Physics-Inspired Optimizers beyond the Edge of Stability: Period-Two Orbits and Delayed Instability
Gradient descent with momentum can be viewed as a particle moving with friction in the loss landscape. In deep learning the learning rate is usually large, so training is a discrete dynamical system: in many full-batch experiments the sharpness grows to the optimizer's stability limit, the edge of stability (EoS), and training continues there. Physics-inspired optimizers change this motion; Velocity-Regularized Adam (VRAdam), for example, shrinks the step at high speed. We study kinetic maps, in which the step is the gradient of a kinetic energy of the momentum, and ask what they do beyond the EoS. (i) In a reduced model, a kinetic map creates a symmetric period-two orbit beyond the edge,...
| Authors | Alexander Itin |
|---|---|
| Primary category | nlin.CD |
| Published | 19 October 2026 |
| Last updated at source | 19 October 2026 |
Popularity, last 2 days
0 now. Counts as reported by the source, snapshotted daily by Silytics.
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 22 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.