Core Viewpoint - The article discusses the significant advancements made by ByteDance's Seed team and Nanjing University in the field of mathematical formalization through the introduction of the CriticLean framework, which enhances the accuracy of converting natural language mathematical statements into formal code. Group 1: CriticLean Framework - The CriticLean framework has improved the accuracy of converting natural language mathematical statements to Lean 4 code from 38% to 84% [2][33]. - The framework innovatively places the evaluation model at its core, utilizing the CriticLeanGPT model trained through reinforcement learning to assess the conformity of formalized code to its original meaning [2][7]. Group 2: Challenges in Mathematical Formalization - The core challenge in mathematical formalization lies in accurately converting natural language descriptions into machine-verifiable formal code, which requires deep understanding and faithful representation of mathematical semantics [4]. - Existing research has made progress in generative models and compilation effectiveness, but significant bottlenecks remain in semantic alignment for complex problems, including semantic gaps and insufficient data diversity [5][6]. Group 3: CriticLeanGPT Model - The CriticLeanGPT model was trained using a dataset of 48,000 entries, enhancing its ability to evaluate semantic accuracy [10]. - The model can identify 12 common error types, with type errors accounting for 24.9% and mathematical representation errors at 23.8% [10]. Group 4: CriticLeanBench Benchmark - CriticLeanBench is the first benchmark focused on semantic evaluation in formalization tasks, designed to assess the model's ability to convert natural language mathematical statements into formally verified theorems [12]. - The benchmark includes 500 test samples, with CriticLeanGPT achieving an accuracy of 87%, surpassing other models like GPT-4o and Claude 3.5 [20][21]. Group 5: FineLeanCorpus Dataset - The FineLeanCorpus dataset consists of 285,957 high-quality formalization samples, covering 16 mathematical fields from high school to university level [26]. - Each sample in the dataset has undergone syntax checks and semantic validation, achieving an accuracy rate of over 84% through manual sampling [27]. Group 6: Performance Improvement - The application of the CriticLean framework in automated formalization processes has led to a significant accuracy increase from 38% to 84%, with the semantic evaluation contributing 30 percentage points to this improvement [33].