Approximation properties of deep ReLU CNNs

Juncai He, Lin Li, Jinchao Xu

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


This paper focuses on establishing L2 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.
Original languageEnglish (US)
JournalResearch in Mathematical Sciences
Issue number3
StatePublished - Sep 1 2022
Externally publishedYes


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