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Approximation Analysis of Convolutional Neural Networks

Chenglong Bao Yau Mathematical Sciences Center, Tsinghua University, China Qianxiao Li Department of Mathematics, National University of Singapore,Singapore; Institute of High Performance Computing, A*STAR, Singapore Zuowei Shen Department of Mathematics, National University of Singapore,Singapore Cheng Tai Beijing Institute of Big Data Research, Peking University, China Lei Wu School of Mathematical Sciences, Peking University, China Xueshuang Xiang Qian Xuesen Laboratory of Space Technology, China

TBD mathscidoc:2206.43002

In its simplest form, convolution neural networks (CNNs) consist of a fully connected layer 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 has the form g ◦ T inherits this property, especially when the kernel size in T is small. In this paper, we show that under suitable conditions, CNNs does 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 number of parameters needed to achieve a desired accuracy.
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@inproceedings{chenglongapproximation,
  title={Approximation Analysis of Convolutional Neural Networks},
  author={Chenglong Bao, Qianxiao Li, Zuowei Shen, Cheng Tai, Lei Wu, and Xueshuang Xiang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220613170257371300351},
}
Chenglong Bao, Qianxiao Li, Zuowei Shen, Cheng Tai, Lei Wu, and Xueshuang Xiang. Approximation Analysis of Convolutional Neural Networks. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220613170257371300351.
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