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

被引：3

作者：

Meng, Yan ^{[1
]}

Ming, Pingbing ^{[2
,3
]}

机构：

[1] Renmin Univ China, Sch Math, Beijing 100872, Peoples R China

[2] Chinese Acad Sci AMSS, Inst Computat Math & Sci Engn Comp LSEC, 55, East Rd Zhong Guan Cun, Beijing 100190, Peoples R China

[3] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

来源：

COMMUNICATIONS IN COMPUTATIONAL PHYSICS | 2022年 / 32卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Fourier transform; Besov space; Sobolev space; radial function; neural network; FOURIER-TRANSFORMS; RIDGE FUNCTIONS; RATES; REGRESSION; CONSTANTS; GROWTH; BOUNDS;

D O I：

10.4208/cicp.OA-2022-0151

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

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 Lq error bound for the two-layer neural network with the Barron spectrum space as the target function space, the rate is dimension independent.

引用

页码：1361 / 1400

页数：40

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