SGD at the Edge of Stability: Stochastic Stabilization with Large Learning Rates
Modern deep learning has been shown to operate at the edge of stability, routinely using learning rates far larger than those justified by classical optimization theory. Most prior analyses of the edge of stability phenomenon focus on deterministic gradient descent, leaving the stochastic setting largely unexplored. In this work, we provide sharp convergence guarantees for Stochastic Gradient Descent (SGD) applied to the multiclass cross-entropy loss, for both linear classifiers and two-layer neural networks. We show that the stochasticity of SGD may cause the dynamics to alternate between an edge-of-stability regime that is dominated by curvature-driven oscillations, and a stable regime ...
| Authors | Konstantinos Emmanouilidis, Lachlan MacDonald, Salma Tarmoun et al. |
|---|---|
| Primary category | stat.ML |
| Published | 29 June 2026 |
| Last updated at source | 29 June 2026 |
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