通过多样化代码风格提升数学大模型推理能力
CoinMath: Harnessing the Power of Coding Instruction for Math LLMs
- 用简洁注释、描述性命名和硬编码解法增强代码型推理
- 新方法在数学基准上超越SOTA模型MAmmoTH
- 适合想提升数学推理的LLM研究者和开发者
大型语言模型在解决数学问题上表现强劲，其中基于代码的解题方案尤为有效。然而，如何利用编程指令数据提升数学推理能力仍不明确。本研究探讨三个关键问题：(1) 不同数学代码推理风格对LLM学习效果的影响；(2) 通用领域编程指令能否提升性能；(3) 训练中融合文本与代码推理是否增强数学推理能力。结果表明，包含简洁注释、描述性命名和硬编码解法的代码型推理有益，而通用编程指令和文本推理的提升有限。基于此，提出CoinMath策略，通过多样化代码风格生成多种代码型推理。实验显示，CoinMath显著优于其基线模型MAmmoTH，该模型为当前最优数学大模型之一。
原文摘要 · Abstract (English)
Large Language Models (LLMs) have shown strong performance in solving mathematical problems, with code-based solutions proving particularly effective. However, the best practice to leverage coding instruction data to enhance mathematical reasoning remains underexplored. This study investigates three key questions: (1) How do different coding styles of mathematical code-based rationales impact LLMs' learning performance? (2) Can general-domain coding instructions improve performance? (3) How does integrating textual rationales with code-based ones during training enhance mathematical reasoning abilities? Our findings reveal that code-based rationales with concise comments, descriptive naming, and hardcoded solutions are beneficial, while improvements from general-domain coding instructions and textual rationales are relatively minor. Based on these insights, we propose CoinMath, a learning strategy designed to enhance mathematical reasoning by diversifying the coding styles of code-based rationales. CoinMath generates a variety of code-based rationales incorporating concise comments, descriptive naming conventions, and hardcoded solutions. Experimental results demonstrate that CoinMath significantly outperforms its baseline model, MAmmoTH, one of the SOTA math LLMs.
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