Autoformalizer with Tool Feedback

Qi Guo; Jianing Wang; Jianfei Zhang; Deyang Kong; Xiangzhou Huang; Xiangyu Xi; Wei Wang; Jingang Wang; Xunliang Cai; Shikun Zhang; Wei Ye

arXiv · 2510.06857

Autoformalizer with Tool Feedback

Qi Guo·Jianing Wang·Jianfei Zhang·Deyang Kong·Xiangzhou Huang·Xiangyu Xi·Wei Wang·Jingang Wang·Xunliang Cai·Shikun Zhang·Wei Ye

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Abstract

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.

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BibTeX RIS

Qi Guo, Jianing Wang, Jianfei Zhang, Deyang Kong, Xiangzhou Huang, Xiangyu Xi, Wei Wang, Jingang Wang, Xunliang Cai, Shikun Zhang, Wei Ye. 2025-10-08. Autoformalizer with Tool Feedback. https://arxiv.org/abs/2510.06857

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