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arXiv · 2310.12960

SEGO: Sequential Subgoal Optimization for Mathematical Problem-Solving

Xueliang Zhao·Xinting Huang·Wei Bi·Lingpeng Kong
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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 \textbf{SE}quential sub\textbf{G}oal \textbf{O}ptimization (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. Data and code associated with this paper will be available at https://github.com/zhaoxlpku/SEGO

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Xueliang Zhao, Xinting Huang, Wei Bi, Lingpeng Kong. 2023-10-19. SEGO: Sequential Subgoal Optimization for Mathematical Problem-Solving. https://arxiv.org/abs/2310.12960

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