Advancing Theorem Proving with Synthetic Proof Data
Overview
Proof assistants like Lean, Isabelle, and Coq ensure high accuracy in mathematical proofs, addressing the growing complexity of modern mathematics that often leads to errors. However, creating computer-verifiable proofs requires significant effort and expertise. Automated theorem proving is increasingly important, with new methods focusing on search algorithms to explore potential solutions. Recent advances in autoformalization offer some relief, but the datasets remain too small to fully leverage large language model (LLM) capabilities.
Practical Solutions
Researchers have developed a method to generate extensive synthetic proof data from high-school and undergraduate math competition problems. By translating these problems into formal statements, filtering low-quality ones, and generating proofs, they created an 8 million statement dataset. Fine-tuning the DeepSeekMath 7B model on this data, they achieved 46.3% accuracy in whole-proof generation on the Lean 4 miniF2F test, surpassing GPT-4’s 23.0%. Their model also solved 5 out of 148 FIMO benchmark problems, outperforming GPT-4. This work advances theorem proving by leveraging large-scale synthetic data.
Value
This approach enhances the performance of automated theorem proving by leveraging large-scale synthetic data. The open-sourced dataset and model aim to advance ATP research and improve large language models’ capabilities in formal mathematical reasoning, with plans to broaden the range of addressed mathematical problems in future work.
Application
For companies looking to evolve with AI, this research demonstrates the potential for AI to redefine work processes. It highlights the importance of identifying automation opportunities, defining KPIs, selecting suitable AI solutions, and implementing AI gradually to drive business outcomes.
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Contact
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