Expanding Search Space with Diverse Prompting Agents: An Efficient Sampling Approach for LLM Mathematical Reasoning
This work addresses the problem of limited exploration in LLM reasoning for researchers and practitioners, though it is incremental as it builds on existing prompting methods.
The study tackled the limitation of single prompting methods in LLM mathematical reasoning by showing that diverse prompting agents explore distinct search spaces, and combining them through efficient sampling expanded the search space and improved performance with fewer runs, achieving a 43% reduction in runs on the MATH-hard dataset.
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.