{"title":"人工神经网络中的奇异摄动和时间尺度","authors":"K. L. Moore, D. Naidu","doi":"10.1109/CDC.1991.261077","DOIUrl":null,"url":null,"abstract":"The learning and computing processes in a recursive neural network of the Hopfield type are identified as slow and fast phenomena. The corresponding dynamical equations are cast to fit into the framework of the theory of singular perturbations and time scales. The issues of degeneration and asymptotic expansions arising in obtaining approximate solutions are addressed.<<ETX>>","PeriodicalId":344553,"journal":{"name":"[1991] Proceedings of the 30th IEEE Conference on Decision and Control","volume":"182 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1991-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Singular perturbations and time scales in artificial neural networks\",\"authors\":\"K. L. Moore, D. Naidu\",\"doi\":\"10.1109/CDC.1991.261077\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The learning and computing processes in a recursive neural network of the Hopfield type are identified as slow and fast phenomena. The corresponding dynamical equations are cast to fit into the framework of the theory of singular perturbations and time scales. The issues of degeneration and asymptotic expansions arising in obtaining approximate solutions are addressed.<<ETX>>\",\"PeriodicalId\":344553,\"journal\":{\"name\":\"[1991] Proceedings of the 30th IEEE Conference on Decision and Control\",\"volume\":\"182 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1991-12-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"[1991] Proceedings of the 30th IEEE Conference on Decision and Control\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CDC.1991.261077\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1991] Proceedings of the 30th IEEE Conference on Decision and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.1991.261077","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Singular perturbations and time scales in artificial neural networks
The learning and computing processes in a recursive neural network of the Hopfield type are identified as slow and fast phenomena. The corresponding dynamical equations are cast to fit into the framework of the theory of singular perturbations and time scales. The issues of degeneration and asymptotic expansions arising in obtaining approximate solutions are addressed.<>