גבול צבירה: חוקים חדשים להגברת ריצה של רגרסיה לוגיסטית

תקציר מקורי באנגליתarXiv:2610.01459v1 Announce Type: new Abstract: We study logistic regression on linearly separable data under gradient descent with a large constant stepsize $\eta$. 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 $\Theta(1)$ bound in dimension $d=2$ as $\eta \to \infty$ and conjectures a bound independent of $\eta$ 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 $\gamma$, the worst-case transition time is $$\Theta\!\left((\log\eta)^{\min\{n-2,d-2\}}\right)$$ uniformly over $d\geq2$. The key challenge in establishing a tigh