标题： 大规模语言模型在数学分析中的应用 显示英文标题

标题： Large Language Models for Mathematical Analysis

摘要： 数学问题求解是人工智能（AI）领域的一个关键方向，也是评估大型语言模型（LLMs）能力的重要基准。尽管已有大量研究聚焦于数学问题求解，但大多数现有工作和数据集主要集中于计算任务，而在需要严谨证明和形式化推理的数学分析等领域存在空白。 我们开发了 DEMI-MathAnalysis 数据集，该数据集包含来自数学分析主题的基于证明的问题，例如数列与极限、无穷级数以及凸函数。 此外，我们还设计了一个指导框架，以严格提升 LLMs 解决这些问题的能力。 通过在该数据集上微调 LLMs 并采用我们的框架，我们观察到它们生成逻辑清晰、完整且优雅的证明的能力显著提高。 这项工作解决了数学推理中的关键空白，并推动了能够处理形式化数学语言的可信 AI 的发展。 代码可在 LLMs for Mathematical Analysis 公开获取。 显示英文摘要

摘要： 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.