English(EN) A Nonlinear Time-Series Theory for Constant-step SGD with Momentum

新理论解释了常数步长带动量的SGD

作者 PulseAugur 编辑部 · [1 个来源] · 2026-10-14 04:00

研究人员开发了一个新的理论框架来分析常数步长随机梯度下降（SGDM）的行为。该框架将耦合参数和动量递归视为一个非线性时间序列，证明在该动量条件下，该过程在几何上会遗忘其初始化。该研究还为平均SGDM建立了不变性原理和淬灭高斯极限，并通过小学习率分析得出了最后一个迭代的高斯极限。 AI

影响提供了对机器学习模型训练中使用的优化算法更深入的理论理解。

排序理由在arXiv上发表的学术论文，详细介绍了机器学习优化算法的新理论框架。[lever_c_demoted from research: ic=1 ai=1.0]

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arXiv stat.ML TIER_1 English(EN) · Younghun Lee, Jake Zummo, Wei Biao Wu · 2026-10-14 04:00

常数步长SGD动量法的非线性时间序列理论

arXiv:2610.16034v1 Announce Type: new Abstract: Constant-step stochastic gradient descent with momentum (SGDM) augments the parameter recursion with a momentum state that carries geometrically decaying memory of past stochastic gradients. We study this coupled recursion as a nonl…