English(EN) Tight Transition Time Bounds for Separable Logistic Regression at the Edge of Stability

逻辑回归过渡时间界限被证伪

作者 PulseAugur 编辑部 · [1 个来源] · 2026-10-02 04:00

研究人员已经证伪了关于在具有大常数步长的梯度下降下，可分离逻辑回归的过渡时间界限的猜想。此前，人们认为在维度大于或等于二的情况下，过渡时间将独立于步长。然而，本文证明了对于固定的样本量和足够小的裕度，过渡时间取决于步长的大小，具体来说，其缩放比例为 $(\log\eta)^{\min\{n-2,d-2\}}$。这一发现是通过控制对梯度影响最大的样本变化并构建匹配的困难实例来确立的。 AI

影响这项研究完善了对梯度下降动力学的理论理解，可能影响优化算法的设计。

排序理由该条目是一篇详细介绍机器学习理论发现的学术论文。[lever_c_demoted from research: ic=1 ai=1.0]

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报道来源 [1]

arXiv stat.ML TIER_1 English(EN) · Haodong Wen, Kaiyue Wen, Jiaye Teng · 2026-10-02 04:00

稳定边缘下可分离逻辑回归的紧过渡时间界限

arXiv:2610.01459v1 Announce Type: cross 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 …

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稳定边缘下可分离逻辑回归的紧过渡时间界限

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