论文标题
使用神经切线层次结构（nth）了解残留网络
Towards an Understanding of Residual Networks Using Neural Tangent Hierarchy (NTH)
论文作者
论文摘要
尽管目标函数的非凸性性质，但梯度下降对于深层神经网络的多项式时间却导致零训练损失。 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.
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.
