{"title":"Approximation Analysis of Convolutional Neural Networks","authors":"N. Null","doi":"10.4208/eajam.2022-270.070123","DOIUrl":null,"url":null,"abstract":". 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.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"18","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"East Asian Journal on Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/eajam.2022-270.070123","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 18
Abstract
. 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.
期刊介绍:
The East Asian Journal on Applied Mathematics (EAJAM) aims at promoting study and research in Applied Mathematics in East Asia. It is the editorial policy of EAJAM to accept refereed papers in all active areas of Applied Mathematics and related Mathematical Sciences. Novel applications of Mathematics in real situations are especially welcome. Substantial survey papers on topics of exceptional interest will also be published occasionally.