Convergence of Hyperbolic Neural Networks Under Riemannian Stochastic Gradient Descent
Wes Whiting , Bao Wang , Jack Xin
Communications on Applied Mathematics and Computation ›› 2023, Vol. 6 ›› Issue (2) : 1175 -1188.
Convergence of Hyperbolic Neural Networks Under Riemannian Stochastic Gradient Descent
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.
Directorate for Mathematical and Physical Sciences(MS-1854434)
Directorate for Mathematical and Physical Sciences(DMS-1952339)
U.S. Department of Energy(DE-SC0021142)
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