SubgoalXL: Subgoal-based Expert Learning for Theorem Proving

Fuente: arXiv
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Main Authors: Zhao, Xueliang, Zheng, Lin, Bo, Haige, Hu, Changran, Thakker, Urmish, Kong, Lingpeng
Format: Preprint
Published: 2024
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_version_ 1866913475276570624
author Zhao, Xueliang
Zheng, Lin
Bo, Haige
Hu, Changran
Thakker, Urmish
Kong, Lingpeng
author_facet Zhao, Xueliang
Zheng, Lin
Bo, Haige
Hu, Changran
Thakker, Urmish
Kong, Lingpeng
contents Formal theorem proving, a field at the intersection of mathematics and computer science, has seen renewed interest with advancements in large language models (LLMs). This paper introduces SubgoalXL, a novel approach that synergizes subgoal-based proofs with expert learning to enhance LLMs' capabilities in formal theorem proving within the Isabelle environment. SubgoalXL addresses two critical challenges: the scarcity of specialized mathematics and theorem-proving data, and the need for improved multi-step reasoning abilities in LLMs. By optimizing data efficiency and employing subgoal-level supervision, SubgoalXL extracts richer information from limited human-generated proofs. The framework integrates subgoal-oriented proof strategies with an expert learning system, iteratively refining formal statement, proof, and subgoal generators. Leveraging the Isabelle environment's advantages in subgoal-based proofs, SubgoalXL achieves a new state-of-the-art performance of 56.1\% in Isabelle on the standard miniF2F dataset, marking an absolute improvement of 4.9\%. Notably, SubgoalXL successfully solves 41 AMC12, 9 AIME, and 3 IMO problems from miniF2F. These results underscore the effectiveness of maximizing limited data utility and employing targeted guidance for complex reasoning in formal theorem proving, contributing to the ongoing advancement of AI reasoning capabilities. The implementation is available at \url{https://github.com/zhaoxlpku/SubgoalXL}.
format Preprint
id arxiv_https___arxiv_org_abs_2408_11172
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle SubgoalXL: Subgoal-based Expert Learning for Theorem Proving
Zhao, Xueliang
Zheng, Lin
Bo, Haige
Hu, Changran
Thakker, Urmish
Kong, Lingpeng
Machine Learning
Artificial Intelligence
Computation and Language
Logic in Computer Science
Formal theorem proving, a field at the intersection of mathematics and computer science, has seen renewed interest with advancements in large language models (LLMs). This paper introduces SubgoalXL, a novel approach that synergizes subgoal-based proofs with expert learning to enhance LLMs' capabilities in formal theorem proving within the Isabelle environment. SubgoalXL addresses two critical challenges: the scarcity of specialized mathematics and theorem-proving data, and the need for improved multi-step reasoning abilities in LLMs. By optimizing data efficiency and employing subgoal-level supervision, SubgoalXL extracts richer information from limited human-generated proofs. The framework integrates subgoal-oriented proof strategies with an expert learning system, iteratively refining formal statement, proof, and subgoal generators. Leveraging the Isabelle environment's advantages in subgoal-based proofs, SubgoalXL achieves a new state-of-the-art performance of 56.1\% in Isabelle on the standard miniF2F dataset, marking an absolute improvement of 4.9\%. Notably, SubgoalXL successfully solves 41 AMC12, 9 AIME, and 3 IMO problems from miniF2F. These results underscore the effectiveness of maximizing limited data utility and employing targeted guidance for complex reasoning in formal theorem proving, contributing to the ongoing advancement of AI reasoning capabilities. The implementation is available at \url{https://github.com/zhaoxlpku/SubgoalXL}.
title SubgoalXL: Subgoal-based Expert Learning for Theorem Proving
topic Machine Learning
Artificial Intelligence
Computation and Language
Logic in Computer Science
url https://arxiv.org/abs/2408.11172