Tight Transition Time Bounds for Separable Logistic Regression at the Edge of Stability
We study logistic regression on linearly separable data under gradient descent with a large constant stepsize $η$. Such dynamics may exhibit a characteristic Edge of Stability phenomenon, in which the loss initially oscillates before transitioning to a stable phase of monotone decrease. Existing work provides a tight $Θ(1)$ bound in dimension $d=2$ as $η\to \infty$ and conjectures a bound independent of $η$ in arbitrary dimensions $d\geq 2$. In this paper, we disprove this conjecture by showing that, for every fixed sample size $n\geq 2$ and sufficiently small margin $γ$, the worst-case transition time is $$Θ\!\left((\logη)^{\min\{n-2,d-2\}}\right)$$ uniformly over $d\geq2$. The key chall...
| Authors | Haodong Wen, Kaiyue Wen, Jiaye Teng |
|---|---|
| Primary category | cs.LG |
| Published | 1 October 2026 |
| Last updated at source | 1 October 2026 |
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