{"title":"黎曼随机梯度下降下双曲神经网络的收敛性","authors":"Wes Whiting, Bao Wang, Jack Xin","doi":"10.1007/s42967-023-00302-9","DOIUrl":null,"url":null,"abstract":"Abstract We prove, under mild conditions, the convergence of a Riemannian gradient descent method for a hyperbolic neural network regression model, both in batch gradient descent and stochastic gradient descent. We also discuss a Riemannian version of the Adam algorithm. We show numerical simulations of these algorithms on various benchmarks.","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"42 1","pages":"0"},"PeriodicalIF":1.4000,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Convergence of Hyperbolic Neural Networks Under Riemannian Stochastic Gradient Descent\",\"authors\":\"Wes Whiting, Bao Wang, Jack Xin\",\"doi\":\"10.1007/s42967-023-00302-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We prove, under mild conditions, the convergence of a Riemannian gradient descent method for a hyperbolic neural network regression model, both in batch gradient descent and stochastic gradient descent. We also discuss a Riemannian version of the Adam algorithm. We show numerical simulations of these algorithms on various benchmarks.\",\"PeriodicalId\":29916,\"journal\":{\"name\":\"Communications on Applied Mathematics and Computation\",\"volume\":\"42 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2023-10-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications on Applied Mathematics and Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s42967-023-00302-9\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications on Applied Mathematics and Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s42967-023-00302-9","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Convergence of Hyperbolic Neural Networks Under Riemannian Stochastic Gradient Descent
Abstract We prove, under mild conditions, the convergence of a Riemannian gradient descent method for a hyperbolic neural network regression model, both in batch gradient descent and stochastic gradient descent. We also discuss a Riemannian version of the Adam algorithm. We show numerical simulations of these algorithms on various benchmarks.
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