Convergence of Hyperbolic Neural Networks Under Riemannian Stochastic Gradient Descent

作     者：Wes Whiting Bao Wang Jack Xin Wes Whiting;Bao Wang;Jack Xin

作者机构：Department of MathematicsUniversity of CaliforniaIrvineCAUSA Department of MathematicsScientific Computing and Imaging InstituteUniversity of UtahSalt Lake CityUTUSA 

出 版 物：《Communications on Applied Mathematics and Computation》 (应用数学与计算数学学报（英文）)

年 卷 期：2024年第6卷第2期

页      面：1175-1188页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 081104[工学-模式识别与智能系统] 08[工学] 0835[工学-软件工程] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：partially supported by NSF Grants DMS-1854434,DMS-1952644,and DMS-2151235 at UC Irvine supported by NSF Grants DMS-1924935,DMS-1952339,DMS-2110145,DMS-2152762,and DMS-2208361,and DOE Grants DE-SC0021142 and DE-SC0002722 

主　　题：Hyperbolic neural network Riemannian gradient descent Riemannian Adam(RAdam) Training convergence 

摘      要：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 *** also discuss a Riemannian version of the Adam *** show numerical simulations of these algorithms on various benchmarks.