Scaling Mathematical Proof Supervision from Structured Textbooks
Youqing Fang, Zhouqi Hua, Yinhao Tang, Yuzhe Gu, Lingkai Kong, Bin Liu, Weiming Zhang, Kai Chen 等 10 位作者
AI 速览：将2,118本大学数学教科书转化为约38万条保留章节顺序与命题-证明结构的证明监督记录，并研究课程学习与规模规律。
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.
Large language models (LLMs) draw on parametric knowledge and retrieval-augmented generation (RAG) to solve knowledge-intensive tasks. Yet problem solving in unfamiliar domains calls for tightly coupled knowledge acquisition and reasoning, beyond factual retrieval and aggregation or learning solely from a preassembled context. We study self-learning -- autonomously retrieving, studying, and applying knowledge from long-form reference materials on the fly. To investigate this capability, we formulate a textbook-based mathematical problem-solving task. LLMs must navigate textbook exposition, learn and apply relevant principles, and construct proofs for exercises, with reference solutions withheld. We introduce a BookNavigator interface to support this human-inspired study process and incentivize self-learning through reinforcement learning (RL) with fine-grained rewards. Experiments show that our method improves performance across in-domain and out-of-domain textbooks and subjects, raising Intern-S2-Preview-35B's overall proof accuracy from 51.5% to 79.5% and outperforming RL-trained textbook-free and fixed-retrieval baselines. These gains extend to complex long-context benchmarks involving different task types, with improvements over the base model of 1.7 and 2.3 percentage points on BrowseComp-Plus and CL-bench, respectively. Together, these findings suggest that RL can foster a domain-agnostic self-learning strategy, highlighting the potential of self-learning from long-form corpora to strengthen broader problem-solving capabilities on complex, long-context tasks.