Poincaré Embeddings for Learning Hierarchical Representations

TLDR: This work introduces a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincare ball -- and introduces an efficient algorithm to learn the embeddings based on Riemannian optimization.

Abstract: Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, state-of-the-art embedding methods typically do not account for latent hierarchical structures which are characteristic for many complex symbolic datasets. In this work, 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 Poincare ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We present an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincare embeddings can outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.