  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.
