TheoremGraph:连接非形式化与形式化数学的统一语句级依赖图
阅读原文· arxiv.orgTheoremGraph 是覆盖非形式化与形式化数学的语句级依赖图。非形式化侧从 arXiv 解析 1170 万定理环境,提取 1830 万条有向依赖;形式化侧 LeanGraph 从 25 个 Lean 项目提取 388,105 声明节点和 1130 万类型化边。通过嵌入自然语言 slogan 将两类图映射到同一语义空间,LLM judge 在余弦阈值 ≥0.8 时确认 47,952 个匹配,阈值 ≥0.9 时接受率升至 87%。形式化概念检索中,name-and-signature 加图扩展的 Recall@10 达 0.775,接近 LeanSearch v2 的 0.780(无需 LM 重排序)。相关数据集、提取器、HTTP API 及 MCP 接口已开源。
Mathematical knowledge is organized around statements and their dependencies, but this structure is exposed unevenly: informal papers cite mostly at the document level, while formal libraries record fine-grained dependencies over a much smaller body of mathematics. We introduce TheoremGraph, a unified statement-level dependency graph spanning both informal and formal mathematics. On the informal side, we parse 11.7M theorem-like environments from mathematics arXiv and recover 18.3M candidate directed dependencies, each labeled by the extractor that proposed it so downstream users can trade coverage for precision. On the formal side, we release LeanGraph, a Lean 4 elaborator-level extractor producing 388,105 declaration nodes and 11.3M typed edges across 25 Lean projects. We bridge the two graphs by embedding generated natural-language slogans into a shared semantic space, linking related statements across papers and across the informal/formal divide; an LLM judge affirms 47,952 such matches above a 0.8 cosine floor, with the judge-acceptance rate rising from 48% across the floor to 87% in the >=0.9 tier. On formal concept retrieval, our name-and-signature representation with graph expansion comes within 0.5pp of LeanSearch v2's reranked Recall@10 (0.775 vs. 0.780) without an LM reranker. We release the dataset, extractors, HTTP API, and MCP interface as infrastructure for mathematical search, attribution, and retrieval-augmented reasoning, available at theoremsearch.com and huggingface.co/datasets/uw-math-ai/theorem-matching.