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https://i.redd.it/eonsgsm74q031.png

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Paper: https://arxiv.org/abs/1905.09791

PyTorch Code: https://github.com/ibalazevic/multirelational-poincare

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Key contributions:

• proposing MuRP, a theoretically inspired method to embed hierarchical multi-relational data in the Poincaré ball model of hyperbolic space which achieves state-of-the-art results on the hierarchical WN18RR knowledge graph dataset;
• showing that our Poincaré embeddings require far fewer dimensions than Euclidean embeddings to achieve comparable performance; and
• visualizing the learned embeddings and analyzing the properties of the Poincaré model compared to its Euclidean analogue.

Abstract:

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 Poincaré ball model of hyperbolic space. Our Multi-Relational Poincaré model (MuRP) learns relation-specific parameters to transform entity embeddings by Möbius matrix-vector multiplication and Möbius addition. Experiments on the hierarchical WN18RR knowledge graph show that our multi-relational Poincaré embeddings outperform their Euclidean counterpart and existing embedding methods on the link prediction task, particularly at lower dimensionality.