BoostStep: Boosting mathematical capability of Large Language Models via improved single-step reasoning

• URL: http://arxiv.org/abs/2501.03226v3
• Date: Mon, 17 Feb 2025 06:27:16 GMT
• Title: BoostStep: Boosting mathematical capability of Large Language Models via improved single-step reasoning
• Authors: Beichen Zhang, Yuhong Liu, Xiaoyi Dong, Yuhang Zang, Pan Zhang, Haodong Duan, Yuhang Cao, Dahua Lin, Jiaqi Wang,
• Abstract summary: BoostStep is a method that enhances reasoning accuracy through step-aligned ICL examples. It integrates seamlessly with chain-of-thought (CoT) and tree search algorithms. It improves DeepSeek-R1-671B's performance on AIME by 2.2%, leveraging simple examples only from the MATH dataset.
• Score: 83.03531832811386
• License:
• Abstract: Large language models (LLMs) have demonstrated impressive ability in solving complex mathematical problems with multi-step reasoning and can be further enhanced with well-designed in-context learning (ICL) examples. However, this potential is often constrained by two major challenges in ICL: granularity mismatch and irrelevant information. We observe that while LLMs excel at decomposing mathematical problems, they often struggle with reasoning errors in fine-grained steps. Moreover, ICL examples retrieved at the question level may omit critical steps or even mislead the model with irrelevant details. To address this issue, we propose BoostStep, a method that enhances reasoning accuracy through step-aligned ICL, a novel mechanism that carefully aligns retrieved reference steps with the corresponding reasoning steps. Additionally, BoostStep incorporates an effective "first-try" strategy to deliver exemplars highly relevant to the current state of reasoning. BoostStep is a flexible and powerful method that integrates seamlessly with chain-of-thought (CoT) and tree search algorithms, refining both candidate selection and decision-making. Empirical results show that BoostStep improves GPT-4o's CoT performance by 4.6% across mathematical benchmarks, significantly surpassing traditional few-shot learning's 1.2%. Moreover, it can achieve an additional 7.5\% gain combined with tree search. Surprisingly, it enhances state-of-the-art LLMs to solve challenging math problems using simpler examples. It improves DeepSeek-R1-671B's performance on AIME by 2.2%, leveraging simple examples only from the MATH dataset.

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