LLM-based Automated Theorem Proving Hinges on Scalable Synthetic Data Generation
This work addresses the challenge of generating diverse training data for LLM-based theorem provers, offering incremental improvements in performance on specific benchmarks.
The paper tackles the problem of automated theorem proving by introducing a proof-state exploration approach for scalable synthetic data generation and an adaptive beam size strategy, achieving average pass rates of 60.74% on MiniF2F and 21.18% on ProofNet under the Pass@1 metric.
Recent advancements in large language models (LLMs) have sparked considerable interest in automated theorem proving and a prominent line of research integrates stepwise LLM-based provers into tree search. In this paper, we introduce a novel proof-state exploration approach for training data synthesis, designed to produce diverse tactics across a wide range of intermediate proof states, thereby facilitating effective one-shot fine-tuning of LLM as the policy model. We also propose an adaptive beam size strategy, which effectively takes advantage of our data synthesis method and achieves a trade-off between exploration and exploitation during tree search. Evaluations on the MiniF2F and ProofNet benchmarks demonstrate that our method outperforms strong baselines under the stringent Pass@1 metric, attaining an average pass rate of $60.74\%$ on MiniF2F and $21.18\%$ on ProofNet. These results underscore the impact of large-scale synthetic data in advancing automated theorem proving.