Which Hyperbolic Model? An Analytical and Empirical Comparison

NeurIPS 2025 Workshop NeurReps Submission147 Authors

Keywords: Hyperbolic geometry, Hyperbolic models, Poincaré disk, Lorentz model, Hyperbolic embeddings, Recommender systems, Matrix factorization, Bayesian personalized ranking, Non-Euclidean representation learning.

TL;DR: five hyperbolic models, analytical/visual comparison, and empirical evaluation in recommender systems

Abstract: Hyperbolic geometry has become central to machine learning for hierarchical and graph-structured data. Several isometric models of hyperbolic space --- including the Poincaré disk, Lorentz (hyperboloid), Klein, Half-space, and Hemisphere --- are theoretically equivalent but behave differently in practice. This work tries to answer the following question: \emph{Which hyperbolic model should one use?} We contribute (i) an analytical and visual comparison of the five classical models, (ii) an experimental framework for recommender systems with hyperbolic matrix factorization (HMF) and Bayesian personalized ranking (BPR), and (iii) preliminary insights on optimization stability across models. The present extended abstract emphasizes contributions (i) and (ii); full experimental results will appear in a longer version.

Submission Number: 147