Approximation properties of deep ReLU CNNs

This paper focuses on establishing $$L^2$$ approximation properties for deep ReLU convolutional neural networks (CNNs) in two-dimensional space. The analysis is based a decomposition theorem kernels with large spatial size and multi-channels. Given the result, property of activation function, specific structure channels, universal CNNs classic obtained by showing its connection one-hidden-layer (NNs). Furthermore, are one version ResNet, pre-act MgNet architecture connections between these networks.