A Solvable Model of Adaptive Learning Rate Rescaling: Acceleration, Stability & Scaling
A recurring design principle in modern optimizers is to decouple update magnitude from the raw gradient norm, yet its consequences for learning-curve and resource scaling remain unclear. We isolate this mechanism by studying normalized SGD in a random-feature model with power-law teacher and data covariance. Fixed-norm updates induce an effective learning rate that grows as gradients shrink. We derive a dynamical mean-field theory (DMFT) describing the joint dependence of the loss on training time, model width and batch size. Normalization initially accelerates SGD, mapping the power-law exponent $r_{\rm SGD}<1$ to $2r_{\rm SGD}/(1-r_{\rm SGD})$, with exponential convergence at $r_{\rm SG...
| Authors | Itay Lavie, Clarissa Lauditi, Cengiz Pehlevan |
|---|---|
| Primary category | stat.ML |
| Published | 5 October 2026 |
| Last updated at source | 5 October 2026 |
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