Expanding Search Space with Diverse Prompting Agents: An Efficient Sampling Approach for LLM Mathematical Reasoning

TL;DR

This paper introduces a sampling approach that combines diverse prompting methods to expand the search space and improve mathematical reasoning in LLMs, achieving better performance with fewer runs.

Contribution

It demonstrates that integrating multiple prompting strategies explores more problem-solving strategies and enhances LLM reasoning efficiency, especially on complex problems.

Findings

Diverse prompting methods explore distinct search spaces.

Combining methods increases maximum search space.

Fewer runs needed for high performance on difficult questions.

Abstract

Large Language Models (LLMs) have exhibited remarkable capabilities in many complex tasks including mathematical reasoning. However, traditional approaches heavily rely on ensuring self-consistency within single prompting method, which limits the exploration of diverse problem-solving strategies. This study addresses these limitations by performing an experimental analysis of distinct prompting methods within the domain of mathematical reasoning. Our findings demonstrate that each method explores a distinct search space, and this differentiation becomes more evident with increasing problem complexity. To leverage this phenomenon, we applied efficient sampling process that uniformly combines samples from these diverse methods, which not only expands the maximum search space but achieves higher performance with fewer runs compared to single methods. Especially, within the subset of difficult questions of MATH dataset named MATH-hard, The maximum search space was achieved while utilizing approximately 43% fewer runs than single methods on average. These findings highlight the importance of integrating diverse problem-solving strategies to enhance the reasoning abilities of LLMs.