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.
MEMENTO: Teaching LLMs to Manage Their Own Context
Vasilis Kontonis, Yuchen Zeng, Shivam Garg, Lingjiao Chen, Hao Tang, Ziyan Wang, Ahmed Awadallah, Eric Horvitz 等 10 位作者
AI 速览：通过将推理过程分块并压缩为稠密摘要（memento），让模型仅依赖摘要向前推理，从而降低上下文、KV 缓存与计算开销。
Reasoning models think in long, unstructured streams with no mechanism for compressing or organizing their own intermediate state. We introduce MEMENTO: a method that teaches models to segment reasoning into blocks, compress each block into a memento, i.e., a dense state summary, and reason forward by attending only to mementos, reducing context, KV cache, and compute. To train MEMENTO models, we release OpenMementos, a public dataset of 228K reasoning traces derived from OpenThoughts-v3, segmented and annotated with intermediate summaries. We show that a two-stage SFT recipe on OpenMementos is effective across different model families (Qwen3, Phi-4, Olmo 3) and scales (8B--32B parameters). Trained models maintain strong accuracy on math, science, and coding benchmarks while achieving ${\sim}2.5\times$ peak KV cache reduction. We extend vLLM to support our inference method, achieving ${\sim}1.75\times$ throughput improvement while also enabling us to perform RL and further improve accuracy. Finally, we identify a dual information stream: information from each reasoning block is carried both by the memento text and by the corresponding KV states, which retain implicit information from the original block. Removing this channel drops accuracy by 15\,pp on AIME24.