Bridging ML and algorithms: comparison of hyperbolic embeddings

Dorota Celińska-Kopczyńska, Eryk Kopczyński

Keywords: hyperbolic embeddings, network theory, social networks

TL;DR: A comparison of hyperbolic embeddings obtained in independent communities. It has nothing to do with GNNs despite naming!

Abstract: Hyperbolic embeddings are well-studied in the machine learning, network theory, and algorithm communities. However, as the research proceeds independently in those communities, comparisons and even awareness seem to be currently lacking. We compare the performance (computation time) and the quality of embeddings obtained by popular approaches as of 2025, both on real-life hierarchies and networks, and simulated networks. According to our results, the algorithm by Bläsius et al (ESA 2016) is about 100 times faster than the Poincar\'e embeddings (NIPS 2017) and Lorentz embeddings (ICML 2018) by Nickel and Kiela, while achieving results of similar (or, in some cases, even better) quality.

Primary Area: learning on graphs and other geometries & topologies

Submission Number: 10604