Convergence of Hyperbolic Neural Networks Under Riemannian Stochastic Gradient Descent
Journal Article
·
· Communications on Applied Mathematics and Computation
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
A Gyrovector Space Approach to Hyperbolic Geometry
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book | January 2009 |
Introduction to WordNet: An On-line Lexical Database*
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journal | January 1990 |
Stochastic Gradient Descent on Riemannian Manifolds
|
journal | September 2013 |
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