LLM-based Automated Theorem Proving Hinges on Scalable Synthetic Data Generation

2025-05-17

AI Summary

This work addresses the challenge of weak generalization and inefficient search in LLM-based automated theorem proving, stemming from scarce high-quality training data. We propose a proof-state-space sampling method for synthetic data generation, systematically covering diverse intermediate proof states and tactic combinations; and introduce an adaptive beam-width control mechanism to dynamically balance exploration and exploitation during tree search. The generated data enables one-shot fine-tuning of policy models, eliminating the need for iterative refinement or reinforcement learning. Our approach achieves 60.74% Pass@1 on MiniF2F and 21.18% on ProofNet—substantially outperforming state-of-the-art baselines. Key contributions are: (1) a scalable, semantically rich paradigm for constructing synthetic theorem-proving data; and (2) a data-driven framework that jointly optimizes search and training.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

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.

Problem

• Enhancing LLM-based theorem proving via scalable synthetic data generation
• Improving proof-state exploration for diverse tactic synthesis
• Optimizing tree search with adaptive beam size strategy

Innovation

• Novel proof-state exploration for data synthesis
• Adaptive beam size strategy for tree search
• One-shot fine-tuning of LLM policy model