Mean--Fluctuation Dynamics at the Edge of Stability
Quick summary
arXiv:2606.05326v2 Announce Type: replace-cross Abstract: We study the dynamics of gradient descent in the Edge of Stability regime, where the learning rate is large enough to induce persistent oscillations in the trajectory, which has been linked to better generalization performance. We introduce the mean--fluctuation dynamics, a tractable continuous-time model coupling the window-averaged trajectory to its fluctuation covariance. Among our contributions, we rigorously derive this model from gradient descent in a sharp-valley framework, characterize its stationary states and their linear stab
Key takeaways
- arXiv:2606.05326v2 Announce Type: replace-cross Abstract: We study the dynamics of gradient descent in the Edge of Stability regime, where the learning rate is large enough to induce persistent oscillations in the trajectory, which has been linked to better generalization performance.
- We introduce the mean--fluctuation dynamics, a tractable continuous-time model coupling the window-averaged trajectory to its fluctuation covariance.
- Among our contributions, we rigorously derive this model from gradient descent in a sharp-valley framework, characterize its stationary states and their linear stab
Why it matters
“Mean--Fluctuation Dynamics at the Edge of Stability” highlights the need for repeatable measurement rather than a single impressive demonstration. Independent validation across datasets and clearly stated limitations determine whether a result can guide product decisions.
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