{"title":"Self averaging and the space of interactions in neural networks","authors":"M. Talagrand","doi":"10.1002/(SICI)1098-2418(199905)14:3%3C199::AID-RSA1%3E3.0.CO;2-6","DOIUrl":null,"url":null,"abstract":"Ž . ABSTRACT: We prove through a precise exponential inequality that the logarithm of the N Ž size of the intersection of M random half spaces with the unit sphere of R resp., the 4N . discrete cube y1, 1 is, as Na`, a self averaging quantity. This provides justification for w Ž . x one of the first steps of a famous computation by E. Gardner J. Phys. A 21 1988 , 257]270 . Q 1999 John Wiley & Sons, Inc. Random Struct. Alg., 14, 199]213, 1999","PeriodicalId":303496,"journal":{"name":"Random Struct. Algorithms","volume":"97 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1999-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Random Struct. Algorithms","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/(SICI)1098-2418(199905)14:3%3C199::AID-RSA1%3E3.0.CO;2-6","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
Ž . ABSTRACT: We prove through a precise exponential inequality that the logarithm of the N Ž size of the intersection of M random half spaces with the unit sphere of R resp., the 4N . discrete cube y1, 1 is, as Na`, a self averaging quantity. This provides justification for w Ž . x one of the first steps of a famous computation by E. Gardner J. Phys. A 21 1988 , 257]270 . Q 1999 John Wiley & Sons, Inc. Random Struct. Alg., 14, 199]213, 1999
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