Approximation properties of deep ReLU CNNs
Approximation properties of deep ReLU CNNs
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DOI：
10.1007/s40687-022-00336-0
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发表时间：
2021-09
影响因子：
1.2
通讯作者：
Juncai He;Lin Li;Jinchao Xu
中科院分区：
文献类型：
--
作者：
Juncai He;Lin Li;Jinchao Xu
本文主要研究深度ReLU卷积神经网络（cnn）在二维空间中的近似性质。该分析是基于大空间尺寸和多通道卷积核的分解定理。根据分解结果、ReLU激活函数的性质以及通道的特定结构，通过展示其与单隐层ReLU神经网络（NNs）的联系，得到了具有经典结构的深度ReLU cnn的通用逼近定理。此外，基于这些网络之间的连接，获得了具有ResNet， pre-act ResNet和MgNet架构的一个版本的神经网络的近似性质。
This paper focuses on establishingapproximation 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.