Title: Poincaré Embeddings for Learning Hierarchical Representations,
Abstract: Representation learning has become an invaluable approach for learning from
symbolic data such as text and graphs. However, while complex symbolic datasets
often exhibit a latent hierarchical structure, state-of-the-art methods
typically learn embeddings in Euclidean vector spaces, which do not account for
this property. For this purpose, we introduce a new approach for learning
hierarchical representations of symbolic data by embedding them into hyperbolic
space -- or more precisely into an n-dimensional Poincaré ball. Due to the
underlying hyperbolic geometry, this allows us to learn parsimonious
representations of symbolic data by simultaneously capturing hierarchy and
similarity. We introduce an efficient algorithm to learn the embeddings based
on Riemannian optimization and show experimentally that Poincaré embeddings
outperform Euclidean embeddings significantly on data with latent hierarchies,
both in terms of representation capacity and in terms of generalization
ability.