SEGO: Sequential Subgoal Optimization for Mathematical Problem-Solving

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 AIdriven mathematical problem-solving. In recent years, the emergence of Large Language Models (LLMs) has marked a significant milestone in the field of artificial intelligence. Models such as ChatGPT and LLaMA have demonstrated remarkable capabilities across diverse tasks. Within this context, addressing mathematical problems has attracted considerable interest from researchers, as it serves as a prominent showcase of the reasoning capabilities inherent in LLMs.