Convergence Properties of Hyperbolic Neural Networks on 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.

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Cite

Text

Alvarado and Burgos. "Convergence Properties of Hyperbolic Neural Networks on Riemannian Manifolds." NeurIPS 2024 Workshops: M3L, 2024.

Markdown

[Alvarado and Burgos. "Convergence Properties of Hyperbolic Neural Networks on Riemannian Manifolds." NeurIPS 2024 Workshops: M3L, 2024.](https://mlanthology.org/neuripsw/2024/alvarado2024neuripsw-convergence/)

BibTeX

@inproceedings{alvarado2024neuripsw-convergence,
  title     = {{Convergence Properties of Hyperbolic Neural Networks on Riemannian Manifolds}},
  author    = {Alvarado, Nico and Burgos, Sebastian},
  booktitle = {NeurIPS 2024 Workshops: M3L},
  year      = {2024},
  url       = {https://mlanthology.org/neuripsw/2024/alvarado2024neuripsw-convergence/}
}