Convergence of Hyperbolic Neural Networks Under Riemannian Stochastic Gradient Descent

Journal Article · 05 October 2023 · Communications on Applied Mathematics and Computation

DOI: https://doi.org/10.1007/s42967-023-00302-9 · OSTI ID:2007675

Whiting, Wes ; Wang, Bao; Xin, Jack

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.

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0021142; SC0002722
• OSTI ID: 2007675
• Journal Information: Communications on Applied Mathematics and Computation, Journal Name: Communications on Applied Mathematics and Computation Journal Issue: 2 Vol. 6; ISSN 2096-6385
• Publisher: Springer Science + Business MediaCopyright Statement
• Country of Publication: China
• Language: English