Convergence Properties of Hyperbolic Neural Networks on Riemannian Manifolds

Nico Alvarado, Sebastian Burgos

Keywords: hyperbolic neural networks, optimization, riemannian manifolds

Abstract: Hyperbolic neural networks have attracted increasing attention within the community in recent years, with various empirical studies on the subject standing out. However, there is little theoretical research on this topic. In this work, we use results from Avelin and Karlsson to ensure convergence of hyperbolic neural networks defined in the Lorentz hyperboloid model. Also, we extend this result to a any Riemannian manifold.

Is Neurips Submission: No

Submission Number: 3