构建数学分析证明数据集，提升大模型严谨推理能力
Large Language Models for Mathematical Analysis
- 创建首个聚焦数学分析的证明题数据集DEMI-MathAnalysis
- 微调后模型生成逻辑完整且优雅的数学证明
- 适合研究形式化推理与可信AI的学者参考
数学问题求解是人工智能的重要领域，也是评估大语言模型能力的关键基准。尽管已有大量研究聚焦于数学求解，但现有工作和数据集多集中于计算任务，忽视了需要严格证明与形式化推理的数学分析领域。为此，我们构建了DEMI-MathAnalysis数据集，包含数列与极限、无穷级数、凸函数等数学分析主题的证明题。同时设计了一套引导框架，系统性提升大模型解决此类问题的能力。通过在该数据集上微调模型并应用框架，显著增强了模型生成逻辑严密、结构完整且表达优美的数学证明的能力。本工作填补了数学推理中的关键空白，推动可信AI处理形式化数学语言的发展。代码已公开于LLMs for Mathematical Analysis。
原文摘要 · Abstract (English)
Mathematical problem-solving is a key field in artificial intelligence (AI) and a critical benchmark for evaluating the capabilities of large language models (LLMs). While extensive research has focused on mathematical problem-solving, most existing work and datasets concentrate on computational tasks, leaving gaps in areas like mathematical analysis, which demands rigorous proofs and formal reasoning. We developed the DEMI-MathAnalysis dataset, comprising proof-based problems from mathematical analysis topics such as Sequences and Limits, Infinite Series, and Convex Functions. We also designed a guiding framework to rigorously enhance LLMs' ability to solve these problems. Through fine-tuning LLMs on this dataset and employing our framework, we observed significant improvements in their capability to generate logical, complete, and elegant proofs. This work addresses critical gaps in mathematical reasoning and contributes to advancing trustworthy AI capable of handling formalized mathematical language. The code is publicly accessible at LLMs for Mathematical Analysis.
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