[2604.01951] Learn by Surprise, Commit by Proof

Computer Science > Machine Learning arXiv:2604.01951 (cs) [Submitted on 2 Apr 2026] Title:Learn by Surprise, Commit by Proof Authors:Kang-Sin Choi View a PDF of the paper titled Learn by Surprise, Commit by Proof, by Kang-Sin Choi View PDF HTML (experimental) Abstract:We propose LSCP, a self-gated post-training framework for autonomous knowledge acquisition: learning only what a model does not already know, verified against what it does know, at a strength proportional to conviction, with no external oracle. When a passage produces anomalously high per-token loss, LSCP flags it, generates a Q&A chain that forces the model to articulate its own knowledge and identify gaps, then adjusts AdamW's $\beta_2$ proportionally to conviction depth k (the number of self-verification steps the passage survives) via $\beta_2 = 0.999 \cdot r^k$. The entire learning intensity is governed by a single parameter $r$. Beyond new knowledge, this process sharpens weakly encoded existing knowledge, which is a primary source of hallucination. The framework is self-extinguishing: as the model learns, per-token loss on learned passages decreases toward the surprisal threshold and the system progressively converges to standard AdamW. This models biological memory consolidation: temporary information in the context window is selectively consolidated into parametric weights, the model's long-term memory. Experiments on the reference model (Qwen3-14B) and across six models (8B--32B, four families) show...