Scale Weight Decay and Train Better
The discovery of scaling laws has motivated training neural networks on ever increasing quantities of data. This is typically done with a constant decoupled weight decay which causes the network weights to shrink steadily over the course of training. Taking inspiration from the Robbins--Monro conditions, we propose to scale weight decay by the fraction of the peak learning rate $η/η_{\max}$. We prove that this scaled weight decay preserves the asymptotic stationarity guarantees of the corresponding unregularized methods for both stochastic gradient descent and the non-Euclidean spectral optimizer Muon, thereby avoiding the additional asymptotic bias introduced by constant decoupled weight...
| Authors | Anuj Apte |
|---|---|
| Primary category | cs.LG |
| Published | 26 July 2026 |
| Last updated at source | 26 July 2026 |
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