  Hyperbolic embeddings have recently gained attention in machine learning due
to their ability to represent hierarchical data more accurately and succinctly
than their Euclidean analogues. However, multi-relational knowledge graphs
often exhibit multiple simultaneous hierarchies, which current hyperbolic
models do not capture. To address this, we propose a model that embeds
multi-relational graph data in the Poincar\'e ball model of hyperbolic space.
Our Multi-Relational Poincar\'e model (MuRP) learns relation-specific
parameters to transform entity embeddings by M\"obius matrix-vector
multiplication and M\"obius addition. Experiments on the hierarchical WN18RR
knowledge graph show that our Poincar\'e embeddings outperform their Euclidean
counterpart and existing embedding methods on the link prediction task,
particularly at lower dimensionality.
