Title: LLM-based Automated Theorem Proving Hinges on Scalable Synthetic Data Generation
Primary area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)
Keywords: large language models; automated theorem proving; tree search methods

Abstract: 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.

TL;DR: A data synthesis method and an adaptive beam size strategy for automated formalized theorem proving.