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

**Authors:** Bin Lei  
**arXiv:** [2404.04735](https://arxiv.org/abs/2404.04735)  
**Date:** 2024-04-06  
**Summary page:** https://www.summarizepaper.com/en/paper/2404.04735v1/

## Key points

- Recent advancements in large language models, particularly with GPT-4, have shown impressive capabilities in processing standard queries.
- These models struggle with complex mathematical problems requiring multi-step logical reasoning.
- Prompting engineering has emerged as a key research area to address this limitation.
- Methodologies like Tree of Thought and Graph of Thought aim to enhance inferential abilities but face challenges in tackling complex mathematical problems and lack generalizability.
- The Multi-Agent System for conditional Mining (MACM) prompting method is introduced to resolve complex mathematical problems and demonstrate strong generalization capabilities across various contexts.
- MACM significantly improves the accuracy of GPT-4 Turbo on challenging level five mathematical problems in the MATH dataset from 54.68% to 76.73%.
- MACM code is available on GitHub for further exploration.
- While effective, MACM increases problem-solving time due to multiple invocations of the model for inference.
- Evaluations using the MATH dataset reveal limitations in addressing geometry problems effectively.
- Future work will focus on advancing cognitive capabilities by leveraging prompting methods like MACM to refine responses and generate expansive datasets for model enhancement.

## Summary

Recent advancements in large language models have showcased impressive capabilities in processing standard queries, particularly with the introduction of GPT-4. However, these models often fall short when faced with advanced mathematical problems that require intricate multi-step logical reasoning. To address this limitation, prompting engineering has emerged as a key area of research. Methodologies like the Tree of Thought and Graph of Thought aim to enhance inferential abilities but face challenges in effectively tackling complex mathematical problems and lack generalizability due to the need for tailored prompts. In response to these limitations, this paper introduces the Multi-Agent System for conditional Mining (MACM) prompting method. This innovative approach not only resolves complex mathematical problems but also demonstrates strong generalization capabilities across various mathematical contexts. By implementing MACM, the accuracy of GPT-4 Turbo on challenging level five mathematical problems in the MATH dataset significantly improves from 54.68% to 76.73%. The code for MACM is readily available on GitHub for further exploration. While MACM proves effective in enhancing large language models' accuracy in handling complex mathematical challenges, it does come with a trade-off of increased problem-solving time due to multiple invocations of the model for inference. Additionally, evaluations using the MATH dataset reveal limitations in effectively addressing geometry problems. Future work will focus on advancing the model's cognitive capabilities by leveraging prompting methods like MACM to refine responses and generate expansive datasets for model enhancement. Overall, this research aims to advance the field of Machine Learning by pushing the boundaries of large language models' reasoning abilities through innovative prompting techniques like MACM. By iteratively refining models with high-quality datasets generated through structured thinking paradigms, we can progressively augment their intrinsic intelligence and pave the way for more accurate and reliable AI-generated content in complex problem-solving scenarios.