Towards an Understanding of Residual Networks Using Neural Tangent Hierarchy (NTH)
This work provides theoretical insights into ResNet training for machine learning researchers, but it is incremental as it builds on existing NTH and NTK frameworks.
The paper tackled the problem of understanding why deep residual networks (ResNets) outperform fully-connected networks by analyzing their training dynamics using the neural tangent hierarchy (NTH). The result showed that for a ResNet with smooth and Lipschitz activation, the requirement on layer width relative to training samples was reduced from quartic to cubic, suggesting skip-connections are key to its success.
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 \cite{Jacot2018Neural}. In this paper, we study dynamics of the NTK for finite width Deep Residual Network (ResNet) using the neural tangent hierarchy (NTH) proposed in \cite{Huang2019Dynamics}. 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.