Multifractal Noise-Stability Monitor

1. Integration point: attach the monitor during training and evaluate it every K optimizer steps on a fixed probe minibatch. Run two independent stochastic forward passes per example using activation noise, dropout masks, stochastic attention edges, or augmentation randomness. Evaluate several effective sizes N, such as 2, 4, 6, and 8 layers, or several recurrent unroll lengths. 2. Pseudocode: for each N and probe example, compute two noisy outputs, form R_N, accumulate M_q for q in {0.5, 1, 2, 3}, regress log M_q on log N to estimate tau(q), compute C = tau(2) - 2 tau(1), smooth C with an exponential moving average, and update g and eta with the clipped exponential controller. 3. The moment-scaling diagnostic is transferred from the paper; response moments, scaling exponents, baseline C_0, and controller gains alpha and beta are estimated or tuned empirically. 4. First experiment: use a 6-layer residual MLP on CIFAR-10 with Gaussian activation noise and compare fixed noise, validation-loss scheduling, and the multifractal controller. Record gradient norm tails, divergence frequency, calibration, and test accuracy. The prediction is that increasing noise or depth raises C before exploding gradients or validation loss, and that controller interventions reduce C toward C_0 while suppressing extreme gradient events. Falsify the mechanism if C has no reproducible lead over gradient variance or if its instability threshold varies by more than 30 percent across seeds.