Closed-Loop Generative Selection: Convergence, Memory, and Noisy Oracles

What the math gives to ML

The paper provides an operational theory for iterative generator–oracle–retraining loops by augmenting the state with the recent training window, making memory-dependent escape probabilities explicit. The most transferable assets are the level-wise decomposition of expected oracle cost, the non-monotone effect of replay-memory depth, and robust repeated-evaluation rules for noisy or heavy-tailed fitness signals. In neural systems, these ideas suggest replacing fixed replay windows and fixed evaluation batches with level-aware memory control and confidence-based sequential evaluation. The resulting experiments can directly measure oracle calls, wall-clock time, convergence per expensive evaluation, and robustness under synthetic reward noise.