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

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Sep 29, 2021 (edited Oct 05, 2021)ICLR 2022 Conference Blind SubmissionReaders: Everyone
  • 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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