Same Loss, Same Noise, Opposite Schedules: Noise Structure and Optimizer Normalization Jointly Determine Whether Learning-Rate Cooldown Helps
The cooldown phase of a warmup-stable-decay (WSD) learning-rate schedule, now a default in large-model pretraining, lowers the final training loss in some settings and does nothing in others. We give a provable account of which case obtains, and it turns on two properties together: the structure of the gradient noise and whether the optimizer normalizes its update. On a strongly convex objective with multiplicative (gradient-proportional) noise, stochastic gradient descent contracts geometrically at a constant learning rate, so cooldown has nothing to improve. Under the same objective and noise, sign-based and normalized methods, the standard surrogates for adaptive optimizers, settle on ...
| Authors | Subham Singh, Ashutosh Mishra, Subha Raut |
|---|---|
| Primary category | cs.LG |
| Published | 14 July 2026 |
| Last updated at source | 14 July 2026 |
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