MPS-Prover: Advancing Stepwise Theorem Proving by Multi-Perspective Search and Data Curation

TL;DR

MPS-Prover introduces a multi-perspective search and data curation approach that significantly improves automated theorem proving efficiency and proof diversity, setting new performance benchmarks in formal reasoning tasks.

Contribution

It presents a novel stepwise ATP system with data pruning and multi-perspective search, enhancing robustness and outperforming existing models on key benchmarks.

Findings

Achieves state-of-the-art results on miniF2F and ProofNet benchmarks.

Prunes 40% of redundant training data without performance loss.

Generates shorter, more diverse proofs compared to prior methods.

Abstract

Automated Theorem Proving (ATP) in formal languages remains a formidable challenge in AI, demanding rigorous logical deduction and navigating vast search spaces. While large language models (LLMs) have shown promising performance, existing stepwise provers often suffer from biased search guidance, leading to inefficiencies and suboptimal proof strategies. This paper introduces the Multi-Perspective Search Prover (MPS-Prover), a novel stepwise ATP system designed to overcome these limitations. MPS-Prover incorporates two key innovations: a highly effective post-training data curation strategy that prunes approximately 40% of redundant training data without sacrificing performance, and a multi-perspective tree search mechanism. This search integrates a learned critic model with strategically designed heuristic rules to diversify tactic selection, prevent getting trapped in unproductive states, and enhance search robustness. Extensive evaluations demonstrate that MPS-Prover achieves state-of-the-art performance on multiple challenging benchmarks, including miniF2F and ProofNet, outperforming prior 7B parameter models. Furthermore, our analyses reveal that MPS-Prover generates significantly shorter and more diverse proofs compared to existing stepwise and whole-proof methods, highlighting its efficiency and efficacy. Our work advances the capabilities of LLM-based formal reasoning and offers a robust framework and a comprehensive analysis for developing more powerful theorem provers.