@inproceedings{peng-etal-2026-criticlean,
title = "{C}ritic{L}ean: Critic-Guided Reinforcement Learning for Mathematical Formalization",
author = "Peng, Zhongyuan and
Yao, Yifan and
Ma, Kaijing and
Guo, Shuyue and
Li, Yizhe and
Zhang, Yichi and
Zhang, Chenchen and
Zhang, Yifan and
Yu, Zhouliang and
Li, Luming and
Liu, Minghao and
Xia, Yihang and
Shen, Jiawei and
Wu, Yuchen and
Cao, Yixin and
Zhang, Zhaoxiang and
Huang, Wenhao and
Liu, Jiaheng and
Zhang, Ge",
editor = "Liakata, Maria and
Moreira, Viviane P. and
Zhang, Jiajun and
Jurgens, David",
booktitle = "Proceedings of the 64th Annual Meeting of the {A}ssociation for {C}omputational {L}inguistics (Volume 1: Long Papers)",
month = jul,
year = "2026",
address = "San Diego, California, United States",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.acl-long.139/",
pages = "3049--3088",
ISBN = "979-8-89176-390-6",
abstract = "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 509K 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."
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<abstract>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 509K 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.</abstract>
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%0 Conference Proceedings
%T CriticLean: Critic-Guided Reinforcement Learning for Mathematical Formalization
%A Peng, Zhongyuan
%A Yao, Yifan
%A Ma, Kaijing
%A Guo, Shuyue
%A Li, Yizhe
%A Zhang, Yichi
%A Zhang, Chenchen
%A Zhang, Yifan
%A Yu, Zhouliang
%A Li, Luming
%A Liu, Minghao
%A Xia, Yihang
%A Shen, Jiawei
%A Wu, Yuchen
%A Cao, Yixin
%A Zhang, Zhaoxiang
%A Huang, Wenhao
%A Liu, Jiaheng
%A Zhang, Ge
%Y Liakata, Maria
%Y Moreira, Viviane P.
%Y Zhang, Jiajun
%Y Jurgens, David
%S Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
%D 2026
%8 July
%I Association for Computational Linguistics
%C San Diego, California, United States
%@ 979-8-89176-390-6
%F peng-etal-2026-criticlean
%X 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 509K 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.
%U https://aclanthology.org/2026.acl-long.139/
%P 3049-3088
Markdown (Informal)
[CriticLean: Critic-Guided Reinforcement Learning for Mathematical Formalization](https://aclanthology.org/2026.acl-long.139/) (Peng et al., ACL 2026)
ACL
- Zhongyuan Peng, Yifan Yao, Kaijing Ma, Shuyue Guo, Yizhe Li, Yichi Zhang, Chenchen Zhang, Yifan Zhang, Zhouliang Yu, Luming Li, Minghao Liu, Yihang Xia, Jiawei Shen, Yuchen Wu, Yixin Cao, Zhaoxiang Zhang, Wenhao Huang, Jiaheng Liu, and Ge Zhang. 2026. CriticLean: Critic-Guided Reinforcement Learning for Mathematical Formalization. In Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 3049–3088, San Diego, California, United States. Association for Computational Linguistics.