English(EN) Dynamics of Gradient Descent with Large Step Size Near a Manifold of Flat Minima

梯度下降理论扩展至复杂最小值和向量输出

作者 PulseAugur 编辑部 · [2 个来源] · 2026-07-09 11:58

本文将大步长梯度下降（GD）的理论扩展到更复杂的场景。它解决了具有向量值输出的过参数化最小二乘问题，并分析了平坦最小值流形的邻域，这对矩阵分解等应用至关重要。该研究推广了现有的范式和收敛定理，并引入了一种求解奇异偏微分方程的新方法。 AI

影响推进了对训练复杂AI模型至关重要的优化算法的理论理解。

排序理由该集群包含一篇详细介绍梯度下降理论进展的学术论文。

AI 生成摘要 · Google Gemini · 来自 2 个来源。我们如何撰写摘要 →

报道来源 [2]

arXiv cs.LG TIER_1 English(EN) · Lachlan Ewen MacDonald, Ren\'e Vidal · 2026-07-10 04:00

Dynamics of Gradient Descent with Large Step Size Near a Manifold of Flat Minima

arXiv:2607.08380v1 Announce Type: new Abstract: An important quantity in the theory of gradient descent (GD) is the \emph{sharpness}, defined as the largest eigenvalue of the objective Hessian. Classical analyses typically require the step size to be uniformly smaller than twice …
arXiv cs.LG TIER_1 English(EN) · René Vidal · 2026-07-09 11:58

Dynamics of Gradient Descent with Large Step Size Near a Manifold of Flat Minima

An important quantity in the theory of gradient descent (GD) is the \emph{sharpness}, defined as the largest eigenvalue of the objective Hessian. Classical analyses typically require the step size to be uniformly smaller than twice the reciprocal of the sharpness, but this condit…