Weight-norm Criticality: A Mechanism for Loss Spikes Induced by the Normalization and Weight Decay
Most explanations of training instability focus on \emph{learning-rate criticality}, typically characterized by the Edge of Stability, beyond which optimization becomes unstable. We argue that, in practical deep neural network training, there is an additional and often overlooked \emph{weight-norm criticality}. This criticality is induced by the interaction between normalization (which introduces scale-invariant components) and weight decay (which persistently shrinks parameter norms). As the weight decay coefficient increases, the norms of scale-invariant weights are progressively driven toward zero. Meanwhile, the sharpness of the loss landscape increases rapidly, destabilizing the opti...
| Authors | Xiaolong Li, Zhangchen Zhou, Zhi-Qin John Xu |
|---|---|
| Primary category | cs.LG |
| Published | 23 July 2026 |
| Last updated at source | 23 July 2026 |
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