Daily Papers

The automatic generation of Verilog code using Large Language Models (LLMs) has garnered significant interest in hardware design automation. However, existing benchmarks for evaluating LLMs in Verilog generation fall short in replicating real-world design workflows due to their designs' simplicity, inadequate design specifications, and less rigorous verification environments. To address these limitations, we present RealBench, the first benchmark aiming at real-world IP-level Verilog generation tasks. RealBench features complex, structured, real-world open-source IP designs, multi-modal and formatted design specifications, and rigorous verification environments, including 100% line coverage testbenches and a formal checker. It supports both module-level and system-level tasks, enabling comprehensive assessments of LLM capabilities. Evaluations on various LLMs and agents reveal that even one of the best-performing LLMs, o1-preview, achieves only a 13.3% pass@1 on module-level tasks and 0% on system-level tasks, highlighting the need for stronger Verilog generation models in the future. The benchmark is open-sourced at https://github.com/IPRC-DIP/RealBench.

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.

SCTP is a transport protocol offering features such as multi-homing, multi-streaming, and message-oriented delivery. Its two main implementations were subjected to conformance tests using the PacketDrill tool. Conformance testing is not exhaustive and a recent vulnerability (CVE-2021-3772) showed SCTP is not immune to attacks. Changes addressing the vulnerability were implemented, but the question remains whether other flaws might persist in the protocol design. We study the security of the SCTP design, taking a rigorous approach rooted in formal methods. We create a formal Promela model of SCTP, and define 10 properties capturing the essential protocol functionality based on its RFC specification and consultation with the lead RFC author. Then we show using the Spin model checker that our model satisfies these properties. We define 4 attacker models - Off-Path, where the attacker is an outsider that can spoof the port and IP of a peer; Evil-Server, where the attacker is a malicious peer; Replay, where an attacker can capture and replay, but not modify, packets; and On-Path, where the attacker controls the channel between peers. We modify an attack synthesis tool designed for transport protocols, Korg, to support our SCTP model and four attacker models. We synthesize 14 unique attacks using the attacker models - including the CVE vulnerability in the Off-Path attacker model, 4 attacks in the Evil-Server attacker model, an opportunistic ABORT attack in the Replay attacker model, and eight connection manipulation attacks in the On-Path attacker model. We show that the proposed patch eliminates the vulnerability and does not introduce new ones according to our model and protocol properties. Finally, we identify and analyze an ambiguity in the RFC, which we show can be interpreted insecurely. We propose an erratum and show that it eliminates the ambiguity.

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.

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

Large language models show promise for autoformalization, the task of automatically translating natural language into formal languages. However, current autoformalization methods remain limited. The last reported state-of-the-art performance on the ProofNet formalization benchmark for the Lean proof assistant, achieved using Codex for Lean 3, only showed successful formalization of 16.1% of informal statements. Similarly, our evaluation of GPT-4o for Lean 4 only produces successful translations 34.9% of the time. Our analysis shows that the performance of these models is largely limited by their inability to generate formal statements that successfully type-check (i.e., are syntactically correct and consistent with types) - with a whopping 86.6% of GPT-4o errors starting from a type-check failure. In this work, we propose a method to fix this issue through decoding with type-check filtering, where we initially sample a diverse set of candidate formalizations for an informal statement, then use the Lean proof assistant to filter out candidates that do not type-check. Using GPT-4o as a base model, and combining our method with self-consistency, we obtain a +18.3% absolute increase in formalization accuracy, and achieve a new state-of-the-art of 53.2% on ProofNet with Lean 4.

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

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).

Proof-oriented programs mix computational content with proofs of program correctness. However, the human effort involved in programming and proving is still substantial, despite the use of Satisfiability Modulo Theories (SMT) solvers to automate proofs in languages such as F*. Seeking to spur research on using AI to automate the construction of proof-oriented programs, we curate a dataset of 600K lines of open-source F* programs and proofs, including software used in production systems ranging from Windows and Linux, to Python and Firefox. Our dataset includes around 32K top-level F* definitions, each representing a type-directed program and proof synthesis problem -- producing a definition given a formal specification expressed as an F* type. We provide a program-fragment checker that queries F* to check the correctness of candidate solutions. We believe this is the largest corpus of SMT-assisted program proofs coupled with a reproducible program-fragment checker. Grounded in this dataset, we investigate the use of AI to synthesize programs and their proofs in F*, with promising results. Our main finding in that the performance of fine-tuned smaller language models (such as Phi-2 or StarCoder) compare favorably with large language models (such as GPT-4), at a much lower computational cost. We also identify various type-based retrieval augmentation techniques and find that they boost performance significantly. With detailed error analysis and case studies, we identify potential strengths and weaknesses of models and techniques and suggest directions for future improvements.

The formalization of existing mathematical proofs is a notoriously difficult process. Despite decades of research on automation and proof assistants, writing formal proofs remains arduous and only accessible to a few experts. While previous studies to automate formalization focused on powerful search algorithms, no attempts were made to take advantage of available informal proofs. In this work, we introduce Draft, Sketch, and Prove (DSP), a method that maps informal proofs to formal proof sketches, and uses the sketches to guide an automated prover by directing its search to easier sub-problems. We investigate two relevant setups where informal proofs are either written by humans or generated by a language model. Our experiments and ablation studies show that large language models are able to produce well-structured formal sketches that follow the same reasoning steps as the informal proofs. Guiding an automated prover with these sketches enhances its performance from 20.9% to 39.3% on a collection of mathematical competition problems.

We introduce CheckEval, a novel evaluation framework using Large Language Models, addressing the challenges of ambiguity and inconsistency in current evaluation methods. CheckEval addresses these challenges by dividing evaluation criteria into detailed sub-aspects and constructing a checklist of Boolean questions for each, simplifying the evaluation. This approach not only renders the process more interpretable but also significantly enhances the robustness and reliability of results by focusing on specific evaluation dimensions. Validated through a focused case study using the SummEval benchmark, CheckEval indicates a strong correlation with human judgments. Furthermore, it demonstrates a highly consistent Inter-Annotator Agreement. These findings highlight the effectiveness of CheckEval for objective, flexible, and precise evaluations. By offering a customizable and interactive framework, CheckEval sets a new standard for the use of LLMs in evaluation, responding to the evolving needs of the field and establishing a clear method for future LLM-based evaluation.

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.

Autoformalization addresses the scarcity of data for Automated Theorem Proving (ATP) by translating mathematical problems from natural language into formal statements. Efforts in recent work shift from directly prompting large language models to training an end-to-end formalizer model from scratch, achieving remarkable advancements. However, existing formalizer still struggles to consistently generate valid statements that meet syntactic validity and semantic consistency. To address this issue, we propose the Autoformalizer with Tool Feedback (ATF), a novel approach that incorporates syntactic and consistency information as tools into the formalization process. By integrating Lean 4 compilers for syntax corrections and employing a multi-LLMs-as-judge approach for consistency validation, the model is able to adaptively refine generated statements according to the tool feedback, enhancing both syntactic validity and semantic consistency. The training of ATF involves a cold-start phase on synthetic tool-calling data, an expert iteration phase to improve formalization capabilities, and Direct Preference Optimization to alleviate ineffective revisions. Experimental results show that ATF markedly outperforms a range of baseline formalizer models, with its superior performance further validated by human evaluations. Subsequent analysis reveals that ATF demonstrates excellent inference scaling properties. Moreover, we open-source Numina-ATF, a dataset containing 750K synthetic formal statements to facilitate advancements in autoformalization and ATP research.

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.

The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO, showing significant progress. However, these studies intertwined multiple skills simultaneously, i.e., problem-solving, reasoning, and writing formal specifications, making it hard to precisely identify the LLMs' strengths and weaknesses in each task. This paper focuses on formal verification, an immediate application scenario of formal reasoning, and decomposes it into six sub-tasks. We constructed 18k high-quality instruction-response pairs across five mainstream formal specification languages (Coq, Lean4, Dafny, ACSL, and TLA+) in six formal-verification-related tasks by distilling GPT-4o. They are split into a 14k+ fine-tuning dataset FM-alpaca and a 4k benchmark FM-Bench. We found that LLMs are good at writing proof segments when given either the code, or the detailed description of proof steps. Also, the fine-tuning brought about a nearly threefold improvement at most. Interestingly, we observed that fine-tuning with formal data also enhances mathematics, reasoning, and coding abilities. We hope our findings inspire further research. Fine-tuned models are released to facilitate subsequent studies

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

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

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

We introduce Goedel-Prover, an open-source large language model (LLM) that achieves the state-of-the-art (SOTA) performance in automated formal proof generation for mathematical problems. The key challenge in this field is the scarcity of formalized math statements and proofs, which we tackle in the following ways. We train statement formalizers to translate the natural language math problems from Numina into formal language (Lean 4), creating a dataset of 1.64 million formal statements. LLMs are used to check that the formal statements accurately preserve the content of the original natural language problems. We then iteratively build a large dataset of formal proofs by training a series of provers. Each prover succeeds in proving many statements that the previous ones could not, and these new proofs are added to the training set for the next prover. The final prover outperforms all existing open-source models in whole-proof generation. On the miniF2F benchmark, it achieves a 57.6% success rate (Pass@32), exceeding the previous best open-source model by 7.6%. On PutnamBench, Goedel-Prover successfully solves 7 problems (Pass@512), ranking first on the leaderboard. Furthermore, it generates 29.7K formal proofs for Lean Workbook problems, nearly doubling the 15.7K produced by earlier works.

Large Language Models (LLMs) have catalyzed vibe coding, where users leverage LLMs to generate and iteratively refine code through natural language interactions until it passes their vibe check. Vibe check is tied to real-world human preference and goes beyond functionality: the solution should feel right, read cleanly, preserve intent, and remain correct. However, current code evaluation remains anchored to pass@k and captures only functional correctness, overlooking the non-functional instructions that users routinely apply. In this paper, we hypothesize that instruction following is the missing piece underlying vibe check that represents human preference in coding besides functional correctness. To quantify models' code instruction following capabilities with measurable signals, we present VeriCode, a taxonomy of 30 verifiable code instructions together with corresponding deterministic verifiers. We use the taxonomy to augment established evaluation suites, resulting in Vibe Checker, a testbed to assess both code instruction following and functional correctness. Upon evaluating 31 leading LLMs, we show that even the strongest models struggle to comply with multiple instructions and exhibit clear functional regression. Most importantly, a composite score of functional correctness and instruction following correlates the best with human preference, with the latter emerging as the primary differentiator on real-world programming tasks. Our work identifies core factors of the vibe check, providing a concrete path for benchmarking and developing models that better align with user preferences in coding.

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.

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.

Autoformalization, which translates natural language mathematics into machine-verifiable formal statements, is critical for using formal mathematical reasoning to solve math problems stated in natural language. While Large Language Models can generate syntactically correct formal statements, they often fail to preserve the original problem's semantic intent. This limitation arises from the LLM approaches' treating autoformalization as a simplistic translation task which lacks mechanisms for self-reflection and iterative refinement that human experts naturally employ. To address these issues, we propose ReForm, a Reflective Autoformalization method that tightly integrates semantic consistency evaluation into the autoformalization process. This enables the model to iteratively generate formal statements, assess its semantic fidelity, and self-correct identified errors through progressive refinement. To effectively train this reflective model, we introduce Prospective Bounded Sequence Optimization (PBSO), which employs different rewards at different sequence positions to ensure that the model develops both accurate autoformalization and correct semantic validations, preventing superficial critiques that would undermine the purpose of reflection. Extensive experiments across four autoformalization benchmarks demonstrate that ReForm achieves an average improvement of 17.2 percentage points over the strongest baselines. To further ensure evaluation reliability, we introduce ConsistencyCheck, a benchmark of 859 expert-annotated items that not only validates LLMs as judges but also reveals that autoformalization is inherently difficult: even human experts produce semantic errors in up to 38.5% of cases.

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.

We describe SeCaV, a sequent calculus verifier for first-order logic in Isabelle/HOL, and the SeCaV Unshortener, an online tool that expands succinct derivations into the full SeCaV syntax. We leverage the power of Isabelle/HOL as a proof checker for our SeCaV derivations. The interactive features of Isabelle/HOL make our system transparent. For instance, the user can simply click on a side condition to see its exact definition. Our formalized soundness and completeness proofs pertain exactly to the calculus as exposed to the user and not just to some model of our tool. Users can also write their derivations in the SeCaV Unshortener, which provides a lighter syntax, and expand them for later verification. We have used both tools in our teaching.

Code review is one of the primary means of assuring the quality of released software along with testing and static analysis. However, code review requires experienced developers who may not always have the time to perform an in-depth review of code. Thus, automating code review can help alleviate the cognitive burden on experienced software developers allowing them to focus on their primary activities of writing code to add new features and fix bugs. In this paper, we describe our experience in using Large Language Models towards automating the code review process in Ericsson. We describe the development of a lightweight tool using LLMs and static program analysis. We then describe our preliminary experiments with experienced developers in evaluating our code review tool and the encouraging results.

Recent advances in large language models show strong promise for formal reasoning. However, most LLM-based theorem provers have long been constrained by the need for expert-written formal statements as inputs, limiting their applicability to real-world problems expressed in natural language. We tackle this gap with Mathesis, the first end-to-end theorem proving pipeline processing informal problem statements. It contributes Mathesis-Autoformalizer, the first autoformalizer using reinforcement learning to enhance the formalization ability of natural language problems, aided by our novel LeanScorer framework for nuanced formalization quality assessment. It also proposes a Mathesis-Prover, which generates formal proofs from the formalized statements. To evaluate the real-world applicability of end-to-end formal theorem proving, we introduce Gaokao-Formal, a benchmark of 488 complex problems from China's national college entrance exam. Our approach is carefully designed, with a thorough study of each component. Experiments demonstrate Mathesis's effectiveness, with the autoformalizer outperforming the best baseline by 22% in pass-rate on Gaokao-Formal. The full system surpasses other model combinations, achieving 64% accuracy on MiniF2F with pass@32 and a state-of-the-art 18% on Gaokao-Formal.

Automated Test Case Generation (ATCG) is crucial for evaluating software reliability, particularly in competitive programming where robust algorithm assessments depend on diverse and accurate test cases. However, existing ATCG methods often fail to meet complex specifications or generate effective corner cases, limiting their utility. In this work, we introduce Context-Free Grammars with Counters (CCFGs), a formalism that captures both syntactic and semantic structures in input specifications. Using a fine-tuned CodeT5 model, we translate natural language input specifications into CCFGs, enabling the systematic generation of high-quality test cases. Experiments on the CodeContests dataset demonstrate that CCFG-based test cases outperform baseline methods in identifying incorrect algorithms, achieving significant gains in validity and effectiveness. Our approach provides a scalable and reliable grammar-driven framework for enhancing automated competitive programming evaluations.

While slow-thinking large language models (LLMs) exhibit reflection-like reasoning, commonly referred to as the "aha moment:, their ability to generate informative critiques and refine prior solutions remains limited. In this paper, we introduce Double-Checker, a principled framework designed to enhance the reasoning capabilities of slow-thinking LLMs by fostering explicit self-critique and iterative refinement of their previous solutions. By fine-tuning on our curated 1,730 self-critical instances, Double-Checker empowers long-CoT LLMs to iteratively critique and refine their outputs during inference until they evaluate their solutions as correct under self-generated critiques. We validate the efficacy of Double-Checker across a comprehensive suite of reasoning benchmarks, demonstrating that iterative self-critique significantly enhances the reasoning capabilities of long-CoT LLMs. Notably, our Double-Checker increases the pass@1 performance on challenging AIME benchmarks from 4.4% to 18.2% compared to the original long-CoT LLMs. These results highlight a promising direction for developing more trustworthy and effective LLMs capable of structured self-critique. Our codes and data are available at https://github.com/XinXU-USTC/DoubleChecker

As software projects progress, quality of code assumes paramount importance as it affects reliability, maintainability and security of software. For this reason, static analysis tools are used in developer workflows to flag code quality issues. However, developers need to spend extra efforts to revise their code to improve code quality based on the tool findings. In this work, we investigate the use of (instruction-following) large language models (LLMs) to assist developers in revising code to resolve code quality issues. We present a tool, CORE (short for COde REvisions), architected using a pair of LLMs organized as a duo comprised of a proposer and a ranker. Providers of static analysis tools recommend ways to mitigate the tool warnings and developers follow them to revise their code. The proposer LLM of CORE takes the same set of recommendations and applies them to generate candidate code revisions. The candidates which pass the static quality checks are retained. However, the LLM may introduce subtle, unintended functionality changes which may go un-detected by the static analysis. The ranker LLM evaluates the changes made by the proposer using a rubric that closely follows the acceptance criteria that a developer would enforce. CORE uses the scores assigned by the ranker LLM to rank the candidate revisions before presenting them to the developer. CORE could revise 59.2% Python files (across 52 quality checks) so that they pass scrutiny by both a tool and a human reviewer. The ranker LLM is able to reduce false positives by 25.8% in these cases. CORE produced revisions that passed the static analysis tool in 76.8% Java files (across 10 quality checks) comparable to 78.3% of a specialized program repair tool, with significantly much less engineering efforts.

This position paper provides a critical but constructive discussion of current practices in benchmarking and evaluative practices in the field of formal reasoning and automated theorem proving. We take the position that open code, open data, and benchmarks that are complete and error-free will accelerate progress in this field. We identify practices that create barriers to contributing to this field and suggest ways to remove them. We also discuss some of the practices that might produce misleading evaluative information. We aim to create discussions that bring together people from various groups contributing to automated theorem proving, autoformalization, and informal reasoning.

We present Lean Finder, a semantic search engine for Lean and mathlib that understands and aligns with the intents of mathematicians. Progress in formal theorem proving is often hindered by the difficulty of locating relevant theorems and the steep learning curve of the Lean 4 language, making advancement slow and labor-intensive. Existing Lean search engines, though helpful, rely primarily on informalizations (natural language translation of the formal statements), while largely overlooking the mismatch with real-world user queries. In contrast, we propose a user-centered semantic search tailored to the needs of mathematicians. Our approach begins by analyzing and clustering the semantics of public Lean discussions, then fine-tuning text embeddings on synthesized queries that emulate user intents. We further align Lean Finder with mathematicians' preferences using diverse feedback signals, encoding it with a rich awareness of their goals from multiple perspectives. Evaluations on real-world queries, informalized statements, and proof states demonstrate that our Lean Finder achieves over 30% relative improvement compared to previous search engines and GPT-4o. In addition, Lean Finder is compatible with LLM-based theorem provers, bridging retrieval with formal reasoning. Lean Finder is available at: https://leanfinder.github.io

We perform a thorough analysis of the formal and informal statements in the miniF2F benchmark from the perspective of an AI system that is tasked to participate in a math Olympiad consisting of the problems in miniF2F. In such setting, the model has to read and comprehend the problems in natural language, formalize them in Lean language, then proceed with proving the problems, and it will get credit for each problem if the formal proof corresponds to the original informal statement presented to the model. Our evaluation results reveal that the best accuracy of such pipeline can be about 36% using the SoTA models in the literature, considerably lower than the individual SoTA accuracies, 97% and 69% reported in the autoformalization and theorem proving literature. Analyzing the failure modes, we trace back a considerable portion of this drop to discrepancies between the formal and informal statements for more than half of the problems in miniF2F. We proceed with correcting all the errors, discrepancies and simplifications in formal and informal statements, and present the miniF2F-v2 with fully verified formal and informal statements and proofs. Evaluating the full theorem proving pipeline on miniF2F-v2 leads to the best accuracy of 70%, a significant improvement from the 40% on the original miniF2F, yet indicating considerable misalignment between the autoformalization models and theorem provers. Our deep analysis suggests that a higher quality benchmark can help the community better evaluate progress in the field of formal reasoning and also better diagnose the failure and success modes of autoformalization and theorem proving models. Our dataset is available at https://github.com/roozbeh-yz/miniF2F_v2.

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

Formal mathematical reasoning remains a critical challenge for artificial intelligence, hindered by limitations of existing benchmarks in scope and scale. To address this, we present FormalMATH, a large-scale Lean4 benchmark comprising 5,560 formally verified problems spanning from high-school Olympiad challenges to undergraduate-level theorems across diverse domains (e.g., algebra, applied mathematics, calculus, number theory, and discrete mathematics). To mitigate the inefficiency of manual formalization, we introduce a novel human-in-the-loop autoformalization pipeline that integrates: (1) specialized large language models (LLMs) for statement autoformalization, (2) multi-LLM semantic verification, and (3) negation-based disproof filtering strategies using off-the-shelf LLM-based provers. This approach reduces expert annotation costs by retaining 72.09% of statements before manual verification while ensuring fidelity to the original natural-language problems. Our evaluation of state-of-the-art LLM-based theorem provers reveals significant limitations: even the strongest models achieve only 16.46% success rate under practical sampling budgets, exhibiting pronounced domain bias (e.g., excelling in algebra but failing in calculus) and over-reliance on simplified automation tactics. Notably, we identify a counterintuitive inverse relationship between natural-language solution guidance and proof success in chain-of-thought reasoning scenarios, suggesting that human-written informal reasoning introduces noise rather than clarity in the formal reasoning settings. We believe that FormalMATH provides a robust benchmark for benchmarking formal mathematical reasoning.

Exceptional mathematical reasoning ability is one of the key features that demonstrate the power of large language models (LLMs). How to comprehensively define and evaluate the mathematical abilities of LLMs, and even reflect the user experience in real-world scenarios, has emerged as a critical issue. Current benchmarks predominantly concentrate on problem-solving capabilities, which presents a substantial risk of model overfitting and fails to accurately represent genuine mathematical reasoning abilities. In this paper, we argue that if a model really understands a problem, it should be robustly and readily applied across a diverse array of tasks. Motivated by this, we introduce MATHCHECK, a well-designed checklist for testing task generalization and reasoning robustness, as well as an automatic tool to generate checklists efficiently. MATHCHECK includes multiple mathematical reasoning tasks and robustness test types to facilitate a comprehensive evaluation of both mathematical reasoning ability and behavior testing. Utilizing MATHCHECK, we develop MATHCHECK-GSM and MATHCHECK-GEO to assess mathematical textual reasoning and multi-modal reasoning capabilities, respectively, serving as upgraded versions of benchmarks including GSM8k, GeoQA, UniGeo, and Geometry3K. We adopt MATHCHECK-GSM and MATHCHECK-GEO to evaluate over 20 LLMs and 11 MLLMs, assessing their comprehensive mathematical reasoning abilities. Our results demonstrate that while frontier LLMs like GPT-4o continue to excel in various abilities on the checklist, many other model families exhibit a significant decline. Further experiments indicate that, compared to traditional math benchmarks, MATHCHECK better reflects true mathematical abilities and represents mathematical intelligence more linearly, thereby supporting our design. On our MATHCHECK, we can easily conduct detailed behavior analysis to deeply investigate models.

Writing competitive programming problems is exacting. Authors must: set constraints, input distributions, and edge cases that rule out shortcuts; target specific algorithms (e.g., max-flow, dynamic programming, data structures); and calibrate complexity beyond the reach of most competitors. We argue that this makes for an ideal test of general large language model capabilities and study whether they can do this reliably. We introduce AutoCode, which uses multiple rounds of validation to yield competition-grade problem statements and test cases. On held-out problems, AutoCode test suites approach 99% consistency with official judgments, a significant improvement over current state-of-the-art methods like HardTests, which achieve less than 81%. Furthermore, starting with a random seed problem, AutoCode can create novel variants with reference and brute-force solutions. By cross-verifying these generated solutions against test cases, we can further filter out malformed problems. Our system ensures high correctness, as verified by human experts. AutoCode successfully produces novel problems judged by Grandmaster-level (top 0.3%) competitive programmers to be of contest quality.

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

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

Recent advancements in the field of natural language generation have facilitated the use of large language models to assess the quality of generated text. Although these models have shown promising results in tasks such as machine translation and summarization, their applicability in code generation tasks remains limited without human involvement. The complexity of programming concepts required for such tasks makes it difficult to develop evaluation metrics that align with human judgment. Token-matching-based metrics, such as BLEU, have demonstrated weak correlations with human practitioners in code generation tasks. Moreover, the utilization of human-written test suites to evaluate functional correctness can be challenging in domains with low resources. To overcome these obstacles, we propose a new evaluation framework based on the GPT-3.5 (GPT-3.5-turbo), for code generation assessments. Our framework addresses the limitations of existing approaches by achieving superior correlations with functional correctness and human preferences, without the need for test oracles or references. We evaluate the efficacy of our framework on two different tasks and four programming languages, comparing its performance with the state-of-the-art CodeBERTScore metric, which relies on a pre-trained model. Our results demonstrate that our framework surpasses CodeBERTScore, delivering high levels of accuracy and consistency across various programming languages and tasks. We also make our evaluation framework and datasets available to the public at https://github.com/terryyz/llm-code-eval, encouraging further research in the evaluation of code generation.

FormalSpecCpp is a dataset designed to fill the gap in standardized benchmarks for verifying formal specifications in C++ programs. To the best of our knowledge, this is the first comprehensive collection of C++ programs with well-defined preconditions and postconditions. It provides a structured benchmark for evaluating specification inference tools and testing theaccuracy of generated specifications. Researchers and developers can use this dataset to benchmark specification inference tools,fine-tune Large Language Models (LLMs) for automated specification generation, and analyze the role of formal specifications in improving program verification and automated testing. By making this dataset publicly available, we aim to advance research in program verification, specification inference, and AI-assisted software development. The dataset and the code are available at https://github.com/MadhuNimmo/FormalSpecCpp.

Using AI to write formal proofs for mathematical problems is a challenging task that has seen some advancements in recent years. Automated systems such as Lean can verify the correctness of proofs written in formal language, yet writing the proofs in formal language can be challenging for humans and machines. The miniF2F benchmark has 20 IMO problems in its test set, yet formal proofs are available only for 6 of these problems (3 of which are only written by mathematicians). The model with best accuracy can only prove 2 of these 20 IMO problems, from 1950s and 60s, while its training set is a secret. In this work, we write complete, original formal proofs for the remaining IMO problems in Lean along with 3 extra problems from IMO 2022 and 2023. This effort expands the availability of proof currently in the public domain by creating 5,880 lines of Lean proof. The goal of the paper is to pave the way for developing AI models that can automatically write the formal proofs for all the IMO problems in miniF2F and beyond by providing an evaluation benchmark. In this pursuit, we devise a method to decompose the proofs of these problems into their building blocks, constructing a dataset of 1,329 lemmas with more than 40k lines of Lean code. These lemmas are not trivial, yet they are approachable, providing the opportunity to evaluate and diagnose the failures and successes of AI models. We evaluate the ability of the SOTA LLMs on our dataset and analyze their success and failure modes from different perspectives. Our dataset and code is available at: https://github.com/roozbeh-yz/IMO-Steps.

Code contains security and functional bugs. The process of identifying and localizing them is difficult and relies on human labor. In this work, we present a novel approach (FLAG) to assist human debuggers. FLAG is based on the lexical capabilities of generative AI, specifically, Large Language Models (LLMs). Here, we input a code file then extract and regenerate each line within that file for self-comparison. By comparing the original code with an LLM-generated alternative, we can flag notable differences as anomalies for further inspection, with features such as distance from comments and LLM confidence also aiding this classification. This reduces the inspection search space for the designer. Unlike other automated approaches in this area, FLAG is language-agnostic, can work on incomplete (and even non-compiling) code and requires no creation of security properties, functional tests or definition of rules. In this work, we explore the features that help LLMs in this classification and evaluate the performance of FLAG on known bugs. We use 121 benchmarks across C, Python and Verilog; with each benchmark containing a known security or functional weakness. We conduct the experiments using two state of the art LLMs in OpenAI's code-davinci-002 and gpt-3.5-turbo, but our approach may be used by other models. FLAG can identify 101 of the defects and helps reduce the search space to 12-17% of source code.

Electronic Health Records (EHRs) are integral for storing comprehensive patient medical records, combining structured data (e.g., medications) with detailed clinical notes (e.g., physician notes). These elements are essential for straightforward data retrieval and provide deep, contextual insights into patient care. However, they often suffer from discrepancies due to unintuitive EHR system designs and human errors, posing serious risks to patient safety. To address this, we developed EHRCon, a new dataset and task specifically designed to ensure data consistency between structured tables and unstructured notes in EHRs. EHRCon was crafted in collaboration with healthcare professionals using the MIMIC-III EHR dataset, and includes manual annotations of 3,943 entities across 105 clinical notes checked against database entries for consistency. EHRCon has two versions, one using the original MIMIC-III schema, and another using the OMOP CDM schema, in order to increase its applicability and generalizability. Furthermore, leveraging the capabilities of large language models, we introduce CheckEHR, a novel framework for verifying the consistency between clinical notes and database tables. CheckEHR utilizes an eight-stage process and shows promising results in both few-shot and zero-shot settings. The code is available at https://github.com/dustn1259/EHRCon.

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.

The demonstrated code-understanding capability of LLMs raises the question of whether they can be used for automated program verification, a task that often demands high-level abstract reasoning about program properties, which is challenging for verification tools. We propose a general methodology to combine the power of LLMs and automated reasoners for automated program verification. We formally describe this methodology as a set of derivation rules and prove its soundness. We instantiate the calculus as a sound automated verification procedure, which led to practical improvements on a set of synthetic and competition benchmarks.

Translating natural language mathematical statements into formal, executable code is a fundamental challenge in automated theorem proving. While prior work has focused on generation and compilation success, little attention has been paid to the critic phase-the evaluation of whether generated formalizations truly capture the semantic intent of the original problem. In this paper, we introduce CriticLean, a novel critic-guided reinforcement learning framework that elevates the role of the critic from a passive validator to an active learning component. Specifically, first, we propose the CriticLeanGPT, trained via supervised fine-tuning and reinforcement learning, to rigorously assess the semantic fidelity of Lean 4 formalizations. Then, we introduce CriticLeanBench, a benchmark designed to measure models' ability to distinguish semantically correct from incorrect formalizations, and demonstrate that our trained CriticLeanGPT models can significantly outperform strong open- and closed-source baselines. Building on the CriticLean framework, we construct FineLeanCorpus, a dataset comprising over 285K problems that exhibits rich domain diversity, broad difficulty coverage, and high correctness based on human evaluation. Overall, our findings highlight that optimizing the critic phase is essential for producing reliable formalizations, and we hope our CriticLean will provide valuable insights for future advances in formal mathematical reasoning.

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

We introduce a novel framework named ClarifyGPT, which aims to enhance code generation by empowering LLMs with the ability to identify ambiguous requirements and ask targeted clarifying questions. In particular, ClarifyGPT first detects whether a given requirement is ambiguous by performing a code consistency check. If it is ambiguous, ClarifyGPT prompts an LLM to generate targeted clarifying questions. After receiving question responses, ClarifyGPT refines the ambiguous requirement and inputs it into the same LLM to generate a final code solution. To evaluate our ClarifyGPT, we first conduct a human evaluation involving ten participants who use ClarifyGPT for code generation on two publicly available benchmarks: MBPP-sanitized and MBPP-ET. The results show that ClarifyGPT elevates the performance (Pass@1) of GPT-4 from 70.96% to 80.80% on MBPP-sanitized. Furthermore, to perform large-scale automated evaluations of ClarifyGPT across different LLMs and benchmarks without requiring user participation, we introduce a high-fidelity simulation method to simulate user responses. The automated evaluation results also demonstrate that ClarifyGPT can significantly enhance code generation performance compared to the baselines. In particular, ClarifyGPT improves the average performance of GPT-4 and ChatGPT across four benchmarks from 68.02% to 75.75% and from 58.55% to 67.22%, respectively. We believe that ClarifyGPT can effectively facilitate the practical application of LLMs in real-world development environments.

This is the first paper in a series of work we have accomplished over the past three years. In this paper, we have constructed a consistent formal plane geometry system. This will serve as a crucial bridge between IMO-level plane geometry challenges and readable AI automated reasoning. Within this formal framework, we have been able to seamlessly integrate modern AI models with our formal system. AI is now capable of providing deductive reasoning solutions to IMO-level plane geometry problems, just like handling other natural languages, and these proofs are readable, traceable, and verifiable. We propose the geometry formalization theory (GFT) to guide the development of the geometry formal system. Based on the GFT, we have established the FormalGeo, which consists of 88 geometric predicates and 196 theorems. It can represent, validate, and solve IMO-level geometry problems. we also have crafted the FGPS (formal geometry problem solver) in Python. It serves as both an interactive assistant for verifying problem-solving processes and an automated problem solver. We've annotated the formalgeo7k and formalgeo-imo datasets. The former contains 6,981 (expand to 133,818 through data augmentation) geometry problems, while the latter includes 18 (expand to 2,627 and continuously increasing) IMO-level challenging geometry problems. All annotated problems include detailed formal language descriptions and solutions. Implementation of the formal system and experiments validate the correctness and utility of the GFT. The backward depth-first search method only yields a 2.42% problem-solving failure rate, and we can incorporate deep learning techniques to achieve lower one. The source code of FGPS and datasets are available at https://github.com/BitSecret/FGPS.

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

Large Language Models (LLMs) have been shown to achieve breakthrough performance on complex logical reasoning tasks. Nevertheless, most existing research focuses on employing formal language to guide LLMs to derive reliable reasoning paths, while systematic evaluations of these capabilities are still limited. In this paper, we aim to conduct a comprehensive evaluation of LLMs across various logical reasoning problems utilizing formal languages. From the perspective of three dimensions, i.e., spectrum of LLMs, taxonomy of tasks, and format of trajectories, our key findings are: 1) Thinking models significantly outperform Instruct models, especially when formal language is employed; 2) All LLMs exhibit limitations in inductive reasoning capability, irrespective of whether they use a formal language; 3) Data with PoT format achieves the best generalization performance across other languages. Additionally, we also curate the formal-relative training data to further enhance the small language models, and the experimental results indicate that a simple rejected fine-tuning method can better enable LLMs to generalize across formal languages and achieve the best overall performance. Our codes and reports are available at https://github.com/jiangjin1999/FormalEval.

Checkboxes are critical in real-world document processing where the presence or absence of ticks directly informs data extraction and decision-making processes. Yet, despite the strong performance of Large Vision and Language Models across a wide range of tasks, they struggle with interpreting checkable content. This challenge becomes particularly pressing in industries where a single overlooked checkbox may lead to costly regulatory or contractual oversights. To address this gap, we introduce the CheckboxQA dataset, a targeted resource designed to evaluate and improve model performance on checkbox-related tasks. It reveals the limitations of current models and serves as a valuable tool for advancing document comprehension systems, with significant implications for applications in sectors such as legal tech and finance. The dataset is publicly available at: https://github.com/Snowflake-Labs/CheckboxQA

Large Language Models (LLMs) and other automated techniques have been increasingly used to support software developers by generating software artifacts such as code snippets, patches, and comments. However, accurately assessing the correctness of these generated artifacts remains a significant challenge. On one hand, human evaluation provides high accuracy but is labor-intensive and lacks scalability. On the other hand, many automatic evaluation metrics are scalable and require minimal human effort, but they often fail to accurately reflect the actual correctness of generated software artifacts. In this paper, we present SE-Jury, the first evaluation metric for LLM-as-Ensemble-Judge specifically designed to accurately assess the correctness of generated software artifacts. SE-Jury first defines five distinct evaluation strategies, each implemented by an independent judge. A dynamic team selection mechanism then identifies the most appropriate subset of judges as a team to produce a final correctness score through ensembling. We evaluate SE-Jury across a diverse set of software engineering (SE) benchmarks that span three popular SE tasks: code generation, automated program repair, and code summarization. Results demonstrate that SE-Jury consistently achieves a higher correlation with human judgments, with improvements ranging from 29.6% to 140.8% over existing automatic metrics. SE-Jury reaches agreement levels with human annotators that are close to inter-annotator agreement in code generation and program repair. These findings underscore SE-Jury's potential as a scalable and reliable alternative to human evaluation in these SE tasks.

Large Language Models (LLMs) have recently achieved remarkable progress in mathematical reasoning. To enable such capabilities, many existing works distill strong reasoning models into long chains of thought or design algorithms to construct high-quality math QA data for training. However, these efforts primarily focus on generating correct reasoning paths and answers, while largely overlooking the validity of the questions themselves. In this work, we propose Math Question Verification (MathQ-Verify), a novel five-stage pipeline designed to rigorously filter ill-posed or under-specified math problems. MathQ-Verify first performs format-level validation to remove redundant instructions and ensure that each question is syntactically well-formed. It then formalizes each question, decomposes it into atomic conditions, and verifies them against mathematical definitions. Next, it detects logical contradictions among these conditions, followed by a goal-oriented completeness check to ensure the question provides sufficient information for solving. To evaluate this task, we use existing benchmarks along with an additional dataset we construct, containing 2,147 math questions with diverse error types, each manually double-validated. Experiments show that MathQ-Verify achieves state-of-the-art performance across multiple benchmarks, improving the F1 score by up to 25 percentage points over the direct verification baseline. It further attains approximately 90% precision and 63% recall through a lightweight model voting scheme. MathQ-Verify offers a scalable and accurate solution for curating reliable mathematical datasets, reducing label noise and avoiding unnecessary computation on invalid questions. Our code and data are available at https://github.com/scuuy/MathQ-Verify.

Large language models (LLMs) have demonstrated an impressive ability to generate code for various programming tasks. In many instances, LLMs can generate a correct program for a task when given numerous trials. Consequently, a recent trend is to do large scale sampling of programs using a model and then filtering/ranking the programs based on the program execution on a small number of known unit tests to select one candidate solution. However, these approaches assume that the unit tests are given and assume the ability to safely execute the generated programs (which can do arbitrary dangerous operations such as file manipulations). Both of the above assumptions are impractical in real-world software development. In this paper, we propose CodeRanker, a neural ranker that can predict the correctness of a sampled program without executing it. Our CodeRanker is fault-aware i.e., it is trained to predict different kinds of execution information such as predicting the exact compile/runtime error type (e.g., an IndexError or a TypeError). We show that CodeRanker can significantly increase the pass@1 accuracy of various code generation models (including Codex, GPT-Neo, GPT-J) on APPS, HumanEval and MBPP datasets.

Large Language Models (LLMs) demonstrate impressive mathematical reasoning abilities, but their solutions frequently contain errors that cannot be automatically verified. Formal theorem proving systems such as Lean 4 offer automated verification with complete accuracy, motivating recent efforts to build specialized prover LLMs that generate verifiable proofs in formal languages. However, a significant gap remains: current prover LLMs solve substantially fewer problems than general-purpose LLMs operating in natural language. We introduce Hilbert, an agentic framework that bridges this gap by combining the complementary strengths of informal reasoning and formal verification. Our system orchestrates four components: an informal LLM that excels at mathematical reasoning, a specialized prover LLM optimized for Lean 4 tactics, a formal verifier, and a semantic theorem retriever. Given a problem that the prover is unable to solve, Hilbert employs recursive decomposition to split the problem into subgoals that it solves with the prover or reasoner LLM. It leverages verifier feedback to refine incorrect proofs as necessary. Experimental results demonstrate that Hilbert substantially outperforms existing approaches on key benchmarks, achieving 99.2% on miniF2F, 6.6% points above the best publicly available method. Hilbert achieves the best known result on PutnamBench. It solves 462/660 problems (70.0%), outperforming proprietary approaches like SeedProver (50.4%) and achieving a 422% improvement over the best publicly available baseline. Thus, Hilbert effectively narrows the gap between informal reasoning and formal proof generation.

Large Language Models (LLMs) have shown promising performance in code generation. However, how to reliably evaluate code generated by LLMs remains an unresolved problem. This paper presents CodeJudge, a code evaluation framework that leverages LLMs to evaluate the semantic correctness of generated code without the need for test cases. We investigate different ways to guide the LLM in performing "slow thinking" to arrive at an in-depth and reliable evaluation. We experimented with four LLMs as evaluators on four code generation datasets and five programming languages. The results show that CodeJudge significantly outperformed existing methods in most settings. Furthermore, compared with a SOTA GPT-3.5-based code evaluation method, CodeJudge achieved better results even when using a much smaller model, Llama-3-8B-Instruct. Our code and datasets are available on GitHub https://github.com/VichyTong/CodeJudge.

Memory safety violations in low-level code, written in languages like C, continues to remain one of the major sources of software vulnerabilities. One method of removing such violations by construction is to port C code to a safe C dialect. Such dialects rely on programmer-supplied annotations to guarantee safety with minimal runtime overhead. This porting, however, is a manual process that imposes significant burden on the programmer and, hence, there has been limited adoption of this technique. The task of porting not only requires inferring annotations, but may also need refactoring/rewriting of the code to make it amenable to such annotations. In this paper, we use Large Language Models (LLMs) towards addressing both these concerns. We show how to harness LLM capabilities to do complex code reasoning as well as rewriting of large codebases. We also present a novel framework for whole-program transformations that leverages lightweight static analysis to break the transformation into smaller steps that can be carried out effectively by an LLM. We implement our ideas in a tool called MSA that targets the CheckedC dialect. We evaluate MSA on several micro-benchmarks, as well as real-world code ranging up to 20K lines of code. We showcase superior performance compared to a vanilla LLM baseline, as well as demonstrate improvement over a state-of-the-art symbolic (non-LLM) technique.

Large Language Models are powerful tools for program synthesis and advanced auto-completion, but come with no guarantee that their output code is syntactically correct. This paper contributes an incremental parser that allows early rejection of syntactically incorrect code, as well as efficient detection of complete programs for fill-in-the-middle (FIM) tasks. We extend the Earley parsing algorithm to allow for left and right quotients of context-free grammars, and develop methods to handle quotienting of several context-sensitive features present in the grammars of many common programming languages. The result of these contributions is an efficient, general, and well-grounded method for left and right quotient parsing. To validate our theoretical contributions -- and the effectiveness of certain design decisions -- we evaluate our method on the particularly difficult case of FIM completion for Python 3, with syntax-correctness constraints. Our results demonstrate that constrained generation can significantly reduce the incidence of syntax errors in recommended code.

The increased use of large language models (LLMs) across a variety of real-world applications calls for mechanisms to verify the factual accuracy of their outputs. Difficulties lie in assessing the factuality of free-form responses in open domains. Also, different papers use disparate evaluation benchmarks and measurements, which renders them hard to compare and hampers future progress. To mitigate these issues, we propose OpenFactCheck, a unified factuality evaluation framework for LLMs. OpenFactCheck consists of three modules: (i) CUSTCHECKER allows users to easily customize an automatic fact-checker and verify the factual correctness of documents and claims, (ii) LLMEVAL, a unified evaluation framework assesses LLM's factuality ability from various perspectives fairly, and (iii) CHECKEREVAL is an extensible solution for gauging the reliability of automatic fact-checkers' verification results using human-annotated datasets. OpenFactCheck is publicly released at https://github.com/yuxiaw/OpenFactCheck.

Automated text evaluation has long been a central issue in Natural Language Processing (NLP). Recently, the field has shifted toward using Large Language Models (LLMs) as evaluators-a trend known as the LLM-as-a-Judge paradigm. While promising and easily adaptable across tasks, this approach has seen limited exploration in multilingual contexts. Existing multilingual studies often rely on proprietary models or require extensive training data for fine-tuning, raising concerns about cost, time, and efficiency. In this paper, we propose Checklist Engineering based LLM-as-a-Judge (CE-Judge), a training-free framework that uses checklist intuition for multilingual evaluation with an open-source model. Experiments across multiple languages and three benchmark datasets, under both pointwise and pairwise settings, show that our method generally surpasses the baselines and performs on par with the GPT-4o model.

Large language models trained on code have shown great potential to increase productivity of software developers. Several execution-based benchmarks have been proposed to evaluate functional correctness of model-generated code on simple programming problems. Nevertheless, it is expensive to perform the same evaluation on complex real-world projects considering the execution cost. On the contrary, static analysis tools such as linters, which can detect errors without running the program, haven't been well explored for evaluating code generation models. In this work, we propose a static evaluation framework to quantify static errors in Python code completions, by leveraging Abstract Syntax Trees. Compared with execution-based evaluation, our method is not only more efficient, but also applicable to code in the wild. For experiments, we collect code context from open source repos to generate one million function bodies using public models. Our static analysis reveals that Undefined Name and Unused Variable are the most common errors among others made by language models. Through extensive studies, we also show the impact of sampling temperature, model size, and context on static errors in code completions.

Translating software written in legacy languages to modern languages, such as C to Rust, has significant benefits in improving memory safety while maintaining high performance. However, manual translation is cumbersome, error-prone, and produces unidiomatic code. Large language models (LLMs) have demonstrated promise in producing idiomatic translations, but offer no correctness guarantees as they lack the ability to capture all the semantics differences between the source and target languages. To resolve this issue, we propose SACTOR, an LLM-driven C-to-Rust zero-shot translation tool using a two-step translation methodology: an "unidiomatic" step to translate C into Rust while preserving semantics, and an "idiomatic" step to refine the code to follow Rust's semantic standards. SACTOR utilizes information provided by static analysis of the source C program to address challenges such as pointer semantics and dependency resolution. To validate the correctness of the translated result from each step, we use end-to-end testing via the foreign function interface to embed our translated code segment into the original code. We evaluate the translation of 200 programs from two datasets and two case studies, comparing the performance of GPT-4o, Claude 3.5 Sonnet, Gemini 2.0 Flash, Llama 3.3 70B and DeepSeek-R1 in SACTOR. Our results demonstrate that SACTOR achieves high correctness and improved idiomaticity, with the best-performing model (DeepSeek-R1) reaching 93% and (GPT-4o, Claude 3.5, DeepSeek-R1) reaching 84% correctness (on each dataset, respectively), while producing more natural and Rust-compliant translations compared to existing methods.

As a seemingly self-explanatory task, problem-solving has been a significant component of science and engineering. However, a general yet concrete formulation of problem-solving itself is missing. With the recent development of AI-based problem-solving agents, the demand for process-level verifiability is rapidly increasing yet underexplored. To fill these gaps, we present a principled formulation of problem-solving as a deterministic Markov decision process; a novel framework, FPS (Formal Problem-Solving), which utilizes existing FTP (formal theorem proving) environments to perform process-verified problem-solving; and D-FPS (Deductive FPS), decoupling solving and answer verification for better human-alignment. The expressiveness, soundness and completeness of the frameworks are proven. We construct three benchmarks on problem-solving: FormalMath500, a formalization of a subset of the MATH500 benchmark; MiniF2F-Solving and PutnamBench-Solving, adaptations of FTP benchmarks MiniF2F and PutnamBench. For faithful, interpretable, and human-aligned evaluation, we propose RPE (Restricted Propositional Equivalence), a symbolic approach to determine the correctness of answers by formal verification. We evaluate four prevalent FTP models and two prompting methods as baselines, solving at most 23.77% of FormalMath500, 27.47% of MiniF2F-Solving, and 0.31% of PutnamBench-Solving.

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.

Verifiers play a crucial role in large language model (LLM) reasoning, needed by post-training techniques such as reinforcement learning. However, reliable verifiers are hard to get for difficult coding problems, because a well-disguised wrong solution may only be detected by carefully human-written edge cases that are difficult to synthesize. To address this issue, we propose HARDTESTGEN, a pipeline for high-quality test synthesis using LLMs. With this pipeline, we curate a comprehensive competitive programming dataset HARDTESTS with 47k problems and synthetic high-quality tests. Compared with existing tests, HARDTESTGEN tests demonstrate precision that is 11.3 percentage points higher and recall that is 17.5 percentage points higher when evaluating LLM-generated code. For harder problems, the improvement in precision can be as large as 40 points. HARDTESTS also proves to be more effective for model training, measured by downstream code generation performance. We will open-source our dataset and synthesis pipeline at https://leililab.github.io/HardTests/.

Nowadays, formal theorem provers have made monumental progress on high-school and competition-level mathematics, but few of them generalize to more advanced mathematics. In this paper, we present REAL-Prover, a new open-source stepwise theorem prover for Lean 4 to push this boundary. This prover, based on our fine-tuned large language model (REAL-Prover-v1) and integrated with a retrieval system (Leansearch-PS), notably boosts performance on solving college-level mathematics problems. To train REAL-Prover-v1, we developed HERALD-AF, a data extraction pipeline that converts natural language math problems into formal statements, and a new open-source Lean 4 interactive environment (Jixia-interactive) to facilitate synthesis data collection. In our experiments, our prover using only supervised fine-tune achieves competitive results with a 23.7% success rate (Pass@64) on the ProofNet dataset-comparable to state-of-the-art (SOTA) models. To further evaluate our approach, we introduce FATE-M, a new benchmark focused on algebraic problems, where our prover achieves a SOTA success rate of 56.7% (Pass@64).

We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of two. Higher order automated theorem provers are particularly useful here, since the underlying framework of higher order set theory coincides with the classical extensional higher order logic of (most) higher order automated theorem provers, so no significant translation or encoding is required. Additionally, many subgoals are first order and so first order automated provers often suffice. We compare the performance of different provers on the subgoals generated from the development. We also discuss possibilities for proof reconstruction, i.e., obtaining formal proof terms when an automated theorem prover claims to have proven the subgoal.

We present and test the largest benchmark for vericoding, LLM-generation of formally verified code from formal specifications - in contrast to vibe coding, which generates potentially buggy code from a natural language description. Our benchmark contains 12,504 formal specifications, with 3,029 in Dafny, 2,334 in Verus/Rust and 7,141 in Lean. Of these, 6,174 are new unseen problems. We find vericoding success rates of 27% in Lean, 44% in Verus/Rust and 82% in Dafny using off-the-shelf LLMs. Adding natural-language descriptions does not significantly improve performance. We also find that LLM progress has improved progress on pure Dafny verification from 68% to 96% over the past year. The benchmark and vericoding results are shared at https://github.com/Beneficial-AI-Foundation/vericoding-benchmark

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%.

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

We introduce refutationally complete superposition calculi for intentional and extensional clausal lambda-free higher-order logic, two formalisms that allow partial application and applied variables. The calculi are parameterized by a term order that need not be fully monotonic, making it possible to employ the lambda-free higher-order lexicographic path and Knuth-Bendix orders. We implemented the calculi in the Zipperposition prover and evaluated them on Isabelle/HOL and TPTP benchmarks. They appear promising as a stepping stone towards complete, highly efficient automatic theorem provers for full higher-order logic.

We show how to "compile" human-readable programs into standard decoder-only transformer models. Our compiler, Tracr, generates models with known structure. This structure can be used to design experiments. For example, we use it to study "superposition" in transformers that execute multi-step algorithms. Additionally, the known structure of Tracr-compiled models can serve as ground-truth for evaluating interpretability methods. Commonly, because the "programs" learned by transformers are unknown it is unclear whether an interpretation succeeded. We demonstrate our approach by implementing and examining programs including computing token frequencies, sorting, and parenthesis checking. We provide an open-source implementation of Tracr at https://github.com/google-deepmind/tracr.

Modern code generation has made significant strides in functional correctness and execution efficiency. However, these systems often overlook a critical dimension in real-world software development: maintainability. To handle dynamic requirements with minimal rework, we propose MaintainCoder as a pioneering solution. It integrates the Waterfall model, design patterns, and multi-agent collaboration to systematically enhance cohesion, reduce coupling, achieving clear responsibility boundaries and better maintainability. We also introduce MaintainCoder, a benchmark comprising requirement changes and novel dynamic metrics on maintenance efforts. Experiments demonstrate that existing code generation methods struggle to meet maintainability standards when requirements evolve. In contrast, MaintainCoder improves dynamic maintainability metrics by more than 60% with even higher correctness of initial codes. Furthermore, while static metrics fail to accurately reflect maintainability and even contradict each other, our proposed dynamic metrics exhibit high consistency. Our work not only provides the foundation for maintainable code generation, but also highlights the need for more realistic and comprehensive code generation research. Resources: https://github.com/IAAR-Shanghai/MaintainCoder.

The advent of large language models (LLMs) has greatly facilitated code generation, but ensuring the functional correctness of generated code remains a challenge. Traditional validation methods are often time-consuming, error-prone, and impractical for large volumes of code. We introduce CodeSift, a novel framework that leverages LLMs as the first-line filter of code validation without the need for execution, reference code, or human feedback, thereby reducing the validation effort. We assess the effectiveness of our method across three diverse datasets encompassing two programming languages. Our results indicate that CodeSift outperforms state-of-the-art code evaluation methods. Internal testing conducted with subject matter experts reveals that the output generated by CodeSift is in line with human preference, reinforcing its effectiveness as a dependable automated code validation tool.

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}.

The correctness of computations remains a significant challenge in computer science, with traditional approaches relying on automated testing or formal verification. Self-testing/correcting programs introduce an alternative paradigm, allowing a program to verify and correct its own outputs via randomized reductions, a concept that previously required manual derivation. In this paper, we present Bitween, a method and tool for automated learning of randomized (self)-reductions and program properties in numerical programs. Bitween combines symbolic analysis and machine learning, with a surprising finding: polynomial-time linear regression, a basic optimization method, is not only sufficient but also highly effective for deriving complex randomized self-reductions and program invariants, often outperforming sophisticated mixed-integer linear programming solvers. We establish a theoretical framework for learning these reductions and introduce RSR-Bench, a benchmark suite for evaluating Bitween's capabilities on scientific and machine learning functions. Our empirical results show that Bitween surpasses state-of-the-art tools in scalability, stability, and sample efficiency when evaluated on nonlinear invariant benchmarks like NLA-DigBench. Bitween is open-source as a Python package and accessible via a web interface that supports C language programs.

This paper presents a program logic for reasoning about multithreaded Java-like programs with dynamic thread creation, thread joining and reentrant object monitors. The logic is based on concurrent separation logic. It is the first detailed adaptation of concurrent separation logic to a multithreaded Java-like language. The program logic associates a unique static access permission with each heap location, ensuring exclusive write accesses and ruling out data races. Concurrent reads are supported through fractional permissions. Permissions can be transferred between threads upon thread starting, thread joining, initial monitor entrancies and final monitor exits. In order to distinguish between initial monitor entrancies and monitor reentrancies, auxiliary variables keep track of multisets of currently held monitors. Data abstraction and behavioral subtyping are facilitated through abstract predicates, which are also used to represent monitor invariants, preconditions for thread starting and postconditions for thread joining. Value-parametrized types allow to conveniently capture common strong global invariants, like static object ownership relations. The program logic is presented for a model language with Java-like classes and interfaces, the soundness of the program logic is proven, and a number of illustrative examples are presented.

Large Multimodal Models (LMMs) have witnessed remarkable growth, showcasing formidable capabilities in handling intricate multimodal tasks with exceptional performance. Recent research has underscored the inclination of large language models to passively accept defective inputs, often resulting in futile reasoning on invalid prompts. However, the same critical question of whether LMMs can actively detect and scrutinize erroneous inputs still remains unexplored. To address this gap, we introduce the Input Scrutiny Ability Evaluation Framework (ISEval), which encompasses seven categories of flawed premises and three evaluation metrics. Our extensive evaluation of ten advanced LMMs has identified key findings. Most models struggle to actively detect flawed textual premises without guidance, which reflects a strong reliance on explicit prompts for premise error identification. Error type affects performance: models excel at identifying logical fallacies but struggle with surface-level linguistic errors and certain conditional flaws. Modality trust varies-Gemini 2.5 pro and Claude Sonnet 4 balance visual and textual info, while aya-vision-8b over-rely on text in conflicts. These insights underscore the urgent need to enhance LMMs' proactive verification of input validity and shed novel insights into mitigating the problem. The code is available at https://github.com/MLGroupJLU/LMM_ISEval.

Large language models (LLMs), such as ChatGPT and Copilot, are transforming software development by automating code generation and, arguably, enable rapid prototyping, support education, and boost productivity. Therefore, correctness and quality of the generated code should be on par with manually written code. To assess the current state of LLMs in generating correct code of high quality, we conducted controlled experiments with ChatGPT and Copilot: we let the LLMs generate simple algorithms in Java and Python along with the corresponding unit tests and assessed the correctness and the quality (coverage) of the generated (test) codes. We observed significant differences between the LLMs, between the languages, between algorithm and test codes, and over time. The present paper reports these results together with the experimental methods allowing repeated and comparable assessments for more algorithms, languages, and LLMs over time.

Large language models (LLMs) are often augmented with tools to solve complex tasks. By generating code snippets and executing them through task-specific Application Programming Interfaces (APIs), they can offload certain functions to dedicated external modules, such as image encoding and performing calculations. However, most existing approaches to augment LLMs with tools are constrained by general-purpose APIs and lack the flexibility for tailoring them to specific tasks. In this work, we present CRAFT, a general tool creation and retrieval framework for LLMs. It creates toolsets specifically curated for the tasks and equips LLMs with a component that retrieves tools from these sets to enhance their capability to solve complex tasks. For each task, we collect specific code solutions by prompting GPT-4 to solve the training examples. Following a validation step ensuring the correctness, these solutions are abstracted into code snippets to enhance reusability, and deduplicated for higher quality. At inference time, the language model retrieves snippets from the toolsets and then executes them or generates the output conditioning on the retrieved snippets. Our method is designed to be flexible and offers a plug-and-play approach to adapt off-the-shelf LLMs to unseen domains and modalities, without any finetuning. Experiments on vision-language, tabular processing, and mathematical reasoning tasks show that our approach achieves substantial improvements compared to strong baselines. In addition, our in-depth analysis reveals that: (1) consistent performance improvement can be achieved by scaling up the number of tools and the capability of the backbone models; (2) each component of our approach contributes to the performance gains; (3) the created tools are well-structured and reliable with low complexity and atomicity. The code is available at https://github.com/lifan-yuan/CRAFT.

In recent years, the use of automated source code generation utilizing transformer-based generative models has expanded, and these models can generate functional code according to the requirements of the developers. However, recent research revealed that these automatically generated source codes can contain vulnerabilities and other quality issues. Despite researchers' and practitioners' attempts to enhance code generation models, retraining and fine-tuning large language models is time-consuming and resource-intensive. Thus, we describe FRANC, a lightweight framework for recommending more secure and high-quality source code derived from transformer-based code generation models. FRANC includes a static filter to make the generated code compilable with heuristics and a quality-aware ranker to sort the code snippets based on a quality score. Moreover, the framework uses prompt engineering to fix persistent quality issues. We evaluated the framework with five Python and Java code generation models and six prompt datasets, including a newly created one in this work (SOEval). The static filter improves 9% to 46% Java suggestions and 10% to 43% Python suggestions regarding compilability. The average improvement over the NDCG@10 score for the ranking system is 0.0763, and the repairing techniques repair the highest 80% of prompts. FRANC takes, on average, 1.98 seconds for Java; for Python, it takes 0.08 seconds.

Recent advances in large language models (LLMs) for mathematical reasoning have largely focused on tasks with easily verifiable final answers; however, generating and verifying natural language math proofs remains an open challenge. We identify the absence of a reliable, fine-grained evaluator for LLM-generated math proofs as a critical gap. To address this, we propose a systematic methodology for developing and validating evaluators that assign fine-grained scores on a 0-7 scale to model-generated math proofs. To enable this study, we introduce ProofBench, the first expert-annotated dataset of fine-grained proof ratings, spanning 145 problems from six major math competitions (USAMO, IMO, Putnam, etc) and 435 LLM-generated solutions from Gemini-2.5-pro, o3, and DeepSeek-R1. %with expert gradings. Using ProofBench as a testbed, we systematically explore the evaluator design space across key axes: the backbone model, input context, instructions and evaluation workflow. Our analysis delivers ProofGrader, an evaluator that combines a strong reasoning backbone LM, rich context from reference solutions and marking schemes, and a simple ensembling method; it achieves a low Mean Absolute Error (MAE) of 0.926 against expert scores, significantly outperforming naive baselines. Finally, we demonstrate its practical utility in a best-of-n selection task: at n=16, ProofGrader achieves an average score of 4.14 (out of 7), closing 78% of the gap between a naive binary evaluator (2.48) and the human oracle (4.62), highlighting its potential to advance downstream proof generation.

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.

Large language models for code (i.e., code LLMs) have shown strong code understanding and generation capabilities. To evaluate the capabilities of code LLMs in various aspects, many benchmarks have been proposed (e.g., HumanEval and ClassEval). Code reasoning is one of the most essential abilities of code LLMs, but existing benchmarks for code reasoning are not sufficient. Typically, they focus on predicting the input and output of a program, ignoring the evaluation of the intermediate behavior during program execution, as well as the logical consistency (e.g., the model should not give the correct output if the prediction of execution path is wrong) when performing the reasoning. To address these problems, in this paper, we propose a framework, namely REval, for evaluating code reasoning abilities and consistency of code LLMs with program execution. We utilize existing code benchmarks and adapt them to new benchmarks within our framework. A large-scale empirical study is conducted and most LLMs show unsatisfactory performance on both Runtime Behavior Reasoning (i.e., an average accuracy of 44.4%) and Incremental Consistency Evaluation (i.e., an average IC score of 10.3). Evaluation results of current code LLMs reflect the urgent need for the community to strengthen the code reasoning capability of code LLMs. Our code, data, and \newname leaderboard are available at https://r-eval.github.io.

Efficient and accurate autoformalization methods, which leverage large-scale datasets of extensive natural language mathematical problems to construct formal language datasets, are key to advancing formal mathematical reasoning. In this paper, we propose an autoformalization pipeline based on large language models with error feedback, achieving a fully automatic and training-free formalization approach. Using this pipeline, we curate an Olympiad-level dataset aligning natural language problems with Lean formalizations. The dataset comprises 3,922 mathematical problems in natural language and 9,787 in Lean, of which 64.46% were assessed as at least above-average quality, making it suitable as a benchmark for automated theorem provers. Additionally, we investigate the formalization and reasoning capabilities of various LLMs and empirically demonstrate that few-shot learning, error feedback, and increasing sampling numbers enhance the autoformalization process. Experiments of three automated theorem provers on the \dataset\ dataset also highlight its challenging nature and its value as a benchmark for formal reasoning tasks.

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

Automated code review (CR) is a key application for Large Language Models (LLMs), but progress is hampered by a "reality gap": existing benchmarks evaluate models on isolated sub-tasks using simplified, context-poor data. This fails to reflect the holistic context-rich nature of real-world CR. To bridge this gap, we introduce CodeFuse-CR-Bench, the first comprehensiveness-aware benchmark for repository-level CR evaluation. CodeFuse-CR-Bench comprises 601 high-quality instances from 70 Python projects covering nine Pull-Request (PR) problem domains, where each instance provides rich, multi-faceted context including the associated issue, PR details, and repository state, enabling end-to-end evaluation. Beyond superficial metrics, we also propose a novel evaluation framework that combines rule-based checks for location and syntax with model-based judgments of review quality. We present the first large-scale assessment of state-of-the-art LLMs on this comprehensive CR task. Our results establish crucial baselines and reveal that (1) no single LLM dominates all aspects of CR; (2) Gemini 2.5 Pro achieves the highest comprehensive performance; and (3) different LLMs exhibit varying robustness to redundant context. These findings highlight the necessity of holistic, multi-dimensional evaluation and provide actionable insights for advancing truly intelligent yet practical CR assistants.

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

Mathematical verfier achieves success in mathematical reasoning tasks by validating the correctness of solutions. However, existing verifiers are trained with binary classification labels, which are not informative enough for the model to accurately assess the solutions. To mitigate the aforementioned insufficiency of binary labels, we introduce step-wise natural language feedbacks as rationale labels (i.e., the correctness of the current step and the explanations). In this paper, we propose Math-Minos, a natural language feedback enhanced verifier by constructing automatically-generated training data and a two-stage training paradigm for effective training and efficient inference. Our experiments reveal that a small set (30k) of natural language feedbacks can significantly boost the performance of the verifier by the accuracy of 1.6\% (86.6\% rightarrow 88.2\%) on GSM8K and 0.8\% (37.8\% rightarrow 38.6\%) on MATH. We have released our code and data for further exploration.

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

Recently, large language models have presented promising results in aiding formal mathematical reasoning. However, their performance is restricted due to the scarcity of formal theorem-proving data, which requires additional effort to be extracted from raw formal language corpora. Meanwhile, a significant amount of human-written formal language corpora remains underutilized. To address this issue, we propose LEAN-GitHub, a dataset consisting of large-scale formal data extracted from almost all Lean 4 repositories on GitHub. After fine-tuning InternLM-math-plus on this dataset, our model achieved accuracies of 48.8% with a single pass and 54.5% with 64 passes on the Lean 4 miniF2F test, surpassing state-of-the-art method at 52%. And it also achieves state-of-the-art on two other Lean 4 benchmarks (ProofNet and Putnam) targeting different fields/levels of math. These results demonstrate that our proposed dataset is beneficial for formal reasoning on a wide range of math topics. We open-source our model at https://GitHub. com/InternLM/InternLM-Math and our data at https://huggingface.co/ datasets/InternLM/Lean-GitHub

The class of tree-adjoining languages can be characterized by various two-level formalisms, consisting of a context-free grammar (CFG) or pushdown automaton (PDA) controlling another CFG or PDA. These four formalisms are equivalent to tree-adjoining grammars (TAG), linear indexed grammars (LIG), pushdown-adjoining automata (PAA), and embedded pushdown automata (EPDA). We define semiring-weighted versions of the above two-level formalisms, and we design new algorithms for computing their stringsums (the weight of all derivations of a string) and allsums (the weight of all derivations). From these, we also immediately obtain stringsum and allsum algorithms for TAG, LIG, PAA, and EPDA. For LIG, our algorithm is more time-efficient by a factor of O(n|N|) (where n is the string length and |N| is the size of the nonterminal set) and more space-efficient by a factor of O(|Gamma|) (where |Gamma| is the size of the stack alphabet) than the algorithm of Vijay-Shanker and Weir (1989). For EPDA, our algorithm is both more space-efficient and time-efficient than the algorithm of Alonso et al. (2001) by factors of O(|Gamma|^2) and O(|Gamma|^3), respectively. Finally, we give the first PAA stringsum and allsum algorithms.

Spreadsheets are widely used for table manipulation and presentation. Stylistic formatting of these tables is an important property for both presentation and analysis. As a result, popular spreadsheet software, such as Excel, supports automatically formatting tables based on rules. Unfortunately, writing such formatting rules can be challenging for users as it requires knowledge of the underlying rule language and data logic. We present CORNET, a system that tackles the novel problem of automatically learning such formatting rules from user examples in the form of formatted cells. CORNET takes inspiration from advances in inductive programming and combines symbolic rule enumeration with a neural ranker to learn conditional formatting rules. To motivate and evaluate our approach, we extracted tables with over 450K unique formatting rules from a corpus of over 1.8M real worksheets. Since we are the first to introduce conditional formatting, we compare CORNET to a wide range of symbolic and neural baselines adapted from related domains. Our results show that CORNET accurately learns rules across varying evaluation setups. Additionally, we show that CORNET finds shorter rules than those that a user has written and discovers rules in spreadsheets that users have manually formatted.

In this paper, we introduce BMMR, a large-scale bilingual, multimodal, multi-disciplinary reasoning dataset for the community to develop and evaluate large multimodal models (LMMs). BMMR comprises 110k college-level questions spanning 300 UNESCO-defined subjects, spanning diverse formats-multiple-choice, fill-in-the-blank, and open-ended QA-and sourced from both print and digital media such as books, exams, and quizzes. All data are curated and filtered via a human-in-the-loop and scalable framework, and each instance is paired with a high-quality reasoning path. The dataset is organized into two parts: BMMR-Eval that comprises 20,458 high-quality instances to comprehensively assess LMMs' knowledge and reasoning across multiple disciplines in both Chinese and English; and BMMR-Train that contains 88,991 instances to support further research and development, extending the current focus on mathematical reasoning to diverse disciplines and domains. In addition, we propose the process-based multi-discipline verifier (i.e., BMMR-Verifier) for accurate and fine-grained evaluation of reasoning paths. Extensive experiments on 24 models reveal that (i) even SOTA models (e.g., o3 and Gemini-2.5-Pro) leave substantial headroom on BMMR-Eval; (ii) reasoning models exhibit discipline bias and outperform LMMs only on specific subjects; (iii) open-source models still trail their proprietary counterparts; and (iv) fine-tuning on BMMR-Train narrows this gap. Additionally, we conduct reasoning-chain analyses using BMMR-Verifier and other in-depth studies, uncovering the challenges LMMs currently face in multidisciplinary reasoning. We will release the data, and we hope our work can offer insights and contributions to the community.

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.

Refactoring is a common software engineering practice that improves code quality without altering program behavior. Although tools like ReExtractor+, RefactoringMiner, and RefDiff have been developed to detect refactorings automatically, they rely on complex rule definitions and static analysis, making them difficult to extend and generalize to other programming languages. In this paper, we investigate the viability of using foundation models for refactoring detection, implemented in a tool named RefModel. We evaluate Phi4-14B, and Claude 3.5 Sonnet on a dataset of 858 single-operation transformations applied to artificially generated Java programs, covering widely-used refactoring types. We also extend our evaluation by including Gemini 2.5 Pro and o4-mini-high, assessing their performance on 44 real-world refactorings extracted from four open-source projects. These models are compared against RefactoringMiner, RefDiff, and ReExtractor+. RefModel is competitive with, and in some cases outperform, traditional tools. In real-world settings, Claude 3.5 Sonnet and Gemini 2.5 Pro jointly identified 97% of all refactorings, surpassing the best-performing static-analysis-based tools. The models showed encouraging generalization to Python and Golang. They provide natural language explanations and require only a single sentence to define each refactoring type.

Many challenging reasoning tasks require not just rapid, intuitive responses, but a more deliberate, multi-step approach. Recent progress in large language models (LLMs) highlights an important shift from the "System 1" way of quick reactions to the "System 2" style of reflection-and-correction problem solving. However, current benchmarks heavily rely on the final-answer accuracy, leaving much of a model's intermediate reasoning steps unexamined. This fails to assess the model's ability to reflect and rectify mistakes within the reasoning process. To bridge this gap, we introduce FINEREASON, a logic-puzzle benchmark for fine-grained evaluation of LLMs' reasoning capabilities. Each puzzle can be decomposed into atomic steps, making it ideal for rigorous validation of intermediate correctness. Building on this, we introduce two tasks: state checking, and state transition, for a comprehensive evaluation of how models assess the current situation and plan the next move. To support broader research, we also provide a puzzle training set aimed at enhancing performance on general mathematical tasks. We show that models trained on our state checking and transition data demonstrate gains in math reasoning by up to 5.1% on GSM8K.

Statically analyzing dynamically-typed code is a challenging endeavor, as even seemingly trivial tasks such as determining the targets of procedure calls are non-trivial without knowing the types of objects at compile time. Addressing this challenge, gradual typing is increasingly added to dynamically-typed languages, a prominent example being TypeScript that introduces static typing to JavaScript. Gradual typing improves the developer's ability to verify program behavior, contributing to robust, secure and debuggable programs. In practice, however, users only sparsely annotate types directly. At the same time, conventional type inference faces performance-related challenges as program size grows. Statistical techniques based on machine learning offer faster inference, but although recent approaches demonstrate overall improved accuracy, they still perform significantly worse on user-defined types than on the most common built-in types. Limiting their real-world usefulness even more, they rarely integrate with user-facing applications. We propose CodeTIDAL5, a Transformer-based model trained to reliably predict type annotations. For effective result retrieval and re-integration, we extract usage slices from a program's code property graph. Comparing our approach against recent neural type inference systems, our model outperforms the current state-of-the-art by 7.85% on the ManyTypes4TypeScript benchmark, achieving 71.27% accuracy overall. Furthermore, we present JoernTI, an integration of our approach into Joern, an open source static analysis tool, and demonstrate that the analysis benefits from the additional type information. As our model allows for fast inference times even on commodity CPUs, making our system available through Joern leads to high accessibility and facilitates security research.

The popularity of the Rust language continues to explode; yet, many critical codebases remain authored in C, and cannot be realistically rewritten by hand. Automatically translating C to Rust is thus an appealing course of action. Several works have gone down this path, handling an ever-increasing subset of C through a variety of Rust features, such as unsafe. While the prospect of automation is appealing, producing code that relies on unsafe negates the memory safety guarantees offered by Rust, and therefore the main advantages of porting existing codebases to memory-safe languages. We instead explore a different path, and explore what it would take to translate C to safe Rust; that is, to produce code that is trivially memory safe, because it abides by Rust's type system without caveats. Our work sports several original contributions: a type-directed translation from (a subset of) C to safe Rust; a novel static analysis based on "split trees" that allows expressing C's pointer arithmetic using Rust's slices and splitting operations; an analysis that infers exactly which borrows need to be mutable; and a compilation strategy for C's struct types that is compatible with Rust's distinction between non-owned and owned allocations. We apply our methodology to existing formally verified C codebases: the HACL* cryptographic library, and binary parsers and serializers from EverParse, and show that the subset of C we support is sufficient to translate both applications to safe Rust. Our evaluation shows that for the few places that do violate Rust's aliasing discipline, automated, surgical rewrites suffice; and that the few strategic copies we insert have a negligible performance impact. Of particular note, the application of our approach to HACL* results in a 80,000 line verified cryptographic library, written in pure Rust, that implements all modern algorithms - the first of its kind.

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

Commit messages are a valuable resource in comprehension of software evolution, since they provide a record of changes such as feature additions and bug repairs. Unfortunately, programmers often neglect to write good commit messages. Different techniques have been proposed to help programmers by automatically writing these messages. These techniques are effective at describing what changed, but are often verbose and lack context for understanding the rationale behind a change. In contrast, humans write messages that are short and summarize the high level rationale. In this paper, we adapt Neural Machine Translation (NMT) to automatically "translate" diffs into commit messages. We trained an NMT algorithm using a corpus of diffs and human-written commit messages from the top 1k Github projects. We designed a filter to help ensure that we only trained the algorithm on higher-quality commit messages. Our evaluation uncovered a pattern in which the messages we generate tend to be either very high or very low quality. Therefore, we created a quality-assurance filter to detect cases in which we are unable to produce good messages, and return a warning instead.

Given the rapid ascent of large language models (LLMs), we study the question: (How) can large language models help in reviewing of scientific papers or proposals? We first conduct some pilot studies where we find that (i) GPT-4 outperforms other LLMs (Bard, Vicuna, Koala, Alpaca, LLaMa, Dolly, OpenAssistant, StableLM), and (ii) prompting with a specific question (e.g., to identify errors) outperforms prompting to simply write a review. With these insights, we study the use of LLMs (specifically, GPT-4) for three tasks: 1. Identifying errors: We construct 13 short computer science papers each with a deliberately inserted error, and ask the LLM to check for the correctness of these papers. We observe that the LLM finds errors in 7 of them, spanning both mathematical and conceptual errors. 2. Verifying checklists: We task the LLM to verify 16 closed-ended checklist questions in the respective sections of 15 NeurIPS 2022 papers. We find that across 119 {checklist question, paper} pairs, the LLM had an 86.6% accuracy. 3. Choosing the "better" paper: We generate 10 pairs of abstracts, deliberately designing each pair in such a way that one abstract was clearly superior than the other. The LLM, however, struggled to discern these relatively straightforward distinctions accurately, committing errors in its evaluations for 6 out of the 10 pairs. Based on these experiments, we think that LLMs have a promising use as reviewing assistants for specific reviewing tasks, but not (yet) for complete evaluations of papers or proposals.

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

Evaluating large language models (LLMs) in diverse and challenging scenarios is essential to align them with human preferences. To mitigate the prohibitive costs associated with human evaluations, utilizing a powerful LLM as a judge has emerged as a favored approach. Nevertheless, this methodology encounters several challenges, including substantial expenses, concerns regarding privacy and security, and reproducibility. In this paper, we propose a straightforward, replicable, and accurate automated evaluation method by leveraging a lightweight LLM as the judge, named RocketEval. Initially, we identify that the performance disparity between lightweight and powerful LLMs in evaluation tasks primarily stems from their ability to conduct comprehensive analyses, which is not easily enhanced through techniques such as chain-of-thought reasoning. By reframing the evaluation task as a multi-faceted Q&A using an instance-specific checklist, we demonstrate that the limited judgment accuracy of lightweight LLMs is largely attributes to high uncertainty and positional bias. To address these challenges, we introduce an automated evaluation process grounded in checklist grading, which is designed to accommodate a variety of scenarios and questions. This process encompasses the creation of checklists, the grading of these checklists by lightweight LLMs, and the reweighting of checklist items to align with the supervised annotations. Our experiments carried out on the automated evaluation benchmarks, MT-Bench and WildBench datasets, reveal that RocketEval, when using Gemma-2-2B as the judge, achieves a high correlation (0.965) with human preferences, which is comparable to GPT-4o. Moreover, RocketEval provides a cost reduction exceeding 50-fold for large-scale evaluation and comparison scenarios. Our code is available at https://github.com/Joinn99/RocketEval-ICLR .

Document parsing aims to transform unstructured PDF images into semi-structured data, facilitating the digitization and utilization of information in diverse domains. While vision language models (VLMs) have significantly advanced this task, achieving reliable, high-quality parsing in real-world scenarios remains challenging. Common practice often selects the top-performing model on standard benchmarks. However, these benchmarks may carry dataset-specific biases, leading to inconsistent model rankings and limited correlation with real-world performance. Moreover, benchmark metrics typically provide only overall scores, which can obscure distinct error patterns in output. This raises a key challenge: how can we reliably and comprehensively assess document parsing quality in the wild? We address this problem with DOCR-Inspector, which formalizes document parsing assessment as fine-grained error detection and analysis. Leveraging VLM-as-a-Judge, DOCR-Inspector analyzes a document image and its parsed output, identifies all errors, assigns them to one of 28 predefined types, and produces a comprehensive quality assessment. To enable this capability, we construct DOCRcase-200K for training and propose the Chain-of-Checklist reasoning paradigm to enable the hierarchical structure of parsing quality assessment. For empirical validation, we introduce DOCRcaseBench, a set of 882 real-world document parsing cases with manual annotations. On this benchmark, DOCR-Inspector-7B outperforms commercial models like Gemini 2.5 Pro, as well as leading open-source models. Further experiments demonstrate that its quality assessments provide valuable guidance for parsing results refinement, making DOCR-Inspector both a practical evaluator and a driver for advancing document parsing systems at scale. Model and code are released at: https://github.com/ZZZZZQT/DOCR-Inspector.

LLMs are widely used in complex AI applications. These applications underscore the need for LLM outputs to adhere to a specific format, for their integration with other components in the systems. Typically the format rules e.g., for data serialization formats such as JSON, YAML, or Code in Programming Language are expressed as context-free grammar (CFG). Due to the hallucinations and unreliability of LLMs, instructing LLMs to adhere to specified syntax becomes an increasingly important challenge. We present SynCode, a novel framework for efficient and general syntactical decoding with LLMs, to address this challenge. SynCode leverages the CFG of a formal language, utilizing an offline-constructed efficient lookup table called DFA mask store based on the discrete finite automaton (DFA) of the language grammar terminals. We demonstrate SynCode's soundness and completeness given the CFG of the formal language, presenting its ability to retain syntactically valid tokens while rejecting invalid ones. SynCode seamlessly integrates with any language defined by CFG, as evidenced by experiments focusing on generating JSON, Python, and Go outputs. Our experiments evaluating the effectiveness of SynCode for JSON generation demonstrate that SynCode eliminates all syntax errors and significantly outperforms state-of-the-art baselines. Furthermore, our results underscore how SynCode significantly reduces 96.07% of syntax errors in generated Python and Go code, showcasing its substantial impact on enhancing syntactical precision in LLM generation. Our code is available at https://github.com/uiuc-focal-lab/syncode

Autoformalization aims to translate natural-language mathematical statements into a formal language. While LLMs have accelerated progress in this area, existing methods still suffer from low accuracy. We identify two key abilities for effective autoformalization: comprehensive mastery of formal-language domain knowledge, and reasoning capability of natural language problem understanding and informal-formal alignment. Without the former, a model cannot identify the correct formal objects; without the latter, it struggles to interpret real-world contexts and map them precisely into formal expressions. To address these gaps, we introduce ThinkingF, a data synthesis and training pipeline that improves both abilities. First, we construct two datasets: one by distilling and selecting large-scale examples rich in formal knowledge, and another by generating informal-to-formal reasoning trajectories guided by expert-designed templates. We then apply SFT and RLVR with these datasets to further fuse and refine the two abilities. The resulting 7B and 32B models exhibit both comprehensive formal knowledge and strong informal-to-formal reasoning. Notably, StepFun-Formalizer-32B achieves SOTA BEq@1 scores of 40.5% on FormalMATH-Lite and 26.7% on ProverBench, surpassing all prior general-purpose and specialized models.

Context: Exhaustive fuzzing of modern JavaScript engines is infeasible due to the vast number of program states and execution paths. Coverage-guided fuzzers waste effort on low-risk inputs, often ignoring vulnerability-triggering ones that do not increase coverage. Existing heuristics proposed to mitigate this require expert effort, are brittle, and hard to adapt. Objective: We propose a data-centric, LLM-boosted alternative that learns from historical vulnerabilities to automatically identify minimal static (code) and dynamic (runtime) features for detecting high-risk inputs. Method: Guided by historical V8 bugs, iterative prompting generated 115 static and 49 dynamic features, with the latter requiring only five trace flags, minimizing instrumentation cost. After feature selection, 41 features remained to train an XGBoost model to predict high-risk inputs during fuzzing. Results: Combining static and dynamic features yields over 85% precision and under 1% false alarms. Only 25% of these features are needed for comparable performance, showing that most of the search space is irrelevant. Conclusion: This work introduces feature-guided fuzzing, an automated data-driven approach that replaces coverage with data-directed inference, guiding fuzzers toward high-risk states for faster, targeted, and reproducible vulnerability discovery. To support open science, all scripts and data are available at https://github.com/KKGanguly/DataCentricFuzzJS .

Scientists often infer abstract procedures from specific instances of problems and use the abstractions to generate new, related instances. For example, programs encoding the formal rules and properties of a system have been useful in fields ranging from RL (procedural environments) to physics (simulation engines). These programs can be seen as functions which execute to different outputs based on their parameterizations (e.g., gridworld configuration or initial physical conditions). We introduce the term EFA (Executable Functional Abstraction) to denote such programs for math problems. EFA-like constructs have been shown to be useful for math reasoning as problem generators for stress-testing models. However, prior work has been limited to abstractions for grade-school math (whose simple rules are easy to encode in programs), while generating EFAs for advanced math has thus far required human engineering. We explore the automatic construction of EFAs for advanced math problems. We operationalize the task of automatically constructing EFAs as a program synthesis task, and develop EFAGen, which conditions an LLM on a seed math problem and its step-by-step solution to generate candidate EFA programs that are faithful to the generalized problem and solution class underlying the seed problem. Furthermore, we formalize properties any valid EFA must possess in terms of executable unit tests, and show how the tests can be used as verifiable rewards to train LLMs to become better writers of EFAs. We demonstrate that EFAs constructed by EFAGen behave rationally by remaining faithful to seed problems, produce learnable problem variations, and that EFAGen can infer EFAs across multiple diverse sources of competition-level math problems. Finally, we show downstream uses of model-written EFAs e.g. finding problem variations that are harder or easier for a learner to solve, as well as data generation.

Recent Language Models (LMs) achieve breakthrough performance in code generation when trained on human-authored problems, even solving some competitive-programming problems. Self-play has proven useful in games such as Go, and thus it is natural to ask whether LMs can generate their own instructive programming problems to improve their performance. We show that it is possible for an LM to synthesize programming problems and solutions, which are filtered for correctness by a Python interpreter. The LM's performance is then seen to improve when it is fine-tuned on its own synthetic problems and verified solutions; thus the model 'improves itself' using the Python interpreter. Problems are specified formally as programming puzzles [Schuster et al., 2021], a code-based problem format where solutions can easily be verified for correctness by execution. In experiments on publicly-available LMs, test accuracy more than doubles. This work demonstrates the potential for code LMs, with an interpreter, to generate instructive problems and improve their own performance.

Premise selection is a crucial yet challenging step in mathematical formalization, especially for users with limited experience. Due to the lack of available formalization projects, existing approaches that leverage language models often suffer from data scarcity. In this work, we introduce an innovative method for training a premise retriever to support the formalization of mathematics. Our approach employs a BERT model to embed proof states and premises into a shared latent space. The retrieval model is trained within a contrastive learning framework and incorporates a domain-specific tokenizer along with a fine-grained similarity computation method. Experimental results show that our model is highly competitive compared to existing baselines, achieving strong performance while requiring fewer computational resources. Performance is further enhanced through the integration of a re-ranking module. To streamline the formalization process, we will release a search engine that enables users to query Mathlib theorems directly using proof states, significantly improving accessibility and efficiency. Codes are available at https://github.com/ruc-ai4math/Premise-Retrieval.

Large language models (LLMs) have recently demonstrated remarkable progress in formal theorem proving. Yet their ability to serve as practical assistants for mathematicians, filling in missing steps within complex proofs, remains underexplored. We identify this challenge as the task of subgoal completion, where an LLM must discharge short but nontrivial proof obligations left unresolved in a human-provided sketch. To study this problem, we introduce FormalML, a Lean 4 benchmark built from foundational theories of machine learning. Using a translation tactic that converts procedural proofs into declarative form, we extract 4937 problems spanning optimization and probability inequalities, with varying levels of difficulty. FormalML is the first subgoal completion benchmark to combine premise retrieval and complex research-level contexts. Evaluation of state-of-the-art provers highlights persistent limitations in accuracy and efficiency, underscoring the need for more capable LLM-based theorem provers for effective subgoal completion,

This paper introduces VeriThoughts, a novel dataset designed for reasoning-based Verilog code generation. We establish a new benchmark framework grounded in formal verification methods to evaluate the quality and correctness of generated hardware descriptions. Additionally, we present a suite of specialized small-scale models optimized specifically for Verilog generation. Our work addresses the growing need for automated hardware design tools that can produce verifiably correct implementations from high-level specifications, potentially accelerating the hardware development process while maintaining rigorous correctness guarantees. Our code and data are available at https://github.com/wilyub/VeriThoughts{this URL}.

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.

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

Existing informal language-based (e.g., human language) Large Language Models (LLMs) trained with Reinforcement Learning (RL) face a significant challenge: their verification processes, which provide crucial training signals, are neither reliable nor scalable. In fact, the prevalent large proprietary models could hardly generate verifiable programs. A promising yet largely uncharted alternative is formal language-based reasoning. Grounding LLMs in rigorous formal systems where generative models operate in formal language spaces (e.g., Dafny) enables the automatic and mathematically provable verification of their reasoning processes and outcomes. This capability is pivotal for achieving large-scale, reliable formal software verification. It is a common practice to employ human-annotated chain-of-thought and other human priors to induce the reasoning and coding capabilities of LLMs. Unfortunately, it becomes unacceptably all-consuming to provide such priors for supervising complex programming tasks. In this work, we systematically explore ways to reduce human priors with the formal language, Dafny, as the main environment for our pilot study. Our pipeline mainly relies on introducing an automatic and scalable data curation pipeline, and careful RL designs integrated with feedback from the formal language verifier. We introduce DafnyComp, a benchmark of compositional formal programs with auto-formalized specifications for specification reasoning. Our supervised fine-tuning (SFT) stage enables even small models (e.g., 0.5B) to generate syntactically valid and verifiable Dafny code, surpassing proprietary models. RL with regularization further improves performance, achieving stronger generalization to out-of-domain tasks and outperforming all strong baselines on the challenging DafnyComp benchmark.