Convergence of Hyperbolic Neural Networks Under Riemannian Stochastic Gradient Descent  

作　　者：Wes Whiting Bao Wang Jack Xin 

机构地区：[1]Department of Mathematics,University of California,Irvine,CA,USA [2]Department of Mathematics,Scientific Computing and Imaging Institute,University of Utah,Salt Lake City,UT,USA

出　　处：《Communications on Applied Mathematics and Computation》2024年第2期1175-1188,共14页应用数学与计算数学学报（英文）

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.

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 descent.We also discuss a Riemannian version of the Adam algorithm.We show numerical simulations of these algorithms on various benchmarks.

关 键 词：Hyperbolic neural network Riemannian gradient descent Riemannian Adam(RAdam) Training convergence 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]