Bridging ML and algorithms: comparison of hyperbolic embeddings

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.