Latent-Outbreak Learning-Rate Controller

1. Integration point: place the controller around SGD, Adam, or Lion. Maintain scalar states x and y per training run, layer, or parameter block. Estimate latent progress x from the fraction of examples whose prediction margin improves consistently over a window, or from the fraction of parameter blocks whose gradient cosine similarity with the previous step exceeds a threshold. Estimate active y from the fraction of blocks receiving high-confidence, high-magnitude updates; initialize y to a small positive value. Use y to interpolate between conservative and aggressive learning rates, or to control hard-example sampling. 2. Pseudocode: initialize x=x0 and y=y0. At each minibatch compute the usual gradient and a soft progress score p. Update x <- clip(x+h*alpha*(1-x)*y,0,1), optionally using an EMA of p to calibrate x. Update y <- clip(y+h*(beta*(x-y)*y-gamma*y),0,x). Set eta <- eta_min+y*(eta_max-eta_min), then apply the optimizer step with eta. Cap y if gradient norm, loss, or validation instability exceeds a safety limit. 3. Computed from the mechanism: the threshold x_c=gamma/beta and predicted growth rate beta*x-gamma. Estimated empirically: alpha, beta, and gamma from pilot runs by least-squares fitting finite differences of x and y; use transformed states if saturation causes bias. 4. First cheap experiment: train a 2-layer MLP and a small Transformer on MNIST or CIFAR-10 with fixed Adam, cosine decay, and this controller at matched average learning rate. Sweep beta/gamma so x_c is 0.3, 0.5, and 0.7. The predicted signature is a long low-y regime while x<x_c, followed by a sharp increase in log y with slope beta*x-gamma after crossing. Measured onset should occur within 20% of x_c=gamma/beta. Compare divergence rate, time-to-target-loss, early loss spikes, and final accuracy against Adam and cosine decay.