Hyperbolic Optimizer as a Dynamical System

Authors: Nico Alvarado, Hans Lobel

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Reproducibility Variable Result LLM Response
Research Type Theoretical 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. We proved the existence of a non-linear differential equation linked to the continuous limit of the Hyperbolic ADMM flow.
Researcher Affiliation Academia Nico Alvarado 1 2 3 Hans Lobel 1 2 3 4 1Department of Computer Science, Pontificia Universidad Cat olica de Chile 2National Center of Artificial Intelligence, Chile 3Millenium Institute Foundational Research on Data, Chile 4Department of Transport and Logistics Engineering, Pontificia Universidad Cat olica de Chile.
Pseudocode No The paper does not contain any structured pseudocode or algorithm blocks.
Open Source Code No The paper does not provide any statement or link regarding the public availability of source code for the methodology described.
Open Datasets No The paper is theoretical and does not use or evaluate on any datasets, thus no information on public availability or access is provided.
Dataset Splits No The paper is theoretical and does not involve dataset splits for training, validation, or testing.
Hardware Specification No The paper is theoretical and does not report on experiments, therefore, no hardware specifications are mentioned.
Software Dependencies No The paper is theoretical and does not report on experiments or their implementation, so no specific software dependencies with version numbers are provided.
Experiment Setup No The paper is theoretical and does not describe an experimental setup with hyperparameters or specific training configurations.