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Logistic Regression Transition Time Bounds Disproven

By PulseAugur Editorial · [1 sources] ·

Researchers have disproven a conjecture regarding the transition time bounds for separable logistic regression under gradient descent with large constant step sizes. Previously, it was believed that the transition time would be independent of the step size in dimensions greater than or equal to two. However, this paper demonstrates that for a fixed sample size and a sufficiently small margin, the transition time is dependent on the logarithm of the step size, specifically scaling with $(\log\eta)^{\min\{n-2,d-2\}}$. This finding was established by controlling the changes in the sample that most strongly influences the gradient and constructing matching hard instances. AI

IMPACT This research refines theoretical understanding of gradient descent dynamics, potentially impacting optimization algorithm design.

RANK_REASON The item is an academic paper detailing theoretical findings in machine learning. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

Logistic Regression Transition Time Bounds Disproven

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The item is an academic paper detailing theoretical findings in machine learning. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv stat.ML TIER_1 English(EN) · Haodong Wen, Kaiyue Wen, Jiaye Teng ·

    Tight Transition Time Bounds for Separable Logistic Regression at the Edge of Stability

    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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