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.

通过将符号数据嵌入超载空间（或更确切地说是 n 维庞加莱球）来学习符号数据的分层表示的方法，通过实验证明 Poincare 嵌入在具有潜在层次结构的数据上显着优于欧几里得嵌入，无论是在表示能力还是泛化能力方面。