@Article{EAJAM-13-524,
author = {Bao , ChenglongLi , QianxiaoShen , ZuoweiTai , ChengWu , Lei and Xiang , Xueshuang},
title = {Approximation Analysis of Convolutional Neural Networks},
journal = {East Asian Journal on Applied Mathematics},
year = {2023},
volume = {13},
number = {3},
pages = {524--549},
abstract = {<p style="text-align: justify;">In its simplest form, convolution neural networks (CNNs) consist of a fully
connected two-layer network $g$ composed with a sequence of convolution layers $T.$ Although $g$ is known to have the universal approximation property, it is not known if
CNNs, which have the form $g◦T$ inherit this property, especially when the kernel size
in $T$ is small. In this paper, we show that under suitable conditions, CNNs do inherit the
universal approximation property and its sample complexity can be characterized. In addition, we discuss concretely how the nonlinearity of $T$ can improve the approximation
power. Finally, we show that when the target function class has a certain compositional
form, convolutional networks are far more advantageous compared with fully connected
networks, in terms of the number of parameters needed to achieve the desired accuracy.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.2022-270.070123 },
url = {http://global-sci.org/intro/article_detail/eajam/21721.html}
}