Review-Period Phase Diagram for Frozen Updates

Integrate this at a neural component whose decision is expensive or noisy: an Adam learning-rate controller, MoE routing logits, RL exploration temperature, target-network parameters, or a learned augmentation policy. Choose an integer review period K. At step t, recompute the control u only when t modulo K equals zero, then reuse u for the next K minibatches. For each candidate K, initialize identical weights and random seeds. At every step, if t modulo K equals zero, compute u=pi(s_t); then apply the update s_(t+1)=F(s_t,u,xi_t). Record a smoothed validation cost J(K) at a fixed optimizer-step budget and at a fixed wall-clock budget. Test K in {1,2,4,8,16,32,64} with at least five seeds. The paper supplies the review-period sensitivity mechanism and derivative or curvature interpretation; J(K), confidence intervals, and the transition location must be estimated empirically. First experiment: train a small Transformer on WikiText-2, comparing per-step against every-K-step recomputation of learning-rate and gradient-clipping controls, with ordinary Adam as baseline. The quantitative prediction is a small-K nonmonotonicity or curvature change: the estimated J'(K) should change sign or estimated J''(K) should change sign across the scan. This transition should persist across seeds and become sharper at larger batch sizes, where stochastic smoothing is weaker. Select K at the first stable curvature regime and test it on a second model.