Reinforcement learning with a textbook-navigation interface taught a 35B model to study on its own, lifting proof accuracy from 51.5 to 79.5 percent
AspireAI community · arXiv
Most retrieval-augmented systems fetch passages and aggregate them; the harder skill is reading long-form material, understanding the principles in it, and applying them to construct a proof. This paper formulates that as self-learning and rewards it with reinforcement learning over a BookNavigator interface that lets a model navigate textbook exposition rather than receive a preassembled context. Intern-S2-Preview-35B's overall proof accuracy rose from 51.5% to 79.5%, outperforming RL-trained textbook-free and fixed-retrieval baselines. The gains carried to other long-context benchmarks, adding 1.7 points on BrowseComp-Plus and 2.3 on CL-bench. The honest limit is scope: the task is textbook-based mathematical problem solving with reference solutions withheld, so the behaviour is not yet shown transferring to arbitrary domains.
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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.