity; their outputs lack faithful explanations and cannot be effectively contested to correct errors, undermining trustworthiness. In this paper, we propose ART (Adaptive Reasoning Trees), a hierarchical method for claim verification. The process begins with a root claim, which branches into supporting and attacking child arguments. An argument's strength is determined bottom-up via a pairwise tournament of its children, adjudicated by a judge LLM, allowing a final, transparent and contestable verdict to be systematically derived which is missing in methods like Chain-of-Thought (CoT). We empirically validate ART on multiple datasets, analyzing different argument generators and comparison strategies. Our findings show that ART's structured reasoning outperforms strong baselines, establishing a new benchmark for explainable claim verification which is more reliable and ensures clarity in the overall decision making step.

Formal theorem proving (FTP) has emerged as a critical foundation for evaluating the reasoning capabilities of large language models, enabling automated verification of mathematical proofs at scale. However, progress has been constrained by limited datasets due to the high cost of manual curation and the scarcity of challenging problems with verified formal-informal correspondences. We propose leveraging theoretical computer science (TCS) as a scalable source of rigorous proof problems, where algorithmic definitions enable automated generation of arbitrarily many challenging theorem-proof pairs. We demonstrate this approach on two TCS domains: Busy Beaver problems, which involve proving bounds on Turing machine halting behavior, and Mixed Boolean Arithmetic problems, which combine logical and arithmetic reasoning. Our framework automatically synthesizes problems with parallel formal (Lean4) and informal (Markdown) specifications, creating a scalable pipeline for generating verified proof challenges. Evaluation on frontier models reveals substantial gaps in automated theorem proving: while DeepSeekProver-V2-671B achieves 57.5\% success on Busy Beaver problems, it manages only 12\% on Mixed Boolean Arithmetic problems. These results highlight the difficulty of long-form proof generation even for problems that are computationally easy to verify, demonstrating the value of TCS domains for advancing automated reasoning research.

As LLMs see wide adoption in software engineering, the reliable assessment of the correctness and security of LLM-generated code is crucial. Notably, prior work has demonstrated that security is often overlooked, exposing that LLMs are prone to generating code with security vulnerabilities. These insights were enabled by specialized benchmarks, crafted through significant manual effort by security experts. However, relying on manually-crafted benchmarks is insufficient in the long term, because benchmarks (i) naturally end up contaminating training data, (ii) must extend to new tasks to provide a more complete picture, and (iii) must increase in difficulty to challenge more capable LLMs. In this work, we address these challenges and present AutoBaxBuilder, a framework that generates tasks and tests for code security benchmarking from scratch. We introduce a robust pipeline with fine-grained plausibility checks, leveraging the code understanding capabilities of LLMs to construct functionality tests and end-to-end security-probing exploits. To confirm the quality of the generated benchmark, we conduct both a qualitative analysis and perform quantitative experiments, comparing it against tasks constructed by human experts. We use AutoBaxBuilder to construct entirely new tasks and release them to the public as AutoBaxBench, together with a thorough evaluation of the security capabilities of LLMs on these tasks. We find that a new task can be generated in under 2 hours, costing less than USD 10.

Code Large Language Models (Code LLMs) are being increasingly employed in real-life applications, so evaluating them is critical. While the conventional accuracy evaluates the performance of Code LLMs on a set of individual tasks, their self-consistency across different tasks is overlooked. Intuitively, a trustworthy model should be self-consistent when generating natural language specifications for its own code and generating code for its own specifications. Failure to preserve self-consistency reveals a lack of understanding of the shared semantics underlying natural language and programming language, and therefore undermines the trustworthiness of a model. In this paper, we first formally define the self-consistency of Code LLMs and then design a framework, IdentityChain, which effectively and efficiently evaluates the self-consistency and conventional accuracy of a model at the same time. We study eleven Code LLMs and show that they fail to preserve self-consistency, which is indeed a distinct aspect from conventional accuracy. Furthermore, we show that IdentityChain can be used as a model debugging tool to expose weaknesses of Code LLMs by demonstrating three major weaknesses that we identify in current models using IdentityChain. Our code is available at https://github.com/marcusm117/IdentityChain.

Formal verification (FV) has witnessed growing significance with current emerging program synthesis by the evolving large language models (LLMs). However, current formal verification mainly resorts to symbolic verifiers or hand-craft rules, resulting in limitations for extensive and flexible verification. On the other hand, formal languages for automated theorem proving, such as Isabelle, as another line of rigorous verification, are maintained with comprehensive rules and theorems. In this paper, we propose FVEL, an interactive Formal Verification Environment with LLMs. Specifically, FVEL transforms a given code to be verified into Isabelle, and then conducts verification via neural automated theorem proving with an LLM. The joined paradigm leverages the rigorous yet abundant formulated and organized rules in Isabelle and is also convenient for introducing and adjusting cutting-edge LLMs. To achieve this goal, we extract a large-scale FVELER3. The FVELER dataset includes code dependencies and verification processes that are formulated in Isabelle, containing 758 theories, 29,125 lemmas, and 200,646 proof steps in total with in-depth dependencies. We benchmark FVELER in the FVEL environment by first fine-tuning LLMs with FVELER and then evaluating them on Code2Inv and SV-COMP. The results show that FVEL with FVELER fine-tuned Llama3- 8B solves 17.39% (69 -> 81) more problems, and Mistral-7B 12% (75 -> 84) more problems in SV-COMP. And the proportion of proof errors is reduced. Project page: https://fveler.github.io/.

Recently, cutting-plane methods such as GCP-CROWN have been explored to enhance neural network verifiers and made significant advances. However, GCP-CROWN currently relies on generic cutting planes (cuts) generated from external mixed integer programming (MIP) solvers. Due to the poor scalability of MIP solvers, large neural networks cannot benefit from these cutting planes. In this paper, we exploit the structure of the neural network verification problem to generate efficient and scalable cutting planes specific for this problem setting. We propose a novel approach, Branch-and-bound Inferred Cuts with COnstraint Strengthening (BICCOS), which leverages the logical relationships of neurons within verified subproblems in the branch-and-bound search tree, and we introduce cuts that preclude these relationships in other subproblems. We develop a mechanism that assigns influence scores to neurons in each path to allow the strengthening of these cuts. Furthermore, we design a multi-tree search technique to identify more cuts, effectively narrowing the search space and accelerating the BaB algorithm. Our results demonstrate that BICCOS can generate hundreds of useful cuts during the branch-and-bound process and consistently increase the number of verifiable instances compared to other state-of-the-art neural network verifiers on a wide range of benchmarks, including large networks that previous cutting plane methods could not scale to. BICCOS is part of the α,β-CROWN verifier, the VNN-COMP 2024 winner. The code is available at http://github.com/Lemutisme/BICCOS .

Large Language Models (LLMs) have shown impressive performance in reasoning tasks. However, LLMs tend to generate excessively long reasoning content, leading to significant computational overhead. Our observations indicate that even on simple problems, LLMs tend to produce unnecessarily lengthy reasoning content, which is against intuitive expectations. Preliminary experiments show that at a certain point during the generation process, the model is already capable of producing the correct solution without completing the full reasoning content. Therefore, we consider that the reasoning process of the model can be exited early to achieve the purpose of efficient reasoning. We introduce a verification model that identifies the exact moment when the model can stop reasoning and still provide the correct answer. Comprehensive experiments on four different benchmarks demonstrate that our proposed method, FlashThink, effectively shortens the reasoning content while preserving the model accuracy. For the Deepseek-R1 and QwQ-32B models, we reduced the length of reasoning content by 77.04% and 77.47%, respectively, without reducing the accuracy.

Test-time scaling for complex reasoning tasks shows that leveraging inference-time compute, by methods such as independently sampling and aggregating multiple solutions, results in significantly better task outcomes. However, a critical bottleneck is verification: sampling is only effective if correct solutions can be reliably identified among candidates. While existing approaches typically evaluate candidates independently via scalar scoring, we demonstrate that models are substantially stronger at pairwise self-verification. Leveraging this insight, we introduce V_1, a framework that unifies generation and verification through efficient pairwise ranking. V_1 comprises two components: V_1-Infer, an uncertainty-guided algorithm using a tournament-based ranking that dynamically allocates self-verification compute to candidate pairs whose relative correctness is most uncertain; and V_1-PairRL, an RL framework that jointly trains a single model as both generator and pairwise self-verifier, ensuring the verifier adapts to the generator's evolving distribution. On code generation (LiveCodeBench, CodeContests, SWE-Bench) and math reasoning (AIME, HMMT) benchmarks, V_1-Infer improves Pass@1 by up to 10% over pointwise verification and outperforms recent test-time scaling methods while being significantly more efficient. Furthermore, V_1-PairRL achieves 7--9% test-time scaling gains over standard RL and pointwise joint training, and improves base Pass@1 by up to 8.7% over standard RL in a code-generation setting.

A primary concern regarding training large language models (LLMs) is whether they abuse copyrighted online text. With the increasing training data scale and the prevalence of LLMs in daily lives, two problems arise: 1) false positive membership inference results misled by similar examples; 2) membership inference methods are usually too complex for end users to understand and use. To address these issues, we propose an alternative insert-and-detect methodology, advocating that web users and content platforms employ \textit{unique identifiers} for reliable and independent membership inference. Users and platforms can create their identifiers, embed them in copyrighted text, and independently detect them in future LLMs. As an initial demonstration, we introduce \textbf{ghost sentences} and a user-friendly last-k words test, allowing end users to chat with LLMs for membership inference. Ghost sentences consist primarily of unique passphrases of random natural words, which can come with customized elements to bypass possible filter rules. The last-k words test requires a significant repetition time of ghost sentences~(ge10). For cases with fewer repetitions, we designed an extra perplexity test, as LLMs exhibit high perplexity when encountering unnatural passphrases. We also conduct a comprehensive study on the memorization and membership inference of ghost sentences, examining factors such as training data scales, model sizes, repetition times, insertion positions, wordlist of passphrases, alignment, etc. Our study shows the possibility of applying ghost sentences in real scenarios and provides instructions for the potential application.

Production assertions are statements embedded in the code to help developers validate their assumptions about the code. They assist developers in debugging, provide valuable documentation, and enhance code comprehension. Current research in this area primarily focuses on assertion generation for unit tests using techniques, such as static analysis and deep learning. While these techniques have shown promise, they fall short when it comes to generating production assertions, which serve a different purpose. This preprint addresses the gap by introducing Assertify, an automated end-to-end tool that leverages Large Language Models (LLMs) and prompt engineering with few-shot learning to generate production assertions. By creating context-rich prompts, the tool emulates the approach developers take when creating production assertions for their code. To evaluate our approach, we compiled a dataset of 2,810 methods by scraping 22 mature Java repositories from GitHub. Our experiments demonstrate the effectiveness of few-shot learning by producing assertions with an average ROUGE-L score of 0.526, indicating reasonably high structural similarity with the assertions written by developers. This research demonstrates the potential of LLMs in automating the generation of production assertions that resemble the original assertions.

Automated Theorem Proving (ATP) in formal languages remains a formidable challenge in AI, demanding rigorous logical deduction and navigating vast search spaces. While large language models (LLMs) have shown promising performance, existing stepwise provers often suffer from biased search guidance, leading to inefficiencies and suboptimal proof strategies. This paper introduces the Multi-Perspective Search Prover (MPS-Prover), a novel stepwise ATP system designed to overcome these limitations. MPS-Prover incorporates two key innovations: a highly effective post-training data curation strategy that prunes approximately 40% of redundant training data without sacrificing performance, and a multi-perspective tree search mechanism. This search integrates a learned critic model with strategically designed heuristic rules to diversify tactic selection, prevent getting trapped in unproductive states, and enhance search robustness. Extensive evaluations demonstrate that MPS-Prover achieves state-of-the-art performance on multiple challenging benchmarks, including miniF2F and ProofNet, outperforming prior 7B parameter models. Furthermore, our analyses reveal that MPS-Prover generates significantly shorter and more diverse proofs compared to existing stepwise and whole-proof methods, highlighting its efficiency and efficacy. Our work advances the capabilities of LLM-based formal reasoning and offers a robust framework and a comprehensive analysis for developing more powerful theorem provers.

We introduce our Leanabell-Prover-V2, a 7B large language models (LLMs) that can produce formal theorem proofs in Lean 4, with verifier-integrated Long Chain-of-Thoughts (CoT). Following our previous work Leanabell-Prover-V1, we continual to choose to posttrain existing strong prover models for further performance improvement. In our V2 version, we mainly upgrade the Reinforcement Learning (RL) with feedback provided by the Lean 4 verifier. Crucially, verifier feedback, such as indicating success or detailing specific errors, allows the LLM to become ``self-aware'' of the correctness of its own reasoning process and learn to reflexively correct errors. Leanabell-Prover-V2 directly optimizes LLM reasoning trajectories with multi-turn verifier interactions, together with feedback token masking for stable RL training and a simple reward strategy. Experiments show that Leanabell-Prover-V2 improves performance by 3.2% (pass@128) with Kimina-Prover-Preview-Distill-7B and 2.0% (pass@128) with DeepSeek-Prover-V2-7B on the MiniF2F test set. The source codes, curated data and models are available at: https://github.com/Leanabell-LM/Leanabell-Prover-V2.

Large Language Models (LLMs) have demonstrated remarkable progress in complex reasoning tasks through both post-training and test-time scaling laws. While prevalent test-time scaling approaches are often realized by using external reward models to guide the model generation process, we find only marginal gains can be acquired when scaling a model post-trained on specific reasoning tasks. We identify that the limited improvement stems from distribution discrepancies between the specific post-trained generator and the general reward model. To address this, we propose a framework that incentivizes LLMs to self-verify their own answers. By unifying answer generation and verification within a single reinforcement learning (RL) process, we train models that can effectively assess the correctness of their own solutions. The trained model can further scale its performance during inference time by verifying its generations, without the need for external verifiers. We train our self-verification models based on Qwen2.5-Math-7B and DeepSeek-R1-Distill-Qwen-1.5B, demonstrating its capabilities across varying reasoning context lengths. Experiments on multiple mathematical reasoning benchmarks show that our models can not only improve post-training performance but also enable effective test-time scaling. Our code is available at https://github.com/mansicer/self-verification.

There is a growing line of research on verifying the correctness of language models' outputs. At the same time, LMs are being used to tackle complex queries that require reasoning. We introduce CoverBench, a challenging benchmark focused on verifying LM outputs in complex reasoning settings. Datasets that can be used for this purpose are often designed for other complex reasoning tasks (e.g., QA) targeting specific use-cases (e.g., financial tables), requiring transformations, negative sampling and selection of hard examples to collect such a benchmark. CoverBench provides a diversified evaluation for complex claim verification in a variety of domains, types of reasoning, relatively long inputs, and a variety of standardizations, such as multiple representations for tables where available, and a consistent schema. We manually vet the data for quality to ensure low levels of label noise. Finally, we report a variety of competitive baseline results to show CoverBench is challenging and has very significant headroom. The data is available at https://huggingface.co/datasets/google/coverbench .

Software testing plays a critical role in ensuring that systems behave as intended. However, existing automated testing approaches struggle to match the capabilities of human engineers due to key limitations such as test locality, lack of general reliability, and business logic blindness. In this work, we propose a novel framework that leverages functional programming and type systems to translate Scala backend code into formal Lean representations. Our pipeline automatically generates theorems that specify the intended behavior of APIs and database operations, and uses LLM-based provers to verify them. When a theorem is proved, the corresponding logic is guaranteed to be correct and no further testing is needed. If the negation of a theorem is proved instead, it confirms a bug. In cases where neither can be proved, human intervention is required. We evaluate our method on realistic backend systems and find that it can formally verify over 50% of the test requirements, which suggests that half of a testing engineer's workload can be automated. Additionally, with an average cost of only $2.19 per API, LLM-based verification is significantly more cost-effective than manual testing and can be scaled easily through parallel execution. Our results indicate a promising direction for scalable, AI-powered software testing, with the potential to greatly improve engineering productivity as models continue to advance.

Test case generation is an important activity, yet a time-consuming and laborious task. Recently, AthenaTest -- a deep learning approach for generating unit test cases -- is proposed. However, AthenaTest can generate less than one-fifth of the test cases correctly, due to a lack of assertion knowledge and test signature verification. In this paper, we propose A3Test, a DL-based test case generation approach that is augmented by assertion knowledge with a mechanism to verify naming consistency and test signatures. A3Test leverages the domain adaptation principles where the goal is to adapt the existing knowledge from an assertion generation task to the test case generation task. We also introduce a verification approach to verify naming consistency and test signatures. Through an evaluation of 5,278 focal methods from the Defects4j dataset, we find that our A3Test (1) achieves 147% more correct test cases and 15% more method coverage, with a lower number of generated test cases than AthenaTest; (2) still outperforms the existing pre-trained models for the test case generation task; (3) contributes substantially to performance improvement via our own proposed assertion pre-training and the verification components; (4) is 97.2% much faster while being more accurate than AthenaTest.