Poincaré Embeddings for Learning Hierarchical Representations

TLDR

Representation learning is widely used for symbolic data, yet most methods embed data in Euclidean space, which fails to capture latent hierarchical structure. The authors propose embedding symbolic data into an n‑dimensional Poincaré ball to learn hierarchical representations. They employ hyperbolic geometry and a Riemannian optimization algorithm to obtain compact embeddings that simultaneously encode hierarchy and similarity. Experiments show that Poincaré embeddings significantly outperform Euclidean embeddings on hierarchically structured data in terms of representation capacity and generalization.

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.