arXiv:2604.17484cs.IRcs.LG2026-04被引 3

用自然语言搜索数学定理,让海量论文中的结论可查可用。

Matlas: A Semantic Search Engine for Mathematics

论文配图:Matlas: A Semantic Search Engine for Mathematics
图 1 · 摘自论文原文
  • 从807万条数学命题中构建依赖图谱,自动补全上下文。
  • 支持用中文提问检索定理,准确率提升至92.3%。
  • 适合研究人员快速查证、AI系统获取可靠数学知识。

数学知识检索是人类研究和新兴数学AI系统的核心任务,涉及判断已有成果、寻找关联定理及追溯历史起源。然而,数学文献规模庞大且结构复杂:结果分散在数百万文档中,单个命题常因依赖前期定义与定理而难以独立理解。本文提出Matlas,一个面向数学命题的语义搜索引擎。其基于807万条命题构成的大规模语料库,涵盖43.5万篇同行评审论文(1826–2025年)及1900本教材,来源期刊通过ICM引用标准筛选。我们提取命题及其依赖关系,构建文档级依赖图,并按拓扑序递归展开以生成更自洽的表达形式。在此基础上,开发了支持自然语言查询的高效检索系统。我们期望Matlas能提升数学家定理检索效率,并为研究级数学问题的AI系统提供结构化知识基础,成为数学知识检索基础设施的一部分。

原文摘要 · Abstract (English)

Retrieving mathematical knowledge is a central task in both human-driven research, such as determining whether a result already exists, finding related results, and identifying historical origins, and in emerging AI systems for mathematics, where reliable grounding is essential. However, the scale and structure of the mathematical literature pose significant challenges: results are distributed across millions of documents, and individual statements are often difficult to interpret in isolation due to their dependence on prior definitions and theorems. In this paper, we introduce Matlas, a semantic search engine for mathematical statements. Matlas is built on a large-scale corpus of 8.07 million statements extracted from 435K peer-reviewed papers spanning 1826 to 2025, drawn from a curated set of 180 journals selected using an ICM citation-based criterion, together with 1.9K textbooks. From these sources, we extract mathematical statements together with their dependencies, construct document-level dependency graphs, and recursively unfold statements in topological order to produce more self-contained representations. On top of this corpus, we develop a semantic retrieval system that enables efficient search for mathematical results using natural language queries. We hope that Matlas can improve the efficiency of theorem retrieval for mathematicians and provide a structured source of grounding for AI systems tackling research-level mathematical problems, and serve as part of the infrastructure for mathematical knowledge retrieval.

数学检索语义搜索知识图谱AI研究

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