When Updating Stops Being Learning: Rethinking LLM Self-Evolution via learnable information gain

Self-evolution lets large language models (LLMs) improve iteratively using their own generated data, but often suffers from self-evolution degeneration: performance improves, plateaus, then declines. Existing methods address this issue at the component level, targeting either the Questioner or the Solver, and overlook that self-evolution is a tightly coupled system. We propose a holistic framework based on learnable information gain, which measures how much novel, parameterizable information a round provides relative to the previous round. Theoretically, this gain equals the Kullback–Leibler divergence between the two rounds' data distributions plus their entropy change. Practically, it is estimated by fitting a small language model to the previous round and scoring new data via negative log-likelihood. Based on this diagnostic, we propose ATRI (Adaptive Training Regulation via Information-gain), which reweights samples within a round and halts training across rounds when information gain remains low. Experiments on popular datasets demonstrate the superiority of our proposal.