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arXiv · 2110.02926

On the Global Convergence of Gradient Descent for multi-layer ResNets in the mean-field regime

Zhiyan Ding·Shi Chen·Qin Li·Stephen Wright
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Abstract

Finding the optimal configuration of parameters in ResNet is a nonconvex minimization problem, but first-order methods nevertheless find the global optimum in the overparameterized regime. We study this phenomenon with mean-field analysis, by translating the training process of ResNet to a gradient-flow partial differential equation (PDE) and examining the convergence properties of this limiting process. The activation function is assumed to be $2$-homogeneous or partially $1$-homogeneous; the regularized ReLU satisfies the latter condition. We show that if the ResNet is sufficiently large, with depth and width depending algebraically on the accuracy and confidence levels, first-order optimization methods can find global minimizers that fit the training data.

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Zhiyan Ding, Shi Chen, Qin Li, Stephen Wright. 2021-10-06. On the Global Convergence of Gradient Descent for multi-layer ResNets in the mean-field regime. https://arxiv.org/abs/2110.02926

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