Hyperbolic Optimizer as a Dynamical System
Abstract
During the last few years, the field of dynamical systems has been developing innovative tools to study the asymptotic behavior of different optimizers in the context of neural networks. In this work, we redefine an extensively studied optimizer, employing classical techniques from hyperbolic geometry. This new definition is linked to a non-linear differential equation as a continuous limit. Additionally, by utilizing Lyapunov stability concepts, we analyze the asymptotic behavior of its critical points.
Cite
Text
Alvarado and Lobel. "Hyperbolic Optimizer as a Dynamical System." International Conference on Machine Learning, 2024.Markdown
[Alvarado and Lobel. "Hyperbolic Optimizer as a Dynamical System." International Conference on Machine Learning, 2024.](https://mlanthology.org/icml/2024/alvarado2024icml-hyperbolic/)BibTeX
@inproceedings{alvarado2024icml-hyperbolic,
title = {{Hyperbolic Optimizer as a Dynamical System}},
author = {Alvarado, Nico and Lobel, Hans},
booktitle = {International Conference on Machine Learning},
year = {2024},
pages = {1243-1260},
volume = {235},
url = {https://mlanthology.org/icml/2024/alvarado2024icml-hyperbolic/}
}