A New Function Space from Barron Class and Application to Neural Network Approximation  

作　　者：Yan Meng Pingbing Ming 

机构地区：[1]School of Mathematics,Renmin University of China,Beijing 100872,China [2]LSEC,Institute of Computational Mathematics and Scientific/Engineering Computing,AMSS,Chinese Academy of Sciences,No.55,East Road Zhong-Guan-Cun,Beijing 100190,China [3]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China.

出　　处：《Communications in Computational Physics》2022年第10期1361-1400,共40页计算物理通讯（英文）

基　　金：supported by the National Natural Science Foundation of China under the grant 11971058;supported by the National Natural Science Foundation of China under the grant 11971467.

摘　　要：We introduce a new function space,dubbed as the Barron spectrum space,which arises from the target function space for the neural network approximation.We give a Bernstein type sufficient condition for functions in this space,and clarify the embedding among the Barron spectrum space,the Bessel potential space,the Besov space and the Sobolev space.Moreover,the unexpected smoothness and the decaying behavior of the radial functions in the Barron spectrum space have been investigated.As an application,we prove a dimension explicit L^(q) error bound for the two-layer neural network with the Barron spectrum space as the target function space,the rate is dimension independent.

关 键 词：Fourier transform Besov space Sobolev space radial function neural network 

分 类 号：O17[理学—数学]