Towards an Understanding of Residual Networks Using Neural Tangent Hierarchy (NTH)

• URL: http://arxiv.org/abs/2007.03714v1
• Date: Tue, 7 Jul 2020 18:08:16 GMT
• Title: Towards an Understanding of Residual Networks Using Neural Tangent Hierarchy (NTH)
• Authors: Yuqing Li, Tao Luo, Nung Kwan Yip
• Abstract summary: Gradient descent yields zero loss in time for deep training networks despite non- infinite nature of the objective function. In this paper, we trained neural dynamics of the NTK for finite width ResNet using Deep Residual Network (ResNet) Our analysis suggests strongly that the particular neural-connection structure ResNet is the main reason for its triumph.
• Score: 2.50686294157537
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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