{"title":"The Universal Approximation Capabilities of 2pi-Periodic Approximate Identity Neural Networks","authors":"Saeed Panahian Fard, Z. Zainuddin","doi":"10.1109/ISCC-C.2013.147","DOIUrl":null,"url":null,"abstract":"A fundamental theoretical aspect of artificial neural networks is related to the investigation of the universal approximation capability of a new type of a three-layer feed forward neural networks. In this study, we present four theorems concerning the universal approximation capabilities of a three-layer feed forward 2pi-periodic approximate identity neural networks. Using 2pi-periodic approximate identity, we prove two theorems which show the universal approximation capability of a three layer feed forward 2pi-periodic approximate identity neural networks in the space of continuous 2pi-periodic functions. The proofs of these theorems are based on the convolution linear operators and the theory of ε-net. Using 2pi-periodic approximate identity again, we also prove another two theorems which show the universal approximation capability of these networks in the space of pth-order Lebesgue integrable 2pi-periodic functions.","PeriodicalId":313511,"journal":{"name":"2013 International Conference on Information Science and Cloud Computing Companion","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2013-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2013 International Conference on Information Science and Cloud Computing Companion","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISCC-C.2013.147","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 10
Abstract
A fundamental theoretical aspect of artificial neural networks is related to the investigation of the universal approximation capability of a new type of a three-layer feed forward neural networks. In this study, we present four theorems concerning the universal approximation capabilities of a three-layer feed forward 2pi-periodic approximate identity neural networks. Using 2pi-periodic approximate identity, we prove two theorems which show the universal approximation capability of a three layer feed forward 2pi-periodic approximate identity neural networks in the space of continuous 2pi-periodic functions. The proofs of these theorems are based on the convolution linear operators and the theory of ε-net. Using 2pi-periodic approximate identity again, we also prove another two theorems which show the universal approximation capability of these networks in the space of pth-order Lebesgue integrable 2pi-periodic functions.