Edge Flow: A Tractable and Predictive Continuous-Time Model for Gradient Descent at the Edge of Stability
Gradient descent in deep learning may operate at the edge of stability (EoS), a regime in which the largest eigenvalue of the loss Hessian hovers near the stability threshold $2/η$, where $η$ is the learning rate. Classical analysis tools such as gradient flow and the descent lemma do not apply here, motivating the search for a continuous-time model valid at EoS. We propose Edge Flow, a system of three coupled ordinary differential equations that provides a tractable, faithful, and predictive model of gradient descent dynamics at EoS. Edge Flow decomposes the dynamics into a center, an oscillation direction, and an oscillation magnitude. The center follows a modified gradient flow on a sy...
| Authors | Pierre Marion |
|---|---|
| Primary category | cs.LG |
| Published | 16 June 2026 |
| Last updated at source | 16 June 2026 |
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