(untitled) (CSIAM Transactions on Applied Mathematics, 2022)
Gradient descent yields zero training loss in polynomial time for deep neural networks despite non-convex nature of the objective function. The behavior of network in the infinite width limit trained by gradient descent can be described by the Neural Tangent Kernel (NTK) introduced in [25]. In this paper, we study dynamics of the NTK for finite width Deep Residual Network (ResNet) using the neural tangent hierarchy (NTH) proposed in [24]. For a ResNet with smooth and Lipschitz activation function, we reduce the requirement on the layer width m with respect to the number of training samples n from quartic to cubic. Our analysis suggests strongly that the particular skip-connection structure of ResNet is the main reason for its triumph over fully-connected network.