MPS-Prover: Advancing Stepwise Theorem Proving by Multi-Perspective
  Search and Data Curation
Authors: name: Zhenwen Liang, name: Linfeng Song, name: Yang Li, name: Tao Yang, name: Feng Zhang, name: Haitao Mi, name: Dong Yu

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.