English(EN) Distribution of hitting times for dissipative random dynamical systems on $\mathbb{R}^d$, with application to stochastic gradient descent

新理论分析深度学习优化收敛性

作者 PulseAugur 编辑部 · [1 个来源] · 2026-09-28 04:00

研究人员开发了一个新的理论框架，用于分析深度学习中使用的优化算法的收敛特性。这种方法借鉴了遍历理论，研究了随机梯度下降等算法接近最小化器的预期时间。研究结果表明，在包括高斯噪声和亚指数噪声在内的假设下，该命中时间围绕其平均值呈指数分布，平均值由目标函数的平稳测度决定。 AI

影响为深度学习优化提供了理论理解，可能导致更高效的训练算法。

排序理由详细介绍深度学习优化算法理论进展的学术论文。[lever_c_demoted from research: ic=1 ai=1.0]

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arXiv stat.ML TIER_1 English(EN) · St\'ephane Galatolo, St\'ephane Chr\'etien · 2026-09-28 04:00

耗散随机动力学系统在$\mathbb{R}^d$上的击中时间分布及其在随机梯度下降中的应用

arXiv:2609.30274v1 Announce Type: new Abstract: Machine Learning and more specifically Deep Learning involves solving large scale nonconvex optimization problems. Several algorithms have been proposed in the literature, that seem to achieve satisfactory practical efficiency for d…