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arXiv · 2109.00190

Approximation Properties of Deep ReLU CNNs

Juncai He·Lin Li·Jinchao Xu
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Abstract

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

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Juncai He, Lin Li, Jinchao Xu. 2021-09-01. Approximation Properties of Deep ReLU CNNs. https://doi.org/10.1007/s40687-022-00336-0

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