{"title":"2pi-周期近似恒等神经网络的通用逼近能力","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":"{\"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}","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}
The Universal Approximation Capabilities of 2pi-Periodic Approximate Identity Neural Networks
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.