Poincar\'e Embeddings for Learning Hierarchical Representations

TL;DR

This paper introduces Poincaré embeddings, a hyperbolic space method for learning hierarchical representations of symbolic data, outperforming Euclidean embeddings in capturing hierarchy and similarity.

Contribution

The paper proposes a novel hyperbolic embedding approach using Poincaré balls, enabling more efficient representation of hierarchical data than traditional Euclidean methods.

Findings

Poincaré embeddings outperform Euclidean embeddings on hierarchical data.

The method captures hierarchy and similarity effectively.

Embeddings generalize well to unseen data.

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 Poincar\'e 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 Poincar\'e embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.