SEGO: Sequential Subgoal Optimization for Mathematical Problem-Solving

Xueliang Zhao, Xinting Huang, Wei Bi, Lingpeng Kong


Abstract
Large Language Models (LLMs) have driven substantial progress in artificial intelligence in recent years, exhibiting impressive capabilities across a wide range of tasks, including mathematical problem-solving. Inspired by the success of subgoal-based methods, we propose a novel framework called SEquential subGoal Optimization (SEGO) to enhance LLMs’ ability to solve mathematical problems. By establishing a connection between the subgoal breakdown process and the probability of solving problems, SEGO aims to identify better subgoals with theoretical guarantees. Addressing the challenge of identifying suitable subgoals in a large solution space, our framework generates problem-specific subgoals and adjusts them according to carefully designed criteria. Incorporating these optimized subgoals into the policy model training leads to significant improvements in problem-solving performance. We validate SEGO’s efficacy through experiments on two benchmarks, GSM8K and MATH, where our approach outperforms existing methods, highlighting the potential of SEGO in AI-driven mathematical problem-solving.
Anthology ID:
2024.acl-long.407
Volume:
Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
Month:
August
Year:
2024
Address:
Bangkok, Thailand
Editors:
Lun-Wei Ku, Andre Martins, Vivek Srikumar
Venue:
ACL
SIG:
Publisher:
Association for Computational Linguistics
Note:
Pages:
7544–7565
Language:
URL:
https://aclanthology.org/2024.acl-long.407
DOI:
Bibkey:
Cite (ACL):
Xueliang Zhao, Xinting Huang, Wei Bi, and Lingpeng Kong. 2024. SEGO: Sequential Subgoal Optimization for Mathematical Problem-Solving. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 7544–7565, Bangkok, Thailand. Association for Computational Linguistics.
Cite (Informal):
SEGO: Sequential Subgoal Optimization for Mathematical Problem-Solving (Zhao et al., ACL 2024)
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PDF:
https://aclanthology.org/2024.acl-long.407.pdf