CriticLean: Critic-Guided Reinforcement Learning for Mathematical Formalization
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, Ge Zhang
cs.CL
Jul 8, 2025 · v1
TL;DR
Builds a critic, benchmark, and 285K-problem dataset for evaluating semantic fidelity of Lean 4 autoformalizations.
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 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.
Problem
Autoformalization systems focus on generation and compilation success, but little attention has been paid to evaluating whether generated formalizations capture the semantic intent of the original problem (the critic phase).
Approach
CriticLean introduces a critic-guided reinforcement learning framework. CriticLeanGPT is trained via supervised fine-tuning and RL to assess the semantic fidelity of Lean 4 formalizations. CriticLeanBench is a benchmark for distinguishing semantically correct from incorrect formalizations. Building on this, FineLeanCorpus is constructed with over 285K problems exhibiting domain diversity, broad difficulty coverage, and high correctness.
Results
Trained CriticLeanGPT models significantly outperform strong open- and closed-source baselines on CriticLeanBench. The FineLeanCorpus of 285K+ problems achieves high correctness based on human evaluation, demonstrating that optimizing the critic phase is essential for reliable formalizations.
