Turning 2,118 university math textbooks into 380,292 proof records with chapter order and dependency links intact moved a base model's mean score from 29.2 to 45.8 percent
AspireAI community · arXiv
Most mathematical supervision for language models is flattened into isolated problem-solution pairs, discarding the curricular organization and evidential structure of the original books. TOME-Math converts 2,118 university-level mathematics textbooks into 380,292 structured proof-supervision records that preserve chapter order, proposition-to-proof links, dependency references and source provenance, split into 205,861 proof QA pairs and 174,431 gap QA pairs across 29 subject categories. Fine-tuning a Qwen3-30B-A3B base checkpoint on it moved the unweighted mean across six held-out and public evaluations from 29.17 to 45.83 percent, a 16.66 point gain, with the best result on five of the six benchmarks and second on AIME 2026. The comparison is the interesting part: the three public instruction-data baselines scored 29.13, 34.64 and 41.10 on the same mean, so corpus size alone does not explain the ranking, and the 364,631-example training split is smaller than OpenMathInstruct-1's 1.82 million. The corpus is stated as released.
Read the story and explore more from the AspireAI community.
Two sparse-autoencoder analyses have resisted scaling: matching semantically similar features across layers, and compressing large feature circuits into interpretable supernodes. This paper argues both are the same underlying problem, estimating semantic distances between SAE features that sit on different activation manifolds. Its representation treats each feature not as a single decoder vector but as an activation-weighted distribution over the hidden states expressing it, projects those distributions into a shared reference space, and compares them with Wasserstein distance. The representation is proved invariant to activation rescaling and stable under perturbation, and recovers true matches under finite-sample margin conditions. Empirically it outperformed decoder-vector and LLM-based baselines and captured subtle functional distinctions between related features, and it compressed large feature circuits into interpretable supernodes automatically. The limitation is that this is interpretability tooling: the paper demonstrates better feature matching and circuit compression, not that downstream interpretability claims become more accurate.