Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry

TL;DR

This paper introduces an efficient method for learning hierarchical embeddings in hyperbolic space using the Lorentz model, outperforming previous models like Poincaré in quality and applicability to real-world hierarchical data.

Contribution

The paper demonstrates that the Lorentz model enables more efficient and higher-quality hyperbolic embeddings for large-scale hierarchies compared to the Poincaré model.

Findings

Lorentz model learning is more efficient than Poincaré for hyperbolic embeddings.

High-quality embeddings of large taxonomies are achievable in low dimensions.

Hyperbolic embeddings reveal organizational and linguistic hierarchies in real datasets.

Abstract

We are concerned with the discovery of hierarchical relationships from large-scale unstructured similarity scores. For this purpose, we study different models of hyperbolic space and find that learning embeddings in the Lorentz model is substantially more efficient than in the Poincar\'e-ball model. We show that the proposed approach allows us to learn high-quality embeddings of large taxonomies which yield improvements over Poincar\'e embeddings, especially in low dimensions. Lastly, we apply our model to discover hierarchies in two real-world datasets: we show that an embedding in hyperbolic space can reveal important aspects of a company's organizational structure as well as reveal historical relationships between language families.