arXiv cs.AI· Youqing Fang, Zhouqi Hua, Yinhao Tang, Yuzhe Gu, Lingkai Kong, Bin Liu, Weiming Zhang, Kai Chen, Yanan Sun, Wenwei Zhang·· 5 小时前AI 评分46
TOME-Math：用结构化教材规模化数学证明监督
Scaling Mathematical Proof Supervision from Structured Textbooks
AI 导读
研究者推出 TOME-Math 语料库，将 2,118 本大学数学教材转换为约 380K 条结构化证明监督数据，保留章节顺序、命题-证明链接与依赖引用。基于这些结构信号开展跨学科课程学习与数据规模扩展实验，全量微调使模型在留出评测与公开基准上的未加权平均分较基座模型提升 16.7 个百分点，超过三个公开指令数据基线的合计表现。语料库将开源发布。
正文 · 原文
Abstract:Mathematical supervision for language models is typically flattened into isolated problem-solution pairs, discarding the curricular organization and evidential structure of the original sources. We introduce TOME-Math (Textbook-Oriented Mathematical Evidence), a large-scale corpus that converts 2,118 textbooks spanning the core areas of university-level mathematics subjects into approximately 380K structured proof-supervision records while preserving chapter order, proposition-proof links, dependency references, and source provenance. Leveraging these structural signals, we explore curriculum learning across multiple mathematical subjects and characterize scaling patterns with supervision volume and source breadth. At full scale, fine-tuning on TOME-Math raises the unweighted mean score across our held-out evaluations and established public benchmarks by 16.7 percentage points over the base model, while exceeding all three public instruction-data baselines evaluated in aggregate. Our findings highlight structured textbooks as both a scalable source of mathematical supervision and an empirical framework for studying the impact of data organization on mathematical reasoning. We will release the corpus to facilitate further research on structured mathematical supervision.
| Comments: | 35 pages, 18 figures, 14 tables |
| Subjects: | Computation and Language (cs.CL); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2610.40394 [cs.CL] |
| (or arXiv:2610.40394v1 [cs.CL] for this version) | |
| https://doi.org/10.48550/arXiv.2610.40394 arXiv-issued DOI via DataCite |
Submission history
From: Youqing Fang [view email]
[v1]
Thu, 29 Oct 2026 16:32:59 UTC (28,078 KB)
来源：arXiv cs.AI · arxiv.org