Kernel-Based Smoothness Analysis of Residual Networks
This work provides theoretical insight into the smoothness properties of ResNets, which is an incremental contribution to understanding their generalization advantages over MLPs.
The paper demonstrates that residual networks (ResNets) produce smoother interpolations than multilayer perceptrons (MLPs) by analyzing their neural tangent kernels, which may explain ResNets' better generalization ability.
A major factor in the success of deep neural networks is the use of sophisticated architectures rather than the classical multilayer perceptron (MLP). Residual networks (ResNets) stand out among these powerful modern architectures. Previous works focused on the optimization advantages of deep ResNets over deep MLPs. In this paper, we show another distinction between the two models, namely, a tendency of ResNets to promote smoother interpolations than MLPs. We analyze this phenomenon via the neural tangent kernel (NTK) approach. First, we compute the NTK for a considered ResNet model and prove its stability during gradient descent training. Then, we show by various evaluation methodologies that for ReLU activations the NTK of ResNet, and its kernel regression results, are smoother than the ones of MLP. The better smoothness observed in our analysis may explain the better generalization ability of ResNets and the practice of moderately attenuating the residual blocks.