arXiv 2407.101672024-10-10cs.CLcs.AI

大型语言模型的关键点驱动数学推理蒸馏

Key-Point-Driven Mathematical Reasoning Distillation of Large Language Model

Institute of Information Engineering, Chinese Academy of Sciences（中国科学院信息工程研究所）；School of Cyber Security, University of Chinese Academy of Sciences（中国科学院大学网络空间安全学院）；School of Artificial Intelligence, Beijing Normal University（北京师范大学人工智能学院）

Xunyu Zhu, Jian Li, Can Ma, Weiping Wang

备注：: Major Updates:1.fix faults in the error analysis, 2. improve our method, 3. use ChatGPT as teacher LLMs to ensure fairness in performance comparisons

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AI总结：

为解决小型语言模型在数学推理中的语义理解错误，提出关键点驱动的数学推理蒸馏方法KPDD，通过三阶段解题流程显著提升推理性能并达到SOTA。

摘要：

大型语言模型（LLMs）凭借其庞大的参数量和在海量数据集上的训练，在数学推理任务中展现出了卓越的能力。尽管具备这些能力，LLMs的部署却因其巨大的计算需求而受到阻碍。将LLM的数学推理能力蒸馏到小型语言模型（SLMs）中已成为应对这一挑战的解决方案，尽管这些较小的模型在计算和语义理解方面经常出现错误。先前的工作提出了思维程序蒸馏（PoTD）来避免计算错误。为了进一步解决语义理解错误，我们提出了关键点驱动的数学推理蒸馏（KPDD）。KPDD通过将解题过程分解为三个阶段来增强SLMs的推理性能：核心问题提取、解题信息提取和逐步解答。该方法进一步分为生成思维链（Chain-of-Thought）原理的KPDD-CoT，以及创建思维程序（Program-of-Thought）原理的KPDD-PoT。实验结果表明，KPDD-CoT显著提升了推理能力，而KPDD-PoT在数学推理任务中达到了最先进的性能。我们的方法有效缓解了理解错误，推动了高效且强大的SLMs的部署。

英文摘要：

Large Language Models (LLMs) have demonstrated exceptional proficiency in mathematical reasoning tasks due to their extensive parameter counts and training on vast datasets. Despite these capabilities, deploying LLMs is hindered by their computational demands. Distilling LLM mathematical reasoning into Smaller Language Models (SLMs) has emerged as a solution to this challenge, although these smaller models often suffer from errors in calculation and semantic understanding. Prior work has proposed Program-of-Thought Distillation (PoTD) to avoid calculation error. To further address semantic understanding errors, we propose Key-Point-Driven Mathematical Reasoning Distillation (KPDD). KPDD enhances the reasoning performance of SLMs by breaking down the problem-solving process into three stages: Core Question Extraction, Problem-Solving Information Extraction, and Step-by-Step Solution. This method is further divided into KPDD-CoT, which generates Chain-of-Thought rationales, and KPDD-PoT, which creates Program-of-Thought rationales. The experiment results show that KPDD-CoT significantly improves reasoning abilities, while KPDD-PoT achieves state-of-the-art performance in mathematical reasoning tasks. Our approach effectively mitigates misunderstanding errors, advancing the deployment of efficient and capable SLMs.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。