Cutting-edge large language models (LLMs) demonstrate promising performance in solving complex math problems with a divide-and-conquer pipeline and the assistance of in-context learning (ICL) examples. However, their potential for improvement is limited by two critical problems within their ICL examples: granularity-mismatch and the ensuing negative-effect noise problem. Specifically, the LLMs are capable of the dividing process yet mostly failed by inaccurate reasoning within a few conquer steps, while the ICL examples retrieved in question-grained sometimes lack relevant steps for a specific challenging reasoning step. Further, this disconnect may hinder the correct reasoning due to its irrelevance. To this end, we focus on improving the reasoning quality within each step and present BoostStep. BoostStep aligns the granularity between the retrieving and reasoning on step grained, and provides highly related ICL examples for each reasoning step with a novel `first-try' strategy. BoostStep provides more relevant examples than the coarse question-grained strategy, enhancing the model reasoning quality within each step steadily. BoostStep is a general and robust reasoning-enhancing method that not only improves standalone reasoning performance but also integrates seamlessly with Monte Carlo Tree Search methods (MCTS) to refine both candidate generation and decision-making. Quantitatively, it improves GPT-4o and Qwen2.5-Math-72B by 3.6\% and 2.0\% respectively on various mathematical benchmarks, and 7.5\% gain combined with MCTS.

本研究解决了大型语言模型（LLMs）在处理复杂数学问题时的推理精度不足和示例相关性不匹配的问题。提出的BoostStep方法通过对推理步骤进行细致对齐，提供更相关的学习示例，从而显著提升了模型在各个推理步骤中的表现。研究发现，BoostStep不仅独立提高了推理性能，还与蒙特卡洛树搜索（MCTS）有机结合，进一步优化了候选生成和决策制定。

BoostStep：通过改进单步推理提升大型语言模型的数学能力