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

• URL: http://arxiv.org/abs/2110.02926v1
• Date: Wed, 6 Oct 2021 17:16:09 GMT
• Title: On the Global Convergence of Gradient Descent for multi-layer ResNets in the mean-field regime
• Authors: Zhiyan Ding and Shi Chen and Qin Li and Stephen Wright
• Abstract summary: First-order methods find the global optimum in the globalized regime. We show that if the ResNet is sufficiently large, with depth width depending on the accuracy and confidence levels, first-order methods can find optimization that fit the data.
• Score: 19.45069138853531
• License: http://creativecommons.org/licenses/by/4.0/
• 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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