Multi-relational Poincaré Graph Embeddings

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.

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Results from the Paper

Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Link Prediction FB15k-237 MuRP MRR 0.336 # 45
Hits@10 0.521 # 41
Hits@3 0.370 # 34
Hits@1 0.245 # 39
Link Prediction WN18RR MuRP MRR 0.481 # 33
Hits@10 0.566 # 38
Hits@3 0.495 # 29
Hits@1 0.440 # 33


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