Convergence of Hyperbolic Neural Networks Under Riemannian Stochastic Gradient Descent

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外文摘要：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 algo-rithm.We show numerical simulations of these algorithms on various benchmarks.

外文关键词：

Hyperbolic neural networkRiemannian gradient descentRiemannian Adam(RAdam)Training convergence

作者：

Wes Whiting、Bao Wang、Jack Xin

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作者单位：

Department of Mathematics,University of California,Irvine,CA,USA

Department of Mathematics,Scientific Computing and Imaging Institute,University of Utah,Salt Lake City,UT,USA

基金：

NSF Grants at UC IrvineNSF Grants at UC IrvineNSF Grants at UC IrvineNSFNSFNSFNSFNSFDOEDOE

项目编号：

DMS-1854434DMS-1952644DMS-2151235DMS-1924935DMS-1952339DMS-2110145DMS-2152762DMS-2208361DE-SC0021142DE-SC0002722

出版年：

2024

DOI：

10.1007/s42967-023-00302-9

应用数学与计算数学学报

上海大学

应用数学与计算数学学报

影响因子：0.165

ISSN：1006-6330

年,卷(期)：2024.6(2)