Daily Papers

In LLM inference, the same prompt may yield different outputs across different runs. At the system level, this non-determinism arises from floating-point non-associativity combined with dynamic batching and GPU kernels whose reduction orders vary with batch size. A straightforward way to eliminate non-determinism is to disable dynamic batching during inference, but doing so severely degrades throughput. Another approach is to make kernels batch-invariant; however, this tightly couples determinism to kernel design, requiring new implementations. This coupling also imposes fixed runtime overheads, regardless of how much of the workload actually requires determinism. Inspired by ideas from speculative decoding, we present LLM-42, a scheduling-based approach to enable determinism in LLM inference. Our key observation is that if a sequence is in a consistent state, the next emitted token is likely to be consistent even with dynamic batching. Moreover, most GPU kernels use shape-consistent reductions. Leveraging these insights, LLM-42 decodes tokens using a non-deterministic fast path and enforces determinism via a lightweight verify-rollback loop. The verifier replays candidate tokens under a fixed-shape reduction schedule, commits those that are guaranteed to be consistent across runs, and rolls back those violating determinism. LLM-42 mostly re-uses existing kernels unchanged and incurs overhead only in proportion to the traffic that requires determinism.

Large Language Models (LLMs) often generate code with subtle but critical bugs, especially for complex tasks. Existing automated repair methods typically rely on superficial pass/fail signals, offering limited visibility into program behavior and hindering precise error localization. In addition, without a way to learn from prior failures, repair processes often fall into repetitive and inefficient cycles. To overcome these challenges, we present TraceCoder, a collaborative multi-agent framework that emulates the observe-analyze-repair process of human experts. The framework first instruments the code with diagnostic probes to capture fine-grained runtime traces, enabling deep insight into its internal execution. It then conducts causal analysis on these traces to accurately identify the root cause of the failure. This process is further enhanced by a novel Historical Lesson Learning Mechanism (HLLM), which distills insights from prior failed repair attempts to inform subsequent correction strategies and prevent recurrence of similar mistakes. To ensure stable convergence, a Rollback Mechanism enforces that each repair iteration constitutes a strict improvement toward the correct solution. Comprehensive experiments across multiple benchmarks show that TraceCoder achieves up to a 34.43\% relative improvement in Pass@1 accuracy over existing advanced baselines. Ablation studies verify the significance of each system component, with the iterative repair process alone contributing a 65.61\% relative gain in accuracy. Furthermore, TraceCoder significantly outperforms leading iterative methods in terms of both accuracy and cost-efficiency.

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.

Automated vulnerability reproduction from CVE descriptions requires generating executable Proof-of-Concept (PoC) exploits and validating them in target environments. This process is critical in software security research and practice, yet remains time-consuming and demands specialized expertise when performed manually. While LLM agents show promise for automating this task, existing approaches often conflate exploring attack directions with fixing implementation details, which leads to unproductive debugging loops when reproduction fails. To address this, we propose CVE2PoC, an LLM-based dual-loop agent framework following a plan-execute-evaluate paradigm. The Strategic Planner analyzes vulnerability semantics and target code to produce structured attack plans. The Tactical Executor generates PoC code and validates it through progressive verification. The Adaptive Refiner evaluates execution results and routes failures to different loops: the Tactical Loop for code-level refinement, while the Strategic Loop for attack strategy replanning. This dual-loop design enables the framework to escape ineffective debugging by matching remediation to failure type. Evaluation on two benchmarks covering 617 real-world vulnerabilities demonstrates that CVE2PoC achieves 82.9% and 54.3% reproduction success rates on SecBench.js and PatchEval, respectively, outperforming the best baseline by 11.3% and 20.4%. Human evaluation confirms that generated PoCs achieve comparable code quality to human-written exploits in readability and reusability.

Code production is now a commodity; the bottleneck is knowing what to build and proving it works. We present the Kitchen Loop, a framework for autonomous, self-evolving software built on a unified trust model: (1) a specification surface enumerating what the product claims to support; (2) 'As a User x 1000', where an LLM agent exercises that surface as a synthetic power user at 1,000x human cadence; (3) Unbeatable Tests, ground-truth verification the code author cannot fake; and (4) Drift Control, continuous quality measurement with automated pause gates. We validate across two production systems over 285+ iterations, producing 1,094+ merged pull requests with zero regressions detected by the regression oracle (methodology in Section 6.1). We observe emergent properties at scale: multi-iteration self-correction chains, autonomous infrastructure healing, and monotonically improving quality gates. The primitives are not new; our contribution is their composition into a production-tested system with the operational discipline that makes long-running autonomous evolution safe.

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).

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.

Code auditing is the process of reviewing code with the aim of identifying bugs. Large Language Models (LLMs) have demonstrated promising capabilities for this task without requiring compilation, while also supporting user-friendly customization. However, auditing a code repository with LLMs poses significant challenges: limited context windows and hallucinations can degrade the quality of bug reports, and analyzing large-scale repositories incurs substantial time and token costs, hindering efficiency and scalability. This work introduces an LLM-based agent, RepoAudit, designed to perform autonomous repository-level code auditing. Equipped with agent memory, RepoAudit explores the codebase on demand by analyzing data-flow facts along feasible program paths within individual functions. It further incorporates a validator module to mitigate hallucinations by verifying data-flow facts and checking the satisfiability of path conditions associated with potential bugs, thereby reducing false positives. RepoAudit detects 40 true bugs across 15 real-world benchmark projects with a precision of 78.43%, requiring on average only 0.44 hours and $2.54 per project. Also, it detects 185 new bugs in high-profile projects, among which 174 have been confirmed or fixed. We have open-sourced RepoAudit at https://github.com/PurCL/RepoAudit.

We study auto research as a closed empirical loop driven by external measurement. Each submitted trial carries a hypothesis, an executable code edit, an evaluator-owned outcome, and feedback that shapes the next proposal. The output is not a generated paper or a single model checkpoint, but an auditable trajectory of proposals, code diffs, experiments, scores, and failure labels. We instantiate this loop with specialist agents that partition recipe surfaces and share measured lineage across trials. The central empirical finding is that lineage feedback lets agents turn evaluator outcomes, including crashes, budget overruns, size failures, and accuracy-gate misses, into later program-level recipe edits rather than one-shot suggestions. Across 1,197 headline-run trials plus 600 Parameter Golf control trials after one-time setup and launch, humans did not choose proposals, edit recipes, override scores, or repair failed trials during the search. In the three headline runs, the same submitted-trial loop reduces Parameter Golf validation bpb by 0.81%, raises NanoChat-D12 CORE by 38.7%, and reduces CIFAR-10 Airbench96 wallclock by 4.59%, with each task measured by its own external evaluator and legality checks. The trace includes a strict architecture-domain audit of 157 headline-run submissions and program rewrites such as a NanoChat attention-kernel path change. Within this scope the loop autonomously writes code, submits experiments, absorbs feedback, applies and combines known techniques inside each environment, and improves public starting recipes.

Large language models (LLMs) can translate natural language into optimization code, but silent failures pose a critical risk: code that executes and returns solver-feasible solutions may encode semantically incorrect formulations, creating a feasibility-correctness gap of up to 90 percentage points on compositional problems. We introduce ReLoop, addressing silent failures from two complementary directions. Structured generation decomposes code production into a four-stage reasoning chain (understand, formalize, synthesize, verify) that mirrors expert modeling practice, with explicit variable-type reasoning and self-verification to prevent formulation errors at their source. Behavioral verification detects errors that survive generation by testing whether the formulation responds correctly to solver-based parameter perturbation, without requiring ground truth -- an external semantic signal that bypasses the self-consistency problem inherent in LLM-based code review. The two mechanisms are complementary: structured generation dominates on complex compositional problems, while behavioral verification becomes the largest single contributor on problems with localized formulation defects. Together with execution recovery via IIS-enhanced diagnostics, ReLoop raises correctness from 22.6% to 31.1% and execution from 72.1% to 100.0% on the strongest model, with consistent gains across five models spanning three paradigms (foundation, SFT, RL) and three benchmarks. We additionally release RetailOpt-190, 190 compositional retail optimization scenarios targeting the multi-constraint interactions where LLMs most frequently fail.

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.

We address the problem of runtime trajectory anomaly detection, a critical capability for enabling trustworthy LLM agents. Current safety measures predominantly focus on static input/output filtering. However, we argue that ensuring LLM agents reliability requires auditing the intermediate execution process. In this work, we formulate the task of Trajectory Anomaly Detection. The goal is not merely detection, but precise error localization. This capability is essential for enabling efficient rollback-and-retry. To achieve this, we construct TrajBench, a dataset synthesized via a perturb-and-complete strategy to cover diverse procedural anomalies. Using this benchmark, we investigate the capability of models in process supervision. We observe that general-purpose LLMs, even with zero-shot prompting, struggle to identify and localize these anomalies. This reveals that generalized capabilities do not automatically translate to process reliability. To address this, we propose TrajAD, a specialized verifier trained with fine-grained process supervision. Our approach outperforms baselines, demonstrating that specialized supervision is essential for building trustworthy agents.

Large Language Models (LLMs) are being increasingly used in software engineering tasks, with an increased focus on bug report resolution over the past year. However, most proposed systems fail to properly handle uncertain or incorrect inputs and outputs. Existing LLM-based tools and coding agents respond to every issue and generate a patch for every case, even when the input is vague or their own output is incorrect. There are no mechanisms in place to abstain when confidence is low. This leads to unreliable behaviour, such as hallucinated code changes or responses based on vague issue reports. We introduce BouncerBench, a benchmark that evaluates whether LLM-based software agents can refuse to act when inputs are ill-defined or refuse to respond when their own outputs are likely to be incorrect. Unlike prior benchmarks that implicitly incentivize models to generate responses even when uncertain, BouncerBench aims to improve precision by targeting two overlooked failure points: (1) vague or underspecified issue descriptions in tickets and (2) logically or functionally incorrect code patches created by the system. It measures whether proposed systems can distinguish actionable issues from vague tickets and valid patches from untrustworthy ones. We also implement a basic input and output bouncer, evaluating how well current LLMs can abstain when needed. Our results show that most models fail to abstain from underspecified inputs or incorrect outputs. Hence, we conclude that there is significant room for improvement before LLMs can be trusted to make correct decisions and recommendations in real-world software engineering workflows. BouncerBench provides a first step toward evaluating and building more cautious, trustworthy code agents. The replication package, dataset, and leaderboard can be found at bouncerbench.com

Training LLMs on decentralized and wimpy computation nodes, e.g., multiple on-spot instances, lowers the training cost and enables model democratization. The inevitable challenge here is the churn of nodes due to failures and the operator's scheduling policies, leading to losing a stage - a part of the model. The conventional approaches to recover from failures are to either use checkpointing, where periodically a copy of the entire model is sent to an additional storage, or redundant computation. These approaches yield significant communication and/or computation overhead even in non-failure cases and scale poorly in settings with large models. In this paper, we propose, CheckFree, an efficient recovery method where a failing stage is substituted by a weighted average of the closest neighboring stages. In contrast to the state of the art, CheckFree requires no additional computation or storage. However, because of the nature of averaging neighbouring stages, it can only recover failures of intermediate stages. We further extend our method to CheckFree+ with out-of-order pipeline execution to tolerate crashes of the first and last stages. Thanks to out-of-order pipelining, behaviour of those stages is mimicked by their neighboring ones, which allows CheckFree+ to recover them by simply copying the weights from the immediate neighbour. To be able to recover the (de)embedding layers, CheckFree+ copies those layers to the neighboring stages, which requires relatively small storage overhead. We extensively evaluate our method on LLaMa models of model sizes from 124M to 1.5B with varying failure frequencies. In the case of low and medium failure rates (5-10%), CheckFree and CheckFree+ outperform both checkpointing and redundant computation in terms of convergence in wall-clock time by over 12%. Both of our proposals can be run via our code available at: https://github.com/gensyn-ai/CheckFree.

Reinforcement Learning from Verifiable Rewards (RLVR) has emerged as a powerful paradigm for enhancing the complex reasoning capabilities of Large Reasoning Models. However, standard outcome-based supervision suffers from a critical limitation that penalizes trajectories that are largely correct but fail due to several missteps as heavily as completely erroneous ones. This coarse feedback signal causes the model to discard valuable largely correct rollouts, leading to a degradation in rollout diversity that prematurely narrows the exploration space. Process Reward Models have demonstrated efficacy in providing reliable step-wise verification for test-time scaling, naively integrating these signals into RLVR as dense rewards proves ineffective.Prior methods attempt to introduce off-policy guided whole-trajectory replacement that often outside the policy model's distribution, but still fail to utilize the largely correct rollouts generated by the model itself and thus do not effectively mitigate the narrowing of the exploration space. To address these issues, we propose SCOPE (Step-wise Correction for On-Policy Exploration), a novel framework that utilizes Process Reward Models to pinpoint the first erroneous step in suboptimal rollouts and applies fine-grained, step-wise off-policy rectification. By applying precise refinement on partially correct rollout, our method effectively salvages partially correct trajectories and increases diversity score by 13.5%, thereby sustaining a broad exploration space. Extensive experiments demonstrate that our approach establishes new state-of-the-art results, achieving an average accuracy of 46.6% on math reasoning and exhibiting robust generalization with 53.4% accuracy on out-of-distribution reasoning tasks.

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.

One-shot Program-of-Thought (PoT) emits a Python program that prints a primitive-action plan; a single invalid action silently invalidates the trajectory. We introduce RePoT (Recoverable PoT): a deterministic verified replay that walks the plan through the environment to its first invalid transition, then one LLM call that resumes from the verified prefix. RePoT costs at most one extra LLM call on the ~14% of problems where PoT fails. RePoT beats PoT by +3 to +11pp across four closed-model configurations on PuzzleZoo-775 and peaks at 96.9% vs 86.3% on gpt-5.4-mini-medium; against the matched-budget PoT-retry baseline, RePoT wins decisively on Gemini (+3.8pp, 95% CI [+2.2,+5.4]), is within sampling noise on GPT-medium and Claude, and loses on GPT-mini -- a capability-scaling pattern we begin to address with Adaptive RePoT, a rule-based dispatcher that routes between suffix repair and a fresh PoT retry based on verified-prefix length (preliminary). We replicate on PlanBench Blocksworld (+1.1 to +11.4pp) and on four open-weights models (+3.3 to +20.0pp on three of four). On Derail-550, our controlled recovery benchmark, every condition with access to checkpoint information clears >=30% on GPT-medium and >=70% on Gemini, vs <=3.1% for error-only feedback -- showing that checkpoint information, not the specific verified-prefix tail, is the load-bearing recovery signal.

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.

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.

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.

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

Reliable evaluation is essential for developing and deploying large language models, yet in practice it often requires substantial manual effort: practitioners must identify appropriate benchmarks, reproduce heterogeneous evaluation codebases, configure dataset schema mappings, and interpret aggregated metrics. To address these challenges, we present One-Eval, an agentic evaluation system that converts natural-language evaluation requests into executable, traceable, and customizable evaluation workflows. One-Eval integrates (i) NL2Bench for intent structuring and personalized benchmark planning, (ii) BenchResolve for benchmark resolution, automatic dataset acquisition, and schema normalization to ensure executability, and (iii) Metrics \& Reporting for task-aware metric selection and decision-oriented reporting beyond scalar scores. The system further incorporates human-in-the-loop checkpoints for review, editing, and rollback, while preserving sample evidence trails for debugging and auditability. Experiments show that One-Eval can execute end-to-end evaluations from diverse natural-language requests with minimal user effort, supporting more efficient and reproducible evaluation in industrial settings. Our framework is publicly available at https://github.com/OpenDCAI/One-Eval.

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.

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

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%.

Self-Correction aims to enable large language models (LLMs) to self-verify and self-refine their initial responses without external feedback. However, LLMs often fail to effectively self-verify and generate correct feedback, further misleading refinement and leading to the failure of self-correction, especially in complex reasoning tasks. In this paper, we propose Program-driven Self-Correction (ProgCo). First, program-driven verification (ProgVe) achieves complex verification logic and extensive validation through self-generated, self-executing verification pseudo-programs. Then, program-driven refinement (ProgRe) receives feedback from ProgVe, conducts dual reflection and refinement on both responses and verification programs to mitigate misleading of incorrect feedback in complex reasoning tasks. Experiments on three instruction-following and mathematical benchmarks indicate that ProgCo achieves effective self-correction, and can be further enhance performance when combined with real program tools.

We describe a verification pipeline that takes production Rust cryptographic code and produces machine-checked correctness proofs in Lean 4. The pipeline combines three components: symbolic extraction tools (Charon and Aeneas, or Hax) that lift Rust into Lean 4; formal cryptographic specification libraries (ArkLib and CompPoly, from the Verified zkEVM project) that provide the mathematical targets; and AI provers (Aristotle from Harmonic AI and Aleph from Logical Intelligence) that close the resulting proof obligations. Every proof is checked by the Lean kernel, so AI output cannot compromise soundness. Within the scope of the Ethereum Foundation's zkEVM Verification Project, we applied the pipeline to cryptographic primitives in Plonky3 (FRI folding, Mersenne31 and KoalaBear field arithmetic, Horner polynomial evaluation) and RISC Zero (Merkle inclusion verification). In addition, Aleph authored proofs of two bounds-style theorems in Plonky3's compute_log_arity_for_round that previously stood as sorry. The paper describes the architecture, walks through a running example based on Aleph's two proofs, reports which classes of proof obligations AI closed and which required manual work, and discusses the engineering gaps we encountered: Lean 4 toolchain drift across tools and specific Aeneas/Hax extraction limits. We also document concrete missing lemmas, tactic gaps, and code-generation friction points discovered during proof development. We hope this contribution lowers the barrier to adoption of formal verification and facilitates more effective use of AI in this pipeline. The result is a working pipeline for formal verification of Rust, with kernel-checked proofs and reproducible artefacts.

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 .

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.

In this paper we present a new "external checker" for the Lean theorem prover, written in Lean itself. This is the first complete typechecker for Lean 4 other than the reference implementation in C++ used by Lean itself, and our new checker is competitive with the original, running between 20% and 50% slower and usable to verify all of Lean's mathlib library, forming an additional step in Lean's aim to self-host the full elaborator and compiler. Moreover, because the checker is written in a language which admits formal verification, it is possible to state and prove properties about the kernel itself, and we report on progress to formalize the Lean type theory abstractly and prove some theorems about it. Finally, we combine these to get a proof of correctness of parts of the kernel. We plan to use this project to help justify any future changes to the kernel and type theory and ensure unsoundness does not sneak in through either the abstract theory or implementation bugs. The verification is already paying off, as one soundness bug has been spotted and fixed as a result of this work.

Autonomous agentic systems are largely static after deployment: they do not learn from user interactions, and recurring failures persist until the next human-driven update ships a fix. Self-evolving agents have emerged in response, but all confine evolution to text-mutable artifacts -- skill files, prompt configurations, memory schemas, workflow graphs -- and leave the agent harness untouched. Since routing, hook ordering, state invariants, and dispatch live in code rather than in any text artifact, an entire class of structural failure is physically unreachable from the text layer. We argue that source-level adaptation is a fundamentally more general medium: it is Turing-complete, a strict superset of every text-mutable scope, takes effect deterministically rather than through base-model compliance, and does not erode under long-context drift. We present MOSS, a system that performs self-rewriting at the source level on production agentic substrates. Each evolution is anchored to an automatically curated batch of production-failure evidence and proceeds through a deterministic multi-stage pipeline; code modification is delegated to a pluggable external coding-agent CLI while MOSS retains stage ordering and verdicts. Candidates are verified by replaying the batch against the candidate image in ephemeral trial workers, then promoted via user-consent-gated, in-place container swap with health-probe-gated rollback. On OpenClaw, MOSS lifts a four-task mean grader score from 0.25 to 0.61 in a single cycle without human intervention.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a promising paradigm for enhancing the reasoning capabilities of large language models (LLMs). In this context, models explore reasoning trajectories and exploit rollouts with correct answers as positive signals for policy optimization. However, these rollouts might involve flawed patterns such as answer-guessing and jump-in-reasoning. Such flawed-positive rollouts are rewarded identically to fully correct ones, causing policy models to internalize these unreliable reasoning patterns. In this work, we first conduct a systematic study of flawed-positive rollouts in RL and find that they enable rapid capability gains during the early optimization stage, while constraining reasoning capability later by reinforcing unreliable patterns. Building on these insights, we propose Flawed-Aware Policy Optimization (FAPO), which presents a parameter-free reward penalty for flawed-positive rollouts, enabling the policy to leverage them as useful shortcuts in the warm-up stage, securing stable early gains, while gradually shifting optimization toward reliable reasoning in the later refinement stage. To accurately and comprehensively detect flawed-positive rollouts, we introduce a generative reward model (GenRM) with a process-level reward that precisely localizes reasoning errors. Experiments show that FAPO is effective in broad domains, improving outcome correctness, process reliability, and training stability without increasing the token budget.

Large language models generate plausible code but cannot verify correctness. Existing multi-agent systems simulate execution or leave verification optional. We introduce execution-grounded verification as a first-class principle: every code change must survive sandboxed execution before propagation. We instantiate this principle in AGENTFORGE, a multi-agent framework where Planner, Coder, Tester, Debugger, and Critic agents coordinate through shared memory and a mandatory Docker sandbox. We formalize software engineering with LLMs as an iterative decision process over repository states, where execution feedback provides a stronger supervision signal than next-token likelihood. AGENTFORGE achieves 40.0\% resolution on SWE-BENCH Lite, outperforming single-agent baselines by 26--28 points. Ablations confirm that execution feedback and role decomposition each independently drive performance. The framework is open-source at https://github.com/raja21068/AutoCodeAI.

Autonomous research systems increasingly make the scientific workflow executable: agents can propose ideas, run code, inspect results, and draft papers. But executable workflows do not by themselves produce research judgment. We analyze where current systems lose trial experience: weak evidence becomes prose, pilot signals become broad claims, memory remains textual, and recurring process failures do not change later behavior. We introduce Sibyl-AutoResearch, a self-evolving AutoResearch framework built around Scientific Trial-and-Error Harnesses. A harness lets agents run bounded trials, preserve positive and negative outcomes, and route lessons into later planning, validation, claim scope, scheduling, critique, writing, and harness repair. We formalize this through two auditable conversion units: trial-to-behavior conversion, which links trial signals to later research actions, and trial-to-harness-behavior conversion, which links recurring process failures to system updates. We implement the framework in SIBYL, a file-backed autonomous research system that exposes the state, roles, memory, gates, and artifact traces needed to inspect these conversion paths. A retrospective audit identifies eight high-confidence conversion events, with a median latency of one iteration and a maximum latency of three iterations. A recovered-failure registry further shows how five naturally occurring failure classes, including duplicate results, stale numbers, and unsupported statistics, were blocked, downgraded, or routed into later repair. These traces do not establish a comparative performance claim; they show that the proposed conversion units are recoverable from realistic autonomous-research workspaces. The SIBYL framework and system are available at https://github.com/Sibyl-Research-Team/AutoResearch-SibylSystem.

Under a unified operational definition, we define LLM memory as a persistent state written during pretraining, finetuning, or inference that can later be addressed and that stably influences outputs. We propose a four-part taxonomy (parametric, contextual, external, procedural/episodic) and a memory quadruple (location, persistence, write/access path, controllability). We link mechanism, evaluation, and governance via the chain write -> read -> inhibit/update. To avoid distorted comparisons across heterogeneous setups, we adopt a three-setting protocol (parametric only, offline retrieval, online retrieval) that decouples capability from information availability on the same data and timeline. On this basis we build a layered evaluation: parametric (closed-book recall, edit differential, memorization/privacy), contextual (position curves and the mid-sequence drop), external (answer correctness vs snippet attribution/faithfulness), and procedural/episodic (cross-session consistency and timeline replay, E MARS+). The framework integrates temporal governance and leakage auditing (freshness hits, outdated answers, refusal slices) and uncertainty reporting via inter-rater agreement plus paired tests with multiple-comparison correction. For updating and forgetting, we present DMM Gov: coordinating DAPT/TAPT, PEFT, model editing (ROME, MEND, MEMIT, SERAC), and RAG to form an auditable loop covering admission thresholds, rollout, monitoring, rollback, and change audits, with specs for timeliness, conflict handling, and long-horizon consistency. Finally, we give four testable propositions: minimum identifiability; a minimal evaluation card; causally constrained editing with verifiable forgetting; and when retrieval with small-window replay outperforms ultra-long-context reading. This yields a reproducible, comparable, and governable coordinate system for research and deployment.

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.

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.

Test-time reinforcement learning (TTRL) has emerged as a promising paradigm for self-evolving large reasoning models (LRMs), enabling online adaptation on unlabeled test inputs via self-induced rewards through majority voting. However, a spurious yet high-frequency unverified consensus can become a biased and reinforced reward signal, leading to incorrect mode collapse. We address this failure mode with T^3RL (Tool-Verification for Test-Time Reinforcement Learning), which introduces test-time tool verification into reward estimation. Concretely, a verifier uses an external tool as evidence (e.g., from code execution) to upweight verified rollouts in a verification-aware voting, producing more reliable pseudo-labels for training. Across various math difficulties (MATH-500, AMC, and AIME 2024) and diverse backbone types, T^3RL significantly improves over TTRL, with larger gains on harder problems. More broadly, T^3RL can be viewed as verified online data synthesis, highlighting test-time tool verification as a key mechanism for stabilizing self-evolution.

The strong performance of large language models (LLMs) on natural language processing tasks raises extensive discussion on their application to code generation. Recent work suggests multiple sampling approaches to improve initial code generation accuracy or program repair approaches to refine the code. However, these methods suffer from LLMs' inefficiencies and limited reasoning capacity. In this work, we propose an LLM programming workflow (LPW) designed to improve both initial code generation and subsequent refinements within a structured two-phase workflow. Specifically, in the solution generation phase, the LLM first outlines a solution plan that decomposes the problem into manageable sub-problems and then verifies the generated solution plan through visible test cases. Subsequently, in the code implementation phase, the LLM initially drafts a code according to the solution plan and its verification. If the generated code fails the visible tests, the plan verification serves as the intended natural language solution to inform the refinement process for correcting bugs. We further introduce SLPW, a sampling variant of LPW, which initially generates multiple solution plans and plan verifications, produces a program for each plan and its verification, and refines each program as necessary until one successfully passes the visible tests. Compared to the state-of-the-art methods across various existing LLMs, our experimental results show that LPW significantly improves the Pass@1 accuracy by up to 16.4% on well-established text-to-code generation benchmarks, especially with a notable improvement of around 10% on challenging benchmarks. Additionally, SLPW demonstrates up to a 5.6% improvement over LPW and sets new state-of-the-art Pass@1 accuracy on various benchmarks, e.g., 98.2% on HumanEval, 84.8% on MBPP, 64.0% on APPS, and 35.3% on CodeContest, using GPT-4o as the backbone.

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.

Reinforcement learning (RL) has become a central post-training tool for improving the reasoning abilities of large language models (LLMs). In these systems, the rollout, the trajectory sampled from a prompt to termination, including intermediate reasoning steps and optional tool or environment interactions, determines the data the optimizer learns from, yet rollout design is often underreported. This survey provides an optimizer-agnostic view of rollout strategies for RL-based post-training of reasoning LLMs. We formalize rollout pipelines with unified notation and introduce Generate-Filter-Control-Replay (GFCR), a lifecycle taxonomy that decomposes rollout pipelines into four modular stages: Generate proposes candidate trajectories and topologies; Filter constructs intermediate signals via verifiers, judges, critics; Control allocates compute and makes continuation/branching/stopping decisions under budgets; and Replay retains and reuses artifacts across rollouts without weight updates, including self-evolving curricula that autonomously generate new training tasks. We complement GFCR with a criterion taxonomy of reliability, coverage, and cost sensitivity that characterizes rollout trade-offs. Using this framework, we synthesize methods spanning RL with verifiable rewards, process supervision, judge-based gating, guided and tree/segment rollouts, adaptive compute allocation, early-exit and partial rollouts, throughput optimization, and replay/recomposition for self-improvement. We ground the framework with case studies in math, code/SQL, multimodal reasoning, tool-using agents, and agentic skill benchmarks that evaluate skill induction, reuse, and cross-task transfer. Finally, we provide a diagnostic index that maps common rollout pathologies to GFCR modules and mitigation levers, alongside open challenges for building reproducible, compute-efficient, and trustworthy rollout pipelines.

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.

Formal specification is essential for rigorous program verification, yet writing correct specifications remains costly and difficult to automate. Although large language models (LLMs) and agents have shown promising progress, their true capabilities and failure modes remain unclear. We present the first systematic and contamination-aware study of LLM- and agent-based formal specification generation for C programs. We introduce LiveFMBench, a continuously evolving benchmark of 630 ACSL (ANSI/ISO C Specification Language)-annotated C programs, including 360 newly collected cases designed to mitigate data leakage. Using this benchmark, we evaluate direct prompting with different sampling sizes, reasoning-enabled (thinking mode) inference, the agentic pipeline, and perform a fine-grained failure analysis. Experimental results reveal that naive evaluation substantially overestimates performance because models under direct prompting may exhibit unfaithful behaviors, such as deceiving automated provers or ignoring code-context constraints; after excluding such cases, the true specification generation accuracy drops by approximately 20\%. We further find that both increased sampling and thinking mode significantly improve success rates, with smaller models benefiting more from thinking mode. Agentic pipelines are particularly effective under low sampling budgets and on harder datasets. Failure analysis further shows that incorrect loop invariants are the dominant error type, while agentic pipelines notably reduce assertion errors. These results expose fundamental limitations in current LLM-based approaches and suggest they remain far from replacing human-authored formal specifications. We release LiveFMBench at https://huggingface.co/datasets/fm-universe/Live-FM-Bench and all evaluation artifacts to support future research.

The automated generation of test code can reduce the time and effort required to build software while increasing its correctness and robustness. In this paper, we present RE-ASSERT, an approach for the automated generation of JUnit test asserts which produces more accurate asserts than previous work with fewer constraints. This is achieved by targeting projects individually, using precise code-to-test traceability for learning and by generating assert statements from the method-under-test directly without the need to write an assert-less test first. We also utilise Reformer, a state-of-the-art deep learning model, along with two models from previous work to evaluate ReAssert and an existing approach, known as ATLAS, using lexical accuracy,uniqueness, and dynamic analysis. Our evaluation of ReAssert shows up to 44% of generated asserts for a single project match exactly with the ground truth, increasing to 51% for generated asserts that compile. We also improve on the ATLAS results through our use of Reformer with 28% of generated asserts matching exactly with the ground truth. Reformer also produces the greatest proportion of unique asserts (71%), giving further evidence that Reformer produces the most useful asserts.

Multi-path speculative decoding accelerates lossless sampling from a target model by using a cheaper draft model to generate a draft tree of tokens, and then applies a verification algorithm that accepts a subset of these. While prior work has proposed various verification algorithms for i.i.d rollouts, their relative performance under matched settings remains unclear. In this work, we firstly present a systematic evaluation of verification strategies across model families, tasks, and sampling regimes, and find that Traversal Verification dominates consistently, with OT-based methods lagging far behind. Our analysis uncovers that this occurs because OT-based methods achieve high multi-token acceptance near the root of the draft tree, while multi-token gains are most impactful deeper in the draft tree, where draft and target distributions diverge. Based on this insight, we propose delayed tree expansion, which drafts a partial single path, delaying the i.i.d. branching point. We show that delayed tree expansion preserves the target distribution and improves on root-node i.i.d rollouts. Further, we develop a dynamic neural selector that estimates the expected block efficiency of optimal-transport-based verification methods from draft and target features, enabling context-dependent expansion decisions. Our neural selector allows OT-based methods like SpecInfer to outperform Traversal Verification for the first time, achieving 5% higher average throughput across a wide range of models, datasets, and sampling settings.

Tool-using automation systems, from scripts and CI bots to agentic assistants, fail in recurring patterns. Common failures include unsafe side effects, invalid arguments, uncontrolled retries, and leakage of sensitive outputs. Many mitigations are model-centric and prompt-dependent, so they are brittle and do not generalize to non-LLM callers. We present Policy-First Tooling, a model-agnostic permission layer that mediates tool invocation through explicit constraints, risk-aware gating, recovery controls, and auditable explanations. The paper contributes a compact policy DSL, a runtime enforcement architecture with actionable rationale and fix hints, and a reproducible benchmark based on trace replay with controlled fault and misuse injection. In 225 controlled runs across five policy packs and three fault profiles, stricter packs improve violation prevention from 0.000 in P0 to 0.681 in P4, while task success drops from 0.356 to 0.067. Retry amplification decreases from 3.774 in P0 to 1.378 in P4, and leakage recall reaches 0.875 under injected secret outputs. These results make safety to utility trade-offs explicit and measurable.

Constructing large-scale datasets for the GitHub issue resolution task is crucial for both training and evaluating the software engineering capabilities of Large Language Models (LLMs). However, the traditional process for creating such benchmarks is notoriously challenging and labor-intensive, particularly in the stages of setting up evaluation environments, grading test outcomes, and validating task instances. In this paper, we propose SWE-Factory, an automated pipeline designed to address these challenges. To tackle these issues, our pipeline integrates three core automated components. First, we introduce SWE-Builder, a multi-agent system that automates evaluation environment construction, which employs four specialized agents that work in a collaborative, iterative loop and leverages an environment memory pool to enhance efficiency. Second, we introduce a standardized, exit-code-based grading method that eliminates the need for manually writing custom parsers. Finally, we automate the fail2pass validation process using these reliable exit code signals. Experiments on 671 issues across four programming languages show that our pipeline can effectively construct valid task instances; for example, with GPT-4.1-mini, our SWE-Builder constructs 269 valid instances at 0.045 per instance, while with Gemini-2.5-flash, it achieves comparable performance at the lowest cost of 0.024 per instance. We also demonstrate that our exit-code-based grading achieves 100% accuracy compared to manual inspection, and our automated fail2pass validation reaches a precision of 0.92 and a recall of 1.00. We hope our automated pipeline will accelerate the collection of large-scale, high-quality GitHub issue resolution datasets for both training and evaluation. Our code and datasets are released at https://github.com/DeepSoftwareAnalytics/swe-factory.

LLM agents struggle with regulatory audit replay: when asked to reproduce a flagged transaction decision with identical inputs, many deployments fail to return consistent results. We introduce the Determinism-Faithfulness Assurance Harness (DFAH), a framework for measuring trajectory determinism, decision determinism, and evidence-conditioned faithfulness in tool-using agents deployed in financial services. Across 4,700+ agentic runs (7 models, 4 providers, 3 financial benchmarks with 50 cases each at T=0.0), we find that decision determinism and task accuracy are not detectably correlated (r = -0.11, 95% CI [-0.49, 0.31], p = 0.63, n = 21 configurations): models can be deterministic without being accurate, and accurate without being deterministic. Because neither metric predicts the other in our sample, both must be measured independently, which is precisely what DFAH provides. Small models (7-20B) achieve near-perfect determinism through rigid pattern matching at the cost of accuracy (20-42%), while frontier models show moderate determinism (50-96%) with variable accuracy. No model achieves both perfect determinism and high accuracy, supporting DFAH's multi-dimensional measurement approach. We provide three financial benchmarks (compliance triage, portfolio constraints, and DataOps exceptions; 50 cases each) together with an open-source stress-test harness. Across these benchmarks and DFAH evaluation settings, Tier 1 models with schema-first architectures achieved determinism levels consistent with audit replay requirements.

Large Language Models (LLMs) have significantly advanced automated test generation, yet existing methods often rely on ground-truth code for verification, risking bug propagation and limiting applicability in test-driven development. We present ConVerTest, a novel two-stage pipeline for synthesizing reliable tests without requiring prior code implementations. ConVerTest integrates three core strategies: (i) Self-Consistency(SC) to generate convergent test cases via majority voting; (ii) Chain-of-Verification (CoVe) for iterative, reasoning-guided code refinement; and (iii) a Dual Execution Agreement to crossvalidate code and tests through consensus. Experiments on BIGCODEBENCH and LESS BASIC PYTHON PROBLEMS (LBPP) benchmarks demonstrate that ConVerTest improves test validity, line coverage, and mutation scores by up to 39%, 28%, and 18% respectively over baselines. Our findings highlight ConVerTest as a robust solution for mitigating hallucinations and enhancing the reliability of autonomous software testing agents.

Reinforcement Learning (RL) with unit test feedback has enhanced large language models (LLMs) code generation, but relies on sparse rewards provided only after complete code evaluation, limiting learning efficiency and incremental improvements. When generated code fails all unit tests, no learning signal is received, hindering progress on complex tasks. To address this, we propose a Process Reward Model (PRM) that delivers dense, line-level feedback on code correctness during generation, mimicking human code refinement and providing immediate guidance. We explore various strategies for training PRMs and integrating them into the RL framework, finding that using PRMs both as dense rewards and for value function initialization significantly boosts performance. Our approach increases our in-house LLM's pass rate from 28.2% to 29.8% on LiveCodeBench and from 31.8% to 35.8% on our internal benchmark. Our experimental results highlight the effectiveness of PRMs in enhancing RL-driven code generation, especially for long-horizon scenarios.

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.

Deploying Large Language Models (LLMs) for regulatory compliance demands rigorous traceability via comprehensive citations across multi-tiered authority structures. Unlike traditional multi-hop or legal QA, this task requires structured procedural lookups and evidence-set closure rather than entity resolution or case-law reasoning. Existing RAG systems struggle here due to flattened citation edges, fragmented retrieval expansions, and fragile post-hoc attribution. We formalize Regulatory Compliance QA with RegOps-Bench, a novel benchmark featuring an Operational Knowledge Graph derived from complex national R\&D regulations. To address these bottlenecks, we propose RefWalk, a unified framework driven by a shared topic anchor. RefWalk traverses cross-document citations, fuses multi-view candidates via max-based aggregation, and enforces per-rule attribution to explicitly map claims to sources. We establish a strong baseline with substantial improvements in retrieval recall and citation accuracy. Finally, a contrastive evaluation on a U.S. health compliance dataset (HIPAA) reveals that existing systems exhibit saturation on flat-structure rules, underscoring the need for RegOps-Bench. Our code is available at https://github.com/yeongjoonJu/RefWalk.

Reinforcement learning with verifiable rewards (RLVR) is a promising approach for improving code generation in large language models, but its effectiveness is limited by weak and static verification signals in existing coding RL datasets. In this paper, we propose a solution-conditioned and adversarial verification framework that iteratively refines test cases based on the execution behaviors of candidate solutions, with the goal of increasing difficulty, improving discriminative power, and reducing redundancy. Based on this framework, we introduce EvolveCoder-22k, a large-scale coding reinforcement learning dataset constructed through multiple rounds of adversarial test case evolution. Empirical analysis shows that iterative refinement substantially strengthens verification, with pass@1 decreasing from 43.80 to 31.22. Reinforcement learning on EvolveCoder-22k yields stable optimization and consistent performance gains, improving Qwen3-4B by an average of 4.2 points across four downstream benchmarks and outperforming strong 4B-scale baselines. Our results highlight the importance of adversarial, solution-conditioned verification for effective and scalable reinforcement learning in code generation.

This is a brief description of a project that has already autoformalized a large portion of the general topology from the Munkres textbook (which has in total 241 pages in 7 chapters and 39 sections). The project has been running since November 21, 2025 and has as of January 4, 2026, produced 160k lines of formalized topology. Most of it (about 130k lines) have been done in two weeks,from December 22 to January 4, for an LLM subscription cost of about \$100. This includes a 3k-line proof of Urysohn's lemma, a 2k-line proof of Urysohn's Metrization theorem, over 10k-line proof of the Tietze extension theorem, and many more (in total over 1.5k lemmas/theorems). The approach is quite simple and cheap: build a long-running feedback loop between an LLM and a reasonably fast proof checker equipped with a core foundational library. The LLM is now instantiated as ChatGPT (mostly 5.2) or Claude Sonnet (4.5) run through the respective Codex or Claude Code command line interfaces. The proof checker is Chad Brown's higher-order set theory system Megalodon, and the core library is Brown's formalization of basic set theory and surreal numbers (including reals, etc). The rest is some prompt engineering and technical choices which we describe here. Based on the fast progress, low cost, virtually unknown ITP/library, and the simple setup available to everyone, we believe that (auto)formalization may become quite easy and ubiquitous in 2026, regardless of which proof assistant is used.

APR (Automated Program Repair) aims to automatically locate program defects, generate patches and validate the repairs. Existing techniques for APR are often combined with LLMs (Large Language Models), which leverages the code-related knowledge of LLMs to improve repair effectiveness. Current LLM-based APR methods typically utilize test cases only during the inference stage, adopting an iterative approach that performs repair first and validates it through test execution afterward. This conventional paradigm neglects two important aspects: the potential contribution of test cases in the training phase, and the possibility of leveraging testing prior to repair. To address this, we propose Repair-R1, which introduces test cases into the model's training phase and shifts test generation to precede repair. The model is required to first generate discriminative test cases that can distinguish defective behaviors, and then perform repair based on these tests. This enables the model to better locate defects and understand the underlying causes of defects, thereby improving repair effectiveness. We implement Repair-R1 with three different backbone models, using RL (reinforcement learning) to co-optimize test generation and bug repair. Experimental results on four widely adopted benchmarks demonstrate the superiority of Repair-R1. Specially, compared to vanilla models, Repair-R1 improves repair success rate by 2.68\% to 48.29\%, test generation success rate by 16.38\% to 53.28\%, and test coverage by 0.78\% to 53.96\%. We publish the code and weights at https://github.com/Tomsawyerhu/APR-RL and https://huggingface.co/tomhu/Qwen3-4B-RL-5000-step.

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

We introduce MacroBench, a code-first benchmark that evaluates whether LLMs can synthesize reusable browser-automation programs (macros) from natural-language goals by reading HTML/DOM and emitting Selenium. MacroBench instantiates seven self-hosted sites covering 681 tasks across interaction complexity and targeting difficulty. Our end-to-end protocol validates generated code via static checks, sandboxed execution, and outcome verification (DOM assertions, database snapshots), and includes a safety suite for scraping, spam/abuse, and credential/privacy prompts. Across 2,636 model-task runs, we observe stratified success: GPT-4o-mini (96.8%), GPT-4o (95.3%), Gemini (89.0%), DeepSeek (83.4%). Models handle simple tasks reliably (91.7%) but fail on complex workflows (0.0%), and none meet production-quality coding practices despite functional completion. We release our complete benchmark pipeline, evaluation framework, and experimental results at https://github.com/hyunjun1121/MacroBench to enable reproducible assessment of macro synthesis for web automation.

Software updates, including bug repair and feature additions, are frequent in modern applications but they often leave test suites outdated, resulting in undetected bugs and increased chances of system failures. A recent study by Meta revealed that 14%-22% of software failures stem from outdated tests that fail to reflect changes in the codebase. This highlights the need to keep tests in sync with code changes to ensure software reliability. In this paper, we present UTFix, a novel approach for repairing unit tests when their corresponding focal methods undergo changes. UTFix addresses two critical issues: assertion failure and reduced code coverage caused by changes in the focal method. Our approach leverages language models to repair unit tests by providing contextual information such as static code slices, dynamic code slices, and failure messages. We evaluate UTFix on our generated synthetic benchmarks (Tool-Bench), and real-world benchmarks. Tool- Bench includes diverse changes from popular open-source Python GitHub projects, where UTFix successfully repaired 89.2% of assertion failures and achieved 100% code coverage for 96 tests out of 369 tests. On the real-world benchmarks, UTFix repairs 60% of assertion failures while achieving 100% code coverage for 19 out of 30 unit tests. To the best of our knowledge, this is the first comprehensive study focused on unit test in evolving Python projects. Our contributions include the development of UTFix, the creation of Tool-Bench and real-world benchmarks, and the demonstration of the effectiveness of LLM-based methods in addressing unit test failures due to software evolution.

Control Flow Attestation (CFA) allows remote verification of run-time software integrity in embedded systems. However, CFA is limited by the storage/transmission costs of generated control flow logs (CFlog). Recent work has proposed application-specific optimizations by speculating on likely sub-paths in CFlog and replacing them with reserved symbols at runtime. Albeit effective, prior approaches do not consider the representation of addresses in a control flow path for speculation. This work proposes RESPEC-CFA, an architectural extension for CFA allowing for speculation on (1) the locality of control flows and (2) their Huffman encoding. Alone, RESPEC-CFA reduces CFlog sizes by up to 90.1%. Combined with prior methods, RESPEC-CFA yields reductions of up to 99.7%, representing a significant step toward practical CFA.

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.

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}.

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.

Existing reinforcement learning strategies based on outcome supervision have proven effective in enhancing the performance of large language models(LLMs) for code generation. While reinforcement learning based on process supervision has shown great promise in handling multi-step reasoning tasks, its effectiveness in code generation remains largely underexplored and underjustified. The primary obstacle stems from the resource-intensive nature of constructing high-quality process-supervised data, which demands substantial human expertise and computational resources. In response to this challenge, we propose a "statement mutation/refactoring-compile and execution verification" strategy: mutating and refactoring code line-by-line through a teacher model, and utilizing compiler execution results to automatically label each line, resulting in line-by-line process-supervised data, which is pivotal for training a process-supervised reward model. The trained reward model is then integrated into the PRLCoder framework, followed by experimental validation on several benchmarks. Experimental results demonstrate that process-supervised reinforcement learning significantly surpasses methods relying solely on outcome supervision. Notably, in tackling complex code generation tasks, process-supervised reinforcement learning shows a clear advantage, ensuring both the integrity of the code generation process and the correctness of the generation results.

Large Language Models (LLMs) show great promise in complex reasoning, with Reinforcement Learning with Verifiable Rewards (RLVR) being a key enhancement strategy. However, a prevalent issue is ``superficial self-reflection'', where models fail to robustly verify their own outputs. We introduce RISE (Reinforcing Reasoning with Self-Verification), a novel online RL framework designed to tackle this. RISE explicitly and simultaneously trains an LLM to improve both its problem-solving and self-verification abilities within a single, integrated RL process. The core mechanism involves leveraging verifiable rewards from an outcome verifier to provide on-the-fly feedback for both solution generation and self-verification tasks. In each iteration, the model generates solutions, then critiques its own on-policy generated solutions, with both trajectories contributing to the policy update. Extensive experiments on diverse mathematical reasoning benchmarks show that RISE consistently improves model's problem-solving accuracy while concurrently fostering strong self-verification skills. Our analyses highlight the advantages of online verification and the benefits of increased verification compute. Additionally, RISE models exhibit more frequent and accurate self-verification behaviors during reasoning. These advantages reinforce RISE as a flexible and effective path towards developing more robust and self-aware reasoners.

Code generation techniques generate code snippets automatically based on the problem requirements in natural language. Recently, large language models (LLMs) achieve the SOTA performance on code generation. However, LLMs still struggle at times to generate accurate code, which diminishes their promised efficiency as developers must spend significant effort evaluating and debugging the generated code. To improve the reliability and quality of the generated codes, researchers propose to leverage Consistency to obtain a better code based on generating and ranking multiple candidates. The existing approach is problematic as Consistency thinks a code is better when (1) the code pass more tests (inter-consistency) (2) more codes share the same behavior (intra-consistency). However, because the tests are also generated by LLMs, they could be wrong as well. As a result, majority voting based on testing results is unreliable. Relying solely on consistency is insufficient to address this issue; integrating user feedback is essential for effectively guiding consistency. We show that with minimal human effort, performance can be significantly enhanced. We propose Consistency-Augmented Iterative Interaction Framework to Enhance the Reliability of Code Generation, ConAIR, which is an approach that aims to improve the performance of a code generator through two distinctive ingredients, i.e., (1) lightweight user effort for validating the correctness of selected tests; and (2) a dynamic strategy for ranking, localizing and correcting multiple tests and codes. Overall, we propose a lightweight interaction framework that incorporates user feedback to correct identified tests and guide the iterative process. The iteration rounds are only 4 in average with the help of consistency. With only lightweight human efforts, we can achieve an improvement of 33% towards the base model.

Large language models (LLMs) have been routinely used to solve various tasks using step-by-step reasoning. However, the structure of intermediate reasoning steps, or thoughts, is rigid and unidirectional, such as chains, trees, or acyclic-directed graphs. Consequently, the resulting inflexible and forward-only reasoning may not address challenging tasks and fail when the LLM frequently gives false responses, i.e., ``hallucinations''. This paper proposes a new reasoning framework, called Thought Rollback (TR), allowing LLMs to adaptively build thought structure while maintaining effective reasoning toward problem-solving under ``hallucinations''. The core mechanism of TR is rolling back thoughts, which allows LLMs to perform error analysis on thoughts, and thus roll back to any previously mistaken thought for revision. Subsequently, by including such trial-and-error in the prompt to guide the LLM, each rollback leads to one more reliable reasoning path. Therefore, starting with a simple prompt without human annotations, LLM with TR adaptively and gradually explores thoughts for a correct solution. Comprehensive experiments on mathematical problems and multi-task reasoning demonstrate the state-of-the-art performance of TR in terms of problem-solving rate and interaction cost. For instance, the solving rate of GPT-4 with TR outperforms the current best by 9% on the MATH dataset.

Typical reinforcement learning (RL) methods for LLM reasoning waste compute on hard problems, where correct on-policy traces are rare, policy gradients vanish, and learning stalls. To bootstrap more efficient RL, we consider reusing old sampling FLOPs (from prior inference or RL training) in the form of off-policy traces. Standard off-policy methods supervise against off-policy data, causing instabilities during RL optimization. We introduce PrefixRL, where we condition on the prefix of successful off-policy traces and run on-policy RL to complete them, side-stepping off-policy instabilities. PrefixRL boosts the learning signal on hard problems by modulating the difficulty of the problem through the off-policy prefix length. We prove that the PrefixRL objective is not only consistent with the standard RL objective but also more sample efficient. Empirically, we discover back-generalization: training only on prefixed problems generalizes to out-of-distribution unprefixed performance, with learned strategies often differing from those in the prefix. In our experiments, we source the off-policy traces by rejection sampling with the base model, creating a self-improvement loop. On hard reasoning problems, PrefixRL reaches the same training reward 2x faster than the strongest baseline (SFT on off-policy data then RL), even after accounting for the compute spent on the initial rejection sampling, and increases the final reward by 3x. The gains transfer to held-out benchmarks, and PrefixRL is still effective when off-policy traces are derived from a different model family, validating its flexibility in practical settings.

Recently, given the docstring for the target problem and the target function signature, large language models (LLMs) have been used not only to generate source code, but also to generate test cases, consisting of test inputs and assertions (e.g., in the form of checking an actual output against the expected output). However, as shown by our empirical study on assertions generated by four LLMs for the HumanEval benchmark, over 62% of the generated assertions are incorrect (i.e., failed on the ground-truth problem solution). To detect incorrect assertions (given the docstring and the target function signature along with a sample of example inputs and outputs), in this paper, we propose a new approach named DeCon to effectively detect incorrect assertions via LLM-generated postconditions for the target problem (a postcondition is a predicate that must always be true just after the execution of the ground-truth problem solution). Our approach requires a small set of I/O examples (i.e., a sample of example inputs and outputs) for the target problem (e.g., the I/O examples included in the docstring for a target problem in HumanEval). We use the given I/O examples to filter out those LLM-generated postconditions that are violated by at least one given I/O example. We then use the remaining postconditions to detect incorrect assertions as those assertions that violate at least one remaining postcondition. Experimental results show that DeCon can detect averagely more than 64% (63% and 65.5% detected by GPT-3.5 and GPT-4, respectively) incorrect assertions generated by four state-of-the-art LLMs, and DeCon can also improve the effectiveness of these LLMs in code generation by 4% in terms of Pass@1. In addition, although DeCon might filter out correct assertions, the fault-finding ability of the remaining correct assertions decreases only slightly.

LLMs demonstrate strong performance on code benchmarks, yet round-trip code execution reveals limitations in their ability to maintain consistent reasoning across forward and backward execution. We present RoundTripCodeEval (RTCE), a comprehensive benchmark consisting of four distinct code execution reasoning tasks designed to rigorously test round-trip consistency. RTCE provides an execution-free, exact-match evaluation of bijection fidelity, assessing whether models preserve a consistent one-to-one mapping between encoding and decoding operations across various algorithms and directions. We systematically evaluate state-of-the-art Code-LLMs using zero-shot prompting, supervised fine-tuning on execution traces, and self-reflection mechanisms. Each yields modest improvements, but none closes the gap, indicating that current LLMs struggle with true round-trip consistency, which demonstrates that they lack the internal coherence required for trustworthy code reasoning. RTCE surfaces several new and previously unmeasured insights that are not captured by existing I/O-prediction, execution-reasoning, or round-trip natural-language benchmarks. We will release the code and the dataset upon acceptance.

Formal verification of floating-point arithmetic remains challenging due to non-linear arithmetic behavior and the tight coupling between control and datapath logic. Existing approaches often rely on high-level C models for equivalence checking against Register Transfer Level (RTL) designs, but this introduces abstraction gaps, translation overhead, and limits scalability at the RTL level. To address these challenges, this paper presents a scalable methodology for verifying floating-point arithmetic using direct RTL-to-RTL model checking against a golden reference model. The approach adopts a divide-and conquer strategy that decomposes verification into modular stages, each captured by helper assertions and lemmas that collectively prove a main correctness theorem. Counterexample (CEX)-guided refinement is used to iteratively localize and resolve implementation defects, while targeted fault injection validates the robustness of the verification process against precision-critical datapath errors. To assess scalability and practicality, the methodology is extended with agentic AI-based formal property generation, integrating large language model (LLM)-driven automation with Human-in-the-Loop (HITL) refinement. Coverage analysis evaluates the effectiveness of the approach by comparing handwritten and AI-generated properties in both RTL-to-RTL model checking and standalone RTL verification settings. Results show that direct RTL-to-RTL model checking achieves higher coverage efficiency and requires fewer assertions than standalone verification, especially when combined with AI-generated properties refined through HITL guidance.

Test-time scaling via solution sampling and aggregation has become a key paradigm for improving the reasoning performance of Large Language Models (LLMs). While reward model selection is commonly employed in this approach, it often fails to identify minority-yet-correct answers, which limits its effectiveness beyond that of simple majority voting. We argue that this limitation stems from a lack of informative critique signals during verifier training. To bridge this gap, we introduce Mirror-Critique, a framework that trains a verifier with informative critiques. Our key insight is to leverage the rich critique signal by contrasting model-generated solutions with ground-truth solutions. We deploy a small instruction-tuned model to synthesize high-quality critique data with rejection sampling that teaches the verifier not only what is wrong, but also why. The synthetic data is used to cold-start the LLMs in the RLVR process to further improve the verification ability. The resulting Mirror-Verifier is deployed to evaluate candidate solutions by generating multiple critiques per solution, aggregating them into a verify score used for weighted voting or selective abstention. The experimental results show that our Mirror-Verifier significantly outperforms majority voting in terms of solution accuracy and also improves the solver's honesty to recognize and abstain from answering beyond its capability boundaries.

Large language models can generate useful code from natural language, but their outputs come without correctness guarantees. Verifiable code generation offers a path beyond testing by requiring models to produce not only executable code, but also formal specifications and machine-checkable proofs. Progress in this direction, however, is difficult to measure: existing benchmarks are often small, focus on only one part of the pipeline, lack ground-truth proofs or rigorous specification validation, or target verification settings far from mainstream software development. We present VeriContest, a benchmark of 946 competitive-programming problems from LeetCode and Codeforces for verifiable code generation in Rust with Verus. Each problem pairs a natural language description with expert-validated formal specifications, judge-accepted Rust code, Verus-checked proofs, and positive and negative test suites. VeriContest is constructed through a three-phase pipeline that scales from manually verified seed problems to semi-automated expansion with human-in-the-loop review. To further strengthen benchmark quality, we use testing as an additional quality-assurance layer for validating postcondition completeness. VeriContest supports isolated and compositional evaluation of specification generation, code generation, proof generation, and end-to-end verified program synthesis. Evaluating ten state-of-the-art models reveals a sharp gap between coding ability and verifiable code generation: the strongest model reaches 92.18% on natural-language-to-code generation, but only 48.31% on specification generation, 13.95% on proof generation, and 5.29% end-to-end. These results identify proof and specification generation as the central bottlenecks for models and establish VeriContest as a rigorous platform for measuring and training future systems that generate code with machine-checkable correctness.

Given a black-box AI system and a task, at what confidence level can a practitioner trust the system's output? We answer with a reliability level -- a single number per system-task pair, derived from self-consistency sampling and conformal calibration, that serves as a black-box deployment gate with exact, finite-sample, distribution-free guarantees. Self-consistency sampling reduces uncertainty exponentially; conformal calibration guarantees correctness within 1/(n+1) of the target level, regardless of the system's errors -- made transparently visible through larger answer sets for harder questions. Weaker models earn lower reliability levels (not accuracy -- see Definition 2.4): GPT-4.1 earns 94.6% on GSM8K and 96.8% on TruthfulQA, while GPT-4.1-nano earns 89.8% on GSM8K and 66.5% on MMLU. We validate across five benchmarks, five models from three families, and both synthetic and real data. Conditional coverage on solvable items exceeds 0.93 across all configurations; sequential stopping reduces API costs by around 50%.

Prompt optimization methods either analyze individual failures in isolation or compare prompt variants across examples, operating on single execution traces with no access to the reasoning process distinguishing success from failure on the same input. We introduce ContraPrompt, built on the observation that when a model fails but succeeds on a retry with feedback, the difference between its two chain-of-thought traces constitutes an optimization signal not captured by prior methods. Unlike prior contrastive methods, we compare complete intermediate reasoning processes: the two traces share model, input, and base prompt, so remaining differences reflect reasoning strategy and appended error feedback -- we call this dyadic reasoning trace analysis. The multi-attempt solving phase is an instrumented agentic retry loop that generates contrastive data automatically without human annotation. Extracted rules are organized into an input-aware decision tree routing instructions by observable input characteristics. On four reasoning and compliance benchmarks, ContraPrompt outperforms GEPA (Agrawal et al., 2026) on all four, with absolute gains of +8.29 pp on HotPotQA (+20.8% rel.), +2.21 pp on GDPR-Bench (+18.2% rel.), +7.14 pp on GPQA Diamond (+10.6% rel.), and +0.74 pp on BBH (+0.85% rel.). Ablations confirm dyadic trace contrastivity is the critical component, with a -16% relative average drop upon its removal. On 53 EvalSet black-box optimization problems, ContraPrompt beats GEPA on 11, ties on 41, and loses on 1 at equal budget. On FiNER-139 financial named entity recognition (Loukas et al., 2022), ContraPrompt achieves +7.77 pp over the unoptimized baseline (+11.6% rel.) and +1.94 pp over GEPA (+2.66% rel.), with branch conditions aligning with standard US GAAP financial-instrument categories.

Recent progress in large language models (LLMs) like GPT-4 and PaLM-2 has brought significant advancements in addressing math reasoning problems. In particular, OpenAI's latest version of GPT-4, known as GPT-4 Code Interpreter, shows remarkable performance on challenging math datasets. In this paper, we explore the effect of code on enhancing LLMs' reasoning capability by introducing different constraints on the Code Usage Frequency of GPT-4 Code Interpreter. We found that its success can be largely attributed to its powerful skills in generating and executing code, evaluating the output of code execution, and rectifying its solution when receiving unreasonable outputs. Based on this insight, we propose a novel and effective prompting method, explicit code-based self-verification~(CSV), to further boost the mathematical reasoning potential of GPT-4 Code Interpreter. This method employs a zero-shot prompt on GPT-4 Code Interpreter to encourage it to use code to self-verify its answers. In instances where the verification state registers as ``False'', the model shall automatically amend its solution, analogous to our approach of rectifying errors during a mathematics examination. Furthermore, we recognize that the states of the verification result indicate the confidence of a solution, which can improve the effectiveness of majority voting. With GPT-4 Code Interpreter and CSV, we achieve an impressive zero-shot accuracy on MATH dataset (53.9\% to 84.3\%).

When multi-agent systems (MAS) fail, identifying where the decisive error occurred is the first step for automated recovery to an earlier state. Error attribution remains a fundamental challenge due to the long interaction traces that large language model-based MAS generate. This paper presents a framework for error attribution based on conformal prediction (CP) which provides finite-sample, distribution-free coverage guarantees. We introduce new algorithms for filtration-based CP designed for sequential data such as agent trajectories. Unlike existing CP algorithms, our approach predicts sets that are contiguous sequences to enable efficient recovery and debugging. We verify our theoretical guarantees on a variety of agents and datasets, show that errors can be precisely isolated, then use prediction sets to rollback MAS to correct their own errors. Our overall approach is model-agnostic, and offers a principled uncertainty layer for MAS error attribution. We release code at https://github.com/layer6ai-labs/conformal-agent-error-attribution.

Augmenting Large Language Models (LLMs) with external tools enables them to execute complex, multi-step tasks. However, tool learning is hampered by the static synthetic data pipelines where data generation and model training are executed as two separate, non-interactive processes. This approach fails to adaptively focus on a model's specific weaknesses and allows noisy labels to persist, degrading training efficiency. We introduce LoopTool, a fully automated, model-aware data evolution framework that closes this loop by tightly integrating data synthesis and model training. LoopTool iteratively refines both the data and the model through three synergistic modules: (1) Greedy Capability Probing (GCP) diagnoses the model's mastered and failed capabilities; (2) Judgement-Guided Label Verification (JGLV) uses an open-source judge model to find and correct annotation errors, progressively purifying the dataset; and (3) Error-Driven Data Expansion (EDDE) generates new, challenging samples based on identified failures. This closed-loop process operates within a cost-effective, open-source ecosystem, eliminating dependence on expensive closed-source APIs. Experiments show that our 8B model trained with LoopTool significantly surpasses its 32B data generator and achieves new state-of-the-art results on the BFCL-v3 and ACEBench benchmarks for its scale. Our work demonstrates that closed-loop, self-refining data pipelines can dramatically enhance the tool-use capabilities of LLMs.

Autonomous GUI agents face two fundamental challenges: early stopping, where agents prematurely declare success without verifiable evidence, and repetitive loops, where agents cycle through the same failing actions without recovery. We present VLAA-GUI, a modular GUI agentic framework built around three integrated components that guide the system on when to Stop, Recover, and Search. First, a mandatory Completeness Verifier enforces UI-observable success criteria and verification at every finish step -- with an agent-level verifier that cross-examines completion claims with decision rules, rejecting those lacking direct visual evidence. Second, a mandatory Loop Breaker provides multi-tier filtering: switching interaction mode after repeated failures, forcing strategy changes after persistent screen-state recurrence, and binding reflection signals to strategy shifts. Third, an on-demand Search Agent searches online for unfamiliar workflows by directly querying a capable LLM with search ability, returning results as plain text. We additionally integrate a Coding Agent for code-intensive actions and a Grounding Agent for precise action grounding, both invoked on demand when required. We evaluate VLAA-GUI across five top-tier backbones, including Opus 4.5, 4.6 and Gemini 3.1 Pro, on two benchmarks with Linux and Windows tasks, achieving top performance on both (77.5% on OSWorld and 61.0% on WindowsAgentArena). Notably, three of the five backbones surpass human performance (72.4%) on OSWorld in a single pass. Ablation studies show that all three proposed components consistently improve a strong backbone, while a weaker backbone benefits more from these tools when the step budget is sufficient. Further analysis also shows that the Loop Breaker nearly halves wasted steps for loop-prone models.

There is an increasing amount of research and commercial tools for automated test case generation using Large Language Models (LLMs). This paper critically examines whether recent LLM-based test generation tools, such as Codium CoverAgent and CoverUp, can effectively find bugs or unintentionally validate faulty code. Considering bugs are only exposed by failing test cases, we explore the question: can these tools truly achieve the intended objectives of software testing when their test oracles are designed to pass? Using real human-written buggy code as input, we evaluate these tools, showing how LLM-generated tests can fail to detect bugs and, more alarmingly, how their design can worsen the situation by validating bugs in the generated test suite and rejecting bug-revealing tests. These findings raise important questions about the validity of the design behind LLM-based test generation tools and their impact on software quality and test suite reliability.

With respect to improving the reasoning accuracy of LLMs, the representative reinforcement learning (RL) method GRPO faces failure due to insignificant reward variance, while verification methods based on process reward models (PRMs) suffer from difficulties with training data acquisition and verification effectiveness. To tackle these problems, this paper introduces ReST-RL, a unified LLM RL paradigm that significantly improves LLM's code reasoning ability by combining an improved GRPO algorithm with a meticulously designed test time decoding method assisted by a value model (VM). As the first stage of policy reinforcement, ReST-GRPO adopts an optimized ReST algorithm to filter and assemble high-value training data, increasing the reward variance of GRPO sampling, thus improving the effectiveness and efficiency of training. After the basic reasoning ability of LLM policy has been improved, we further propose a test time decoding optimization method called VM-MCTS. Through Monte-Carlo Tree Search (MCTS), we collect accurate value targets with no annotation required, on which VM training is based. When decoding, the VM is deployed by an adapted MCTS algorithm to provide precise process signals as well as verification scores, assisting the LLM policy to achieve high reasoning accuracy. We validate the effectiveness of the proposed RL paradigm through extensive experiments on coding problems. Upon comparison, our approach significantly outperforms other reinforcement training baselines (e.g., naive GRPO and ReST-DPO), as well as decoding and verification baselines (e.g., PRM-BoN and ORM-MCTS) on well-known coding benchmarks of various levels (e.g., APPS, BigCodeBench, and HumanEval), indicating its power to strengthen the reasoning ability of LLM policies. Codes for our project can be found at https://github.com/THUDM/ReST-RL.

Training modern neural networks is increasingly fragile, with rare but severe destabilizing updates often causing irreversible divergence or silent performance degradation. Existing optimization methods primarily rely on preventive mechanisms embedded within the optimizer, offering limited ability to detect and recover from instability once it occurs. We introduce a supervisory runtime stability framework that treats optimization as a controlled stochastic process. By isolating an innovation signal derived from secondary measurements, such as validation probes, the framework enables automatic detection and recovery from destabilizing updates without modifying the underlying optimizer. We provide theoretical runtime safety guarantees that formalize bounded degradation and recovery. Our implementation incurs minimal overhead and is compatible with memory-constrained training settings.

We introduce the Formally Verified Automated Programming Progress Standards, or FVAPPS, a benchmark of 4715 samples for writing programs and proving their correctness, the largest formal verification benchmark, including 1083 curated and quality controlled samples. Previously, APPS provided a benchmark and dataset for programming puzzles to be completed in Python and checked against unit tests, of the kind seen in technical assessments in the software engineering industry. Building upon recent approaches for benchmarks in interactive theorem proving, we generalize the unit tests to Lean 4 theorems given without proof (i.e., using Lean's "sorry" keyword). On the 406 theorems of 100 randomly selected samples, Sonnet correctly proves 30% and Gemini correctly proves 18%. We challenge the machine learning and program synthesis communities to solve both each general purpose programming problem and its associated correctness specifications. The benchmark is available at https://huggingface.co/datasets/quinn-dougherty/fvapps.

In software development, bug report reproduction is a challenging task. This paper introduces ReBL, a novel feedback-driven approach that leverages GPT-4, a large-scale language model, to automatically reproduce Android bug reports. Unlike traditional methods, ReBL bypasses the use of Step to Reproduce (S2R) entities. Instead, it leverages the entire textual bug report and employs innovative prompts to enhance GPT's contextual reasoning. This approach is more flexible and context-aware than the traditional step-by-step entity matching approach, resulting in improved accuracy and effectiveness. In addition to handling crash reports, ReBL has the capability of handling non-crash bug reports. Our evaluation of 96 Android bug reports (73 crash and 23 non-crash) demonstrates that ReBL successfully reproduced 90.63% of these reports, averaging only 74.98 seconds per bug report. Additionally, ReBL outperformed three existing tools in both success rate and speed.

Backdoor inversion, the process of finding a backdoor trigger inserted into a machine learning model, has become the pillar of many backdoor detection and defense methods. Previous works on backdoor inversion often recover the backdoor through an optimization process to flip a support set of clean images into the target class. However, it is rarely studied and understood how large this support set should be to recover a successful backdoor. In this work, we show that one can reliably recover the backdoor trigger with as few as a single image. Specifically, we propose the SmoothInv method, which first constructs a robust smoothed version of the backdoored classifier and then performs guided image synthesis towards the target class to reveal the backdoor pattern. SmoothInv requires neither an explicit modeling of the backdoor via a mask variable, nor any complex regularization schemes, which has become the standard practice in backdoor inversion methods. We perform both quantitaive and qualitative study on backdoored classifiers from previous published backdoor attacks. We demonstrate that compared to existing methods, SmoothInv is able to recover successful backdoors from single images, while maintaining high fidelity to the original backdoor. We also show how we identify the target backdoored class from the backdoored classifier. Last, we propose and analyze two countermeasures to our approach and show that SmoothInv remains robust in the face of an adaptive attacker. Our code is available at https://github.com/locuslab/smoothinv .

To achieve reliable, robust, and safe AI systems, it is vital to implement fallback strategies when AI predictions cannot be trusted. Certifiers for neural networks are a reliable way to check the robustness of these predictions. They guarantee for some predictions that a certain class of manipulations or attacks could not have changed the outcome. For the remaining predictions without guarantees, the method abstains from making a prediction, and a fallback strategy needs to be invoked, which typically incurs additional costs, can require a human operator, or even fail to provide any prediction. While this is a key concept towards safe and secure AI, we show for the first time that this approach comes with its own security risks, as such fallback strategies can be deliberately triggered by an adversary. In addition to naturally occurring abstains for some inputs and perturbations, the adversary can use training-time attacks to deliberately trigger the fallback with high probability. This transfers the main system load onto the fallback, reducing the overall system's integrity and/or availability. We design two novel availability attacks, which show the practical relevance of these threats. For example, adding 1% poisoned data during training is sufficient to trigger the fallback and hence make the model unavailable for up to 100% of all inputs by inserting the trigger. Our extensive experiments across multiple datasets, model architectures, and certifiers demonstrate the broad applicability of these attacks. An initial investigation into potential defenses shows that current approaches are insufficient to mitigate the issue, highlighting the need for new, specific solutions.

Best-of-N decoding methods instruct large language models (LLMs) to generate multiple solutions, score each using a scoring function, and select the highest scored as the final answer to mathematical reasoning problems. However, this repeated independent process often leads to the same mistakes, making the selected solution still incorrect. We propose a novel prompting method named Stepwise Correction (StepCo) that helps LLMs identify and revise incorrect steps in their generated reasoning paths. It iterates verification and revision phases that employ a process-supervised verifier. The verify-then-revise process not only improves answer correctness but also reduces token consumption with fewer paths needed to generate. With StepCo, a series of LLMs demonstrate exceptional performance. Notably, using GPT-4o as the backend LLM, StepCo achieves an average accuracy of 94.1 across eight datasets, significantly outperforming the state-of-the-art Best-of-N method by +2.4, while reducing token consumption by 77.8%.

Recent studies have revealed that self-sustaining cascading failures in distributed systems frequently lead to widespread outages, which are challenging to contain and recover from. Existing failure detection techniques struggle to expose such failures prior to deployment, as they typically require a complex combination of specific conditions to be triggered. This challenge stems from the inherent nature of cascading failures, as they typically involve a sequence of fault propagations, each activated by distinct conditions. This paper presents CSnake, a fault injection framework to expose self-sustaining cascading failures in distributed systems. CSnake uses the novel idea of causal stitching, which causally links multiple single-fault injections in different tests to simulate complex fault propagation chains. To identify these chains, CSnake designs a counterfactual causality analysis of fault propagations - fault causality analysis (FCA): FCA compares the execution trace of a fault injection run with its corresponding profile run (i.e., same test w/o the injection) and identifies any additional faults triggered, which are considered to have a causal relationship with the injected fault. To address the large search space of fault and workload combinations, CSnake employs a three-phase allocation protocol of test budget that prioritizes faults with unique and diverse causal consequences, increasing the likelihood of uncovering conditional fault propagations. Furthermore, to avoid incorrectly connecting fault propagations from workloads with incompatible conditions, CSnake performs a local compatibility check that approximately checks the compatibility of the path constraints associated with connected fault propagations with low overhead. CSnake detected 15 bugs that cause self-sustaining cascading failures in five systems, five of which have been confirmed with two fixed.

Agentic Reinforcement Learning (RL) has empowered Large Language Models (LLMs) to utilize tools like Python interpreters for complex problem-solving. However, for parameter-constrained models (e.g., 4B--7B), the exploration phase is often plagued by frequent execution failures, creating noisy trajectories that hinder policy optimization. Under standard outcome-based reward settings, this noise leads to a critical credit assignment issue, where erroneous actions are inadvertently reinforced alongside successful outcomes. Existing mitigations face a dilemma: dense rewards often trigger reward hacking, while supersampling incurs prohibitive computational costs. To address these challenges, we propose CLEANER. Distinct from external filtering methods, CLEANER exploits the model's intrinsic self-correction capabilities to eliminate error-contaminated context directly during data collection. At its core, the Similarity-Aware Adaptive Rollback (SAAR) mechanism autonomously constructs clean, purified trajectories by retrospectively replacing failures with successful self-corrections. Based on semantic similarity, SAAR adaptively regulates replacement granularity from shallow execution repairs to deep reasoning substitutions. By training on these self-purified paths, the model internalizes correct reasoning patterns rather than error-recovery loops. Empirical results on AIME24/25, GPQA, and LiveCodeBench show average accuracy gains of 6%, 3%, and 5% over baselines. Notably, CLEANER matches state-of-the-art performance using only one-third of the training steps, highlighting trajectory purification as a scalable solution for efficient agentic RL. Our models and code are available at GitHub

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.

Answer verification is crucial not only for evaluating large language models (LLMs) by matching their unstructured outputs against standard answers, but also serves as the reward model to guide LLM optimization. Most evaluation frameworks rely on regularized matching or employ general LLMs for answer verification, which demands extensive, repetitive customization for regex rules or evaluation prompts. Two fundamental limitations persist in current methodologies: 1) the absence of comprehensive benchmarks that systematically evaluate verification capabilities across different LLMs; and 2) the nascent stage of verifier development, where existing approaches lack both the robustness to handle complex edge cases and the generalizability across different domains. In this work, we develop CompassVerifier, an accurate and robust lightweight verifier model for evaluation and outcome reward. It demonstrates multi-domain competency spanning math, knowledge, and diverse reasoning tasks, with the capability to process various answer types, including multi-subproblems, formulas, and sequence answers, while effectively identifying abnormal/invalid responses. We introduce VerifierBench benchmark comprising model outputs collected from multiple data sources, augmented through manual analysis of metaerror patterns to enhance CompassVerifier. We anticipate that CompassVerifier and VerifierBench will facilitate answer verification, evaluation protocols, and reinforcement learning research. Code and dataset are available at https://github.com/open-compass/CompassVerifier.

Large Language Models (LLMs) have demonstrated impressive capabilities in complex reasoning tasks, yet they still struggle to reliably verify the correctness of their own outputs. Existing solutions to this verification challenge often depend on separate verifier models or require multi-stage self-correction training pipelines, which limit scalability. In this paper, we propose Policy as Generative Verifier (PAG), a simple and effective framework that empowers LLMs to self-correct by alternating between policy and verifier roles within a unified multi-turn reinforcement learning (RL) paradigm. Distinct from prior approaches that always generate a second attempt regardless of model confidence, PAG introduces a selective revision mechanism: the model revises its answer only when its own generative verification step detects an error. This verify-then-revise workflow not only alleviates model collapse but also jointly enhances both reasoning and verification abilities. Extensive experiments across diverse reasoning benchmarks highlight PAG's dual advancements: as a policy, it enhances direct generation and self-correction accuracy; as a verifier, its self-verification outperforms self-consistency.

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.

Asynchronous reinforcement learning improves rollout throughput for large language model agents by decoupling sample generation from policy optimization, but it also introduces a critical failure mode for PPO-style off-policy correction. In heterogeneous training systems, the total importance ratio should ideally be decomposed into two semantically distinct factors: a training--inference discrepancy term that aligns inference-side and training-side distributions at the same behavior-policy version, and a policy-staleness term that constrains the update from the historical policy to the current policy. We show that practical asynchronous pipelines with delayed updates and partial rollouts often lose the required historical training-side logits, or old logits. This missing-old-logit problem entangles discrepancy repair with staleness correction, breaks the intended semantics of decoupled correction, and makes clipping and masking thresholds interact undesirably. To address this issue, we study both exact and approximate correction routes. We propose three exact old-logit acquisition strategies: snapshot-based version tracking, a dedicated old-logit model, and synchronization via partial rollout interruption, and compare their system trade-offs. From the perspective of approximate correction, we focus on preserving the benefits of decoupled correction through a more appropriate approximate policy when exact old logits cannot be recovered at low cost, without incurring extra system overhead. Following this analysis, we adopt a revised PPO-EWMA method, which achieves significant gains in both training speed and optimization performance. Code at https://github.com/millioniron/ROLL.

A critical part of creating code suggestion systems is the pre-training of Large Language Models on vast amounts of source code and natural language text, often of questionable origin or quality. This may contribute to the presence of bugs and vulnerabilities in code generated by LLMs. While efforts to identify bugs at or after code generation exist, it is preferable to pre-train or fine-tune LLMs on curated, high-quality, and compliant datasets. The need for vast amounts of training data necessitates that such curation be automated, minimizing human intervention. We propose an automated source code autocuration technique that leverages the complete version history of open-source software projects to improve the quality of training data. This approach leverages the version history of all OSS projects to identify training data samples that have been modified or have undergone changes in at least one OSS project, and pinpoint a subset of samples that include fixes for bugs or vulnerabilities. We evaluate this method using The Stack v2 dataset, and find that 17% of the code versions in the dataset have newer versions, with 17% of those representing bug fixes, including 2.36% addressing known CVEs. The deduplicated version of Stack v2 still includes blobs vulnerable to 6,947 known CVEs. Furthermore, 58% of the blobs in the dataset were never modified after creation, suggesting they likely represent software with minimal or no use. Misidentified blob origins present an additional challenge, as they lead to the inclusion of non-permissively licensed code, raising serious compliance concerns. By addressing these issues, the training of new models can avoid perpetuating buggy code patterns or license violations. We expect our results to inspire process improvements for automated data curation, with the potential to enhance the reliability of outputs generated by AI tools.

Large Reasoning Models possess remarkable capabilities for self-correction in general domain; however, they frequently struggle to recover from unsafe reasoning trajectories under adversarial attacks. Existing alignment methods attempt to mitigate this vulnerability by fine-tuning the model on expert data including reflection traces or adversarial prefixes. Crucially, these approaches are often hindered by static training data which inevitably deviate from model's dynamic, on-policy reasoning traces, resulting in model hardly covering its vast generation space and learning to recover from its own failures. To bridge this gap, we propose Self-ReSET, a pure reinforcement learning framework designed to equip LRMs with the intrinsic capacity to recover from their own safety error trajectories, which are subsequently reused as an initial state for reinforcement learning. Extensive experiments across various LRMs and benchmarks demonstrate that Self-ReSET significantly enhances robustness against adversarial attacks especially out-of-distribution (OOD) jailbreak prompts while maintaining general utility, along with efficient data utilization. Further analysis reveals that our method effectively fosters self-recovery patterns, enabling models to better identify and recover from unsafe intermediate error states back to benign paths. Our codes and data are available at https://github.com/Ing1024/Self-ReSET.

Automated issue solving aims to resolve real-world issues in software repositories. The most popular benchmarks for automated issue solving are SWE-bench and its human-filtered subset SWE-bench Verified. These benchmarks leverage testing to validate generated patches. However, because testing is rarely exhaustive, a patch may pass the tests but nevertheless fail to match the developers' expectations. Unfortunately, it is currently unclear to what extent evaluations performed with SWE-bench suffer from such plausible but incorrect patches. This paper presents an in-depth empirical study of the correctness of plausible patches generated by three state-of-the-art issue-solving tools evaluated on SWE-bench Verified. We extensively test and inspect generated patches, and compare them against human-written ground truth patches. The core of our methodology is a novel technique PatchDiff for differential patch testing, which automatically exposes behavioral discrepancies between two patches. Our findings reveal critical weaknesses in SWE-bench's patch validation mechanism, which causes 7.8% of all patches to count as correct while failing the developer-written test suite. Moreover, our novel automated technique reveals that even more (29.6%) plausible patches induce different behavior than the ground truth patches. These behavioral differences are often due to similar, but divergent implementations (46.8%) and due to generated patches that adapt more behavior than the ground truth patches (27.3%). Our manual inspection shows that 28.6% of behaviorally divergent patches are certainly incorrect. Combined, the different weaknesses lead to an inflation of reported resolution rates by 6.2 absolute percent points. Our findings are a call to arms for more robust and reliable evaluation of issue-solving tools. We envision our automated differential patch testing technique to be useful for this purpose.

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.

Large Language Models (LLMs) increasingly rely on reinforcement learning with verifiable rewards (RLVR) to elicit reliable chain-of-thought reasoning. However, the training process remains bottlenecked by the computationally expensive rollout stage. Existing acceleration methods-such as parallelization, objective- and data-driven modifications, and replay buffers-either incur diminishing returns, introduce bias, or overlook redundancy across iterations. We identify that rollouts from consecutive training epochs frequently share a large portion of overlapping segments, wasting computation. To address this, we propose SPEC-RL, a novel framework that integrates SPECulative decoding with the RL rollout process. SPEC-RL reuses prior trajectory segments as speculative prefixes and extends them via a draft-and-verify mechanism, avoiding redundant generation while ensuring policy consistency. Experiments on diverse math reasoning and generalization benchmarks, including GSM8K, MATH-500, OlympiadBench, MMLU-STEM, and others, demonstrate that SPEC-RL reduces rollout time by 2-3x without compromising policy quality. As a purely rollout-stage enhancement, SPEC-RL integrates seamlessly with mainstream algorithms (e.g., PPO, GRPO, DAPO), offering a general and practical path to scale RLVR for large reasoning models. Our code is available at https://github.com/ShopeeLLM/Spec-RL

Code editing is an essential step towards reliable program synthesis to automatically correct critical errors generated from code LLMs. Recent studies have demonstrated that closed-source LLMs (i.e., ChatGPT and GPT-4) are capable of generating corrective feedback to edit erroneous inputs. However, it remains challenging for open-source code LLMs to generate feedback for code editing, since these models tend to adhere to the superficial formats of feedback and provide feedback with misleading information. Hence, the focus of our work is to leverage open-source code LLMs to generate helpful feedback with correct guidance for code editing. To this end, we present Coffee, a collected dataset specifically designed for code fixing with feedback. Using this dataset, we construct CoffeePots, a framework for COde Fixing with FEEdback via Preference-Optimized Tuning and Selection. The proposed framework aims to automatically generate helpful feedback for code editing while minimizing the potential risk of superficial feedback. The combination of Coffee and CoffeePots marks a significant advancement, achieving state-of-the-art performance on HumanEvalFix benchmark. Codes and model checkpoints are publicly available at https://github.com/Lune-Blue/COFFEE.

Memory-safety bugs introduce critical software-security issues. Rust provides memory-safe mechanisms to avoid memory-safety bugs in programming, while still allowing unsafe escape hatches via unsafe code. However, the unsafe code that enhances the usability of Rust provides clear spots for finding memory-safety bugs in Rust source code. In this paper, we claim that these unsafe spots can still be identifiable in Rust binary code via machine learning and be leveraged for finding memory-safety bugs. To support our claim, we propose the tool textttrustspot, that enables reverse engineering to learn an unsafe classifier that proposes a list of functions in Rust binaries for downstream analysis. We empirically show that the function proposals by textttrustspot can recall 92.92% of memory-safety bugs, while it covers only 16.79% of the entire binary code. As an application, we demonstrate that the function proposals are used in targeted fuzzing on Rust packages, which contribute to reducing the fuzzing time compared to non-targeted fuzzing.

We present SQL Query Engine, an open-source, self-hosted service that translates natural language questions into validated PostgreSQL queries through a two-stage LLM pipeline. The first stage performs automatic schema introspection and SQL generation; a multi-strategy response parser extracts SQL from any LLM output format (JSON, code blocks, or raw text) without requiring structured output APIs. The second stage executes the query against PostgreSQL and, upon failure or empty results, enters an iterative self-healing loop in which the LLM diagnoses the error using full SQLSTATE codes and PostgreSQL diagnostic messages. Two mechanisms prevent regressions: early-accept returns successful queries immediately without LLM re-evaluation, and best-result tracking preserves the best partial result across retries. Schema context is cached per session in Redis, progress events stream via Redis Pub/Sub and SSE, and an OpenAI-compatible /v1/chat/completions endpoint lets existing tools work without modification. All database connections are read-only at the driver level. We evaluate across five LLM backends on a synthetic benchmark (75 questions, three databases) where the self-healing loop yields up to +9.3pp accuracy gains with zero regressions on the best model (Llama 4 Scout 17B, 57.3%), and on BIRD (437 questions, 11 databases migrated from SQLite to PostgreSQL) where the full pipeline reaches 49.0% execution accuracy (GPT-OSS-120B, +4.6pp). Source code: https://github.com/codeadeel/sqlqueryengine.

Qiskit is an open-source quantum computing framework that allows users to design, simulate, and run quantum circuits on real quantum hardware. We explore post-training techniques for LLMs to assist in writing Qiskit code. We introduce quantum verification as an effective method for ensuring code quality and executability on quantum hardware. To support this, we developed a synthetic data pipeline that generates quantum problem-unit test pairs and used it to create preference data for aligning LLMs with DPO. Additionally, we trained models using GRPO, leveraging quantum-verifiable rewards provided by the quantum hardware. Our best-performing model, combining DPO and GRPO, surpasses the strongest open-source baselines on the challenging Qiskit-HumanEval-hard benchmark.

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.

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.

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.

We study the right to be forgotten (GDPR Art. 17) for large language models and frame unlearning as a reproducible systems problem. Our approach treats training as a deterministic program and logs a minimal per-microbatch record (ordered ID hash, RNG seed, learning-rate value, optimizer-step counter, and accumulation boundary). Under a pinned stack and deterministic kernels, replaying the training tail while filtering only the forget closure yields the same parameters as training on the retain set (bit-identical in the training dtype) when preconditions hold. To meet latency and availability constraints, we add complementary paths: (i) exact reverts of recent steps via micro-checkpoints or dense per-step deltas, (ii) cohort-scoped adapter deletion when the base is frozen, and (iii) a curvature-guided anti-update followed by a short retain-tune, audit-gated with escalation to exact replay. We report storage/latency budgets and a toy artifact validating mechanics; in a controlled run that satisfies the preconditions we demonstrate byte-identical equality of model and optimizer states.

Selecting LLM-generated code candidates using LLM-generated tests is challenging because the tests themselves may be incorrect. Existing methods either treat all tests equally or rely on ad-hoc heuristics to filter unreliable tests. Yet determining test correctness requires knowing which codes are correct, creating a circular dependency. Our key insight is that we need not determine test correctness at all: test votes should rank, not merely count. What matters is not how many codes pass a test, but whether the test can distinguish correct from incorrect code. We break the circular dependency via leave-one-out evaluation: hold out one test, rank codes by their aggregate scores on all remaining tests, and measure whether the held-out test's pass/fail pattern agrees with this ranking. We formalize this agreement as the leave-one-out AUC~(LOO-AUC) and prove that the expected LOO-AUC is proportional to each test's ability to separate correct code from incorrect code. Building on this, we propose ACES~(AUC ConsistEncy Scoring) with two complementary variants: ACES-C provides closed-form weights that provably approximate the oracle in expectation under a mild assumption on average test quality; ACES-O drops this assumption and iteratively optimizes a differentiable LOO-AUC objective. Both operate solely on the binary pass matrix with negligible overhead, and achieve state-of-the-art Pass@k on multiple code generation benchmarks.

Reward-guided search methods have demonstrated strong potential in enhancing tool-using agents by effectively guiding sampling and exploration over complex action spaces. As a core design, those search methods utilize process reward models (PRMs) to provide step-level rewards, enabling more fine-grained monitoring. However, there is a lack of systematic and reliable evaluation benchmarks for PRMs in tool-using settings. In this paper, we introduce ToolPRMBench, a large-scale benchmark specifically designed to evaluate PRMs for tool-using agents. ToolPRMBench is built on top of several representative tool-using benchmarks and converts agent trajectories into step-level test cases. Each case contains the interaction history, a correct action, a plausible but incorrect alternative, and relevant tool metadata. We respectively utilize offline sampling to isolate local single-step errors and online sampling to capture realistic multi-step failures from full agent rollouts. A multi-LLM verification pipeline is proposed to reduce label noise and ensure data quality. We conduct extensive experiments across large language models, general PRMs, and tool-specialized PRMs on ToolPRMBench. The results reveal clear differences in PRM effectiveness and highlight the potential of specialized PRMs for tool-using. Code and data will be released at https://github.com/David-Li0406/ToolPRMBench.

Reinforcement Learning with Verifiable Rewards (RLVR) elicits long chain-of-thought reasoning in large language models (LLMs), but outcome-based rewards lead to coarse-grained advantage estimation. While existing approaches improve RLVR via token-level entropy or sequence-level length control, they lack a semantically grounded, step-level measure of reasoning progress. As a result, LLMs fail to distinguish necessary deduction from redundant verification: they may continue checking after reaching a correct solution and, in extreme cases, overturn a correct trajectory into an incorrect final answer. To remedy the lack of process supervision, we introduce a training-free probing mechanism that extracts intermediate confidence and correctness and combines them into a Step Potential signal that explicitly estimates the reasoning state at each step. Building on this signal, we propose Step Potential Advantage Estimation (SPAE), a fine-grained credit assignment method that amplifies potential gains, penalizes potential drops, and applies penalty after potential saturates to encourage timely termination. Experiments across multiple benchmarks show SPAE consistently improves accuracy while substantially reducing response length, outperforming strong RL baselines and recent efficient reasoning and token-level advantage estimation methods. The code is available at https://github.com/cii030/SPAE-RL.

LLM-agent budget overruns are a documented production failure class: a single retry loop can spend thousands of dollars before an operator notices, and the in-process integrity properties that would prevent it (no aliasing, no double-spend, no use-after-delegation of a cost-bearing value) are enforced, if at all, by ad-hoc wrappers rather than by the type system. Our central contribution is empirical: a catalog of 63 confirmed production incidents from 21 orchestration frameworks (2023-2026), each backed by a quoted GitHub issue and, where reported, a dollar loss, organized into an eight-cluster failure taxonomy (inter-rater Cohen's kappa = 0.837, N = 113), plus 47 supplementary structural entries. As one mitigation evaluated against this taxonomy, we build token-budgets, an 1,180-line Rust crate (no unsafe) that operationalizes affine ownership so that cloning, double-spending, or using a budget after delegating it are compile errors rather than runtime hazards an operator must remember to avoid. The dollar cap is runtime arithmetic under an estimator assumption; the affine layer makes that arithmetic non-bypassable. On single-agent workloads a 4-line Python counter matches the crate at 0/30 overshoot, so the distinguishing value is non-bypassability under operator error in multi-agent delegation: the delegation-fanout race documented in 11 incidents is rejected by the borrow checker at compile time, while the same pattern under asyncio overshoots 30/30 and three disciplined alternatives overshoot 0/30. Across five runtimes, three providers, and a temperature-stratified live-API test (N = 160), the approach reports zero cap violations and zero false refusals, at operational parity with concurrent work. Static over-reservation is 4-6x (2.11x adaptive). Binary-level cap-soundness on the running binary is left open.

The deployment of autonomous AI agents in sensitive domains, such as healthcare, introduces critical risks to safety, security, and privacy. These agents may deviate from user objectives, violate data handling policies, or be compromised by adversarial attacks. Mitigating these dangers necessitates a mechanism to formally guarantee that an agent's actions adhere to predefined safety constraints, a challenge that existing systems do not fully address. We introduce VeriGuard, a novel framework that provides formal safety guarantees for LLM-based agents through a dual-stage architecture designed for robust and verifiable correctness. The initial offline stage involves a comprehensive validation process. It begins by clarifying user intent to establish precise safety specifications. VeriGuard then synthesizes a behavioral policy and subjects it to both testing and formal verification to prove its compliance with these specifications. This iterative process refines the policy until it is deemed correct. Subsequently, the second stage provides online action monitoring, where VeriGuard operates as a runtime monitor to validate each proposed agent action against the pre-verified policy before execution. This separation of the exhaustive offline validation from the lightweight online monitoring allows formal guarantees to be practically applied, providing a robust safeguard that substantially improves the trustworthiness of LLM agents.

We present RepoST, a scalable method to construct environments that provide execution feedback for repository-level code generation for both training and evaluation. Unlike existing works that aim to build entire repositories for execution, which is challenging for both human and LLMs, we provide execution feedback with sandbox testing, which isolates a given target function and its dependencies to a separate script for testing. Sandbox testing reduces the complexity of external dependencies and enables constructing environments at a large scale. We use our method to construct RepoST-Train, a large-scale train set with 7,415 functions from 832 repositories. Training with the execution feedback provided by RepoST-Train leads to a performance gain of 5.5% Pass@1 on HumanEval and 3.5% Pass@1 on RepoEval. We also build an evaluation dataset, RepoST-Eval, and benchmark 12 code generation models.

This paper presents a case study on applying two model checkers, SPIN and DIVINE, to verify key properties of a C++ software framework, known as ADAPRO, originally developed at CERN. SPIN was used for verifying properties on the design level. DIVINE was used for verifying simple test applications that interacted with the implementation. Both model checkers were found to have their own respective sets of pros and cons, but the overall experience was positive. Because both model checkers were used in a complementary manner, they provided valuable new insights into the framework, which would arguably have been hard to gain by traditional testing and analysis tools only. Translating the C++ source code into the modeling language of the SPIN model checker helped to find flaws in the original design. With DIVINE, defects were found in parts of the code base that had already been subject to hundreds of hours of unit tests, integration tests, and acceptance tests. Most importantly, model checking was found to be easy to integrate into the workflow of the software project and bring added value, not only as verification, but also validation methodology. Therefore, using model checking for developing library-level code seems realistic and worth the effort.

Recent advances in reinforcement learning (RL) with verifiable outcome rewards have significantly improved the reasoning capabilities of large language models (LLMs), especially when combined with multi-turn tool interactions. However, existing methods lack both meaningful verification signals from realistic environments and explicit optimization for verification, leading to unreliable self-verification. To address these limitations, we propose ReVeal, a multi-turn reinforcement learning framework that interleaves code generation with explicit self-verification and tool-based evaluation. ReVeal enables LLMs to autonomously generate test cases, invoke external tools for precise feedback, and improves performance via a customized RL algorithm with dense, per-turn rewards. As a result, ReVeal fosters the co-evolution of a model's generation and verification capabilities through RL training, expanding the reasoning boundaries of the base model, demonstrated by significant gains in Pass@k on LiveCodeBench. It also enables test-time scaling into deeper inference regimes, with code consistently evolving as the number of turns increases during inference, ultimately surpassing DeepSeek-R1-Zero-Qwen-32B. These findings highlight the promise of ReVeal as a scalable and effective paradigm for building more robust and autonomous AI agents.

While large language models have made significant strides in code generation, the pass rate of the generated code is bottlenecked on subtle errors, often requiring human intervention to pass tests, especially for complex problems. Existing LLM-based debugging systems treat generated programs as monolithic units, failing to address bugs at multiple levels of granularity, from low-level syntax errors to high-level algorithmic flaws. In this paper, we introduce Multi-Granularity Debugger (MGDebugger), a hierarchical code debugger by isolating, identifying, and resolving bugs at various levels of granularity. MGDebugger decomposes problematic code into a hierarchical tree structure of subfunctions, with each level representing a particular granularity of error. During debugging, it analyzes each subfunction and iteratively resolves bugs in a bottom-up manner. To effectively test each subfunction, we propose an LLM-simulated Python executor, which traces code execution and tracks important variable states to pinpoint errors accurately. Extensive experiments demonstrate that MGDebugger outperforms existing debugging systems, achieving an 18.9% improvement in accuracy over seed generations in HumanEval and a 97.6% repair success rate in HumanEvalFix. Furthermore, MGDebugger effectively fixes bugs across different categories and difficulty levels, demonstrating its robustness and effectiveness.

Large language models (LLMs) are leading significant progress in code generation. Beyond one-pass code generation, recent works further integrate unit tests and program verifiers into LLMs to iteratively refine the generated programs. However, these works consider the generated programs as an indivisible entity, which falls short for LLMs in debugging the programs, especially when the programs contain complex logic flows and data operations. In contrast, when human developers debug programs, they typically set breakpoints and selectively examine runtime execution information. The execution flow and the intermediate variables play a crucial role in the debugging process, yet they are underutilized in the existing literature on code generation. In this study, we introduce Large Language Model Debugger (LDB), a novel debugging framework that enables LLMs to refine their generated programs with the runtime execution information. Specifically, LDB segments the programs into basic blocks and tracks the values of intermediate variables after each block throughout the runtime execution. This allows LLMs to concentrate on simpler code units within the overall execution flow, verify their correctness against the task description block by block, and efficiently pinpoint any potential errors. Experiments demonstrate that LDB consistently enhances the baseline performance by up to 9.8% across the HumanEval, MBPP, and TransCoder benchmarks, archiving new state-of-the-art performance in code debugging for various LLM selections.

Post-training for reasoning of large language models (LLMs) increasingly relies on verifiable rewards: deterministic checkers that provide 0-1 correctness signals. While reliable, such binary feedback is brittle--many tasks admit partially correct or alternative answers that verifiers under-credit, and the resulting all-or-nothing supervision limits learning. Reward models offer richer, continuous feedback, which can serve as a complementary supervisory signal to verifiers. We introduce HERO (Hybrid Ensemble Reward Optimization), a reinforcement learning framework that integrates verifier signals with reward-model scores in a structured way. HERO employs stratified normalization to bound reward-model scores within verifier-defined groups, preserving correctness while refining quality distinctions, and variance-aware weighting to emphasize challenging prompts where dense signals matter most. Across diverse mathematical reasoning benchmarks, HERO consistently outperforms RM-only and verifier-only baselines, with strong gains on both verifiable and hard-to-verify tasks. Our results show that hybrid reward design retains the stability of verifiers while leveraging the nuance of reward models to advance reasoning.

Step-by-step verifiers -- also known as process reward models (PRMs) -- are a key ingredient for test-time scaling. PRMs require step-level supervision, making them expensive to train. This work aims to build data-efficient PRMs as verbalized step-wise reward models that verify every step in the solution by generating a verification chain-of-thought (CoT). We propose ThinkPRM, a long CoT verifier fine-tuned on orders of magnitude fewer process labels than those required by discriminative PRMs. Our approach capitalizes on the inherent reasoning abilities of long CoT models, and outperforms LLM-as-a-Judge and discriminative verifiers -- using only 1% of the process labels in PRM800K -- across several challenging benchmarks. Specifically, ThinkPRM beats the baselines on ProcessBench, MATH-500, and AIME '24 under best-of-N selection and reward-guided search. In an out-of-domain evaluation on a subset of GPQA-Diamond and LiveCodeBench, our PRM surpasses discriminative verifiers trained on the full PRM800K by 8% and 4.5%, respectively. Lastly, under the same token budget, ThinkPRM scales up verification compute more effectively compared to LLM-as-a-Judge, outperforming it by 7.2% on a subset of ProcessBench. Our work highlights the value of generative, long CoT PRMs that can scale test-time compute for verification while requiring minimal supervision for training. Our code, data, and models will be released at https://github.com/mukhal/thinkprm.

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.

As production code evolves, the test suite must co-evolve to remain effective. Existing benchmarks for test evolution operate at method-level granularity with pre-paired inputs, bypassing the task of locating affected tests from the full project and excluding the need for new tests entirely. We present TEBench, the first project-level benchmark for test evolution. Given a project repository and a code-changing commit, TEBench requires systems to autonomously identify tests requiring modification, determine where new tests are needed, and produce the corresponding test patch. We construct TEBench through a four-stage pipeline over Defects4J projects, curating 314 task instances from 10 projects with developer-written ground truth. Each instance is annotated with one or more of three evolution types: Test-Breaking (tests that fail), Test-Stale (tests that pass but no longer meaningfully validate updated behavior), and Test-Missing (new tests needed for introduced behavior). We evaluate seven configurations spanning three industrial agent frameworks (Claude Code, Codex CLI, OpenCode) and six base models, alongside a heuristic baseline. All seven configurations converge on an identification F1 of 45.7% to 49.4%, revealing a shared performance ceiling across both frameworks and base models. Test-Stale is the most challenging type, averaging F1 around 36%, since configurations rely on execution failure signals and lack proactive semantic reasoning. On the update task, configurations produce highly executable test modifications whose surface form diverges substantially from ground truth. Trajectory analysis reveals a reactive "execute-fail-fix" loop that succeeds for breaking tests but structurally cannot address stale or missing tests. TEBench is available at https://github.com/iSEngLab/TEBench with a leaderboard at https://tebench-leadership.vercel.app.