MACM: Utilizing a Multi-Agent System for Condition Mining in Solving Complex Mathematical Problems

TL;DR

This paper introduces MACM, a multi-agent prompting method that significantly improves GPT-4 Turbo's accuracy on complex mathematical problems by enhancing reasoning and generalization capabilities.

Contribution

The paper presents MACM, a novel multi-agent system that overcomes limitations of existing prompting methods in solving advanced mathematical problems with better generalization.

Findings

GPT-4 Turbo accuracy on level five MATH problems increased from 54.68% to 76.73%.

MACM demonstrates strong generalization across various mathematical contexts.

The approach outperforms existing prompting techniques in complex problem solving.

Abstract

Recent advancements in large language models, such as GPT-4, have demonstrated remarkable capabilities in processing standard queries. Despite these advancements, their performance substantially declines in \textbf{advanced mathematical problems requiring complex, multi-step logical reasoning}. To enhance their inferential capabilities, current research has delved into \textit{prompting engineering}, exemplified by methodologies such as the Tree of Thought and Graph of Thought. Nonetheless, these existing approaches encounter two significant limitations. Firstly, their effectiveness in tackling complex mathematical problems is somewhat constrained. Secondly, the necessity to design distinct prompts for individual problems hampers their generalizability. In response to these limitations, this paper introduces the \textit{Multi-Agent System for conditional Mining} (\textbf{MACM}) prompting method. It not only resolves intricate mathematical problems but also demonstrates strong generalization capabilities across various mathematical contexts. With the assistance of MACM, the accuracy of GPT-4 Turbo on the most challenging level five mathematical problems in the MATH dataset increase from $\mathbf{54.68\%} \text{ to } \mathbf{76.73\%}$. The code is available in \url{https://github.com/bin123apple/MACM}.