Multi-relational Poincaré Graph Embeddings

By Ivana Balazevic, Carl Allen, Timothy M. Hospedales. Neural Information Processing Systems, 2019

326 citations recorded by the source corpus.

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

Subfields: Artificial Intelligence

View Paper: https://www.semanticscholar.org/paper/a059785b56f0f285422c098e972baed062f93661

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In Artificial Intelligence

Citations in the corpus

Knowledge Graphs (2020, unknown): “, MuRP [9] uses relation embeddings that transform entity embeddings in the hyperbolic space of the Poincaré ball mode, whose curvature provides more “space” to separate entities with respect to the dimensionality.”
Low-Dimensional Hyperbolic Knowledge Graph Embeddings (2020, methodology): “We report the Krackhardt hierarchy score ∗Code available at https://github.com/ tensorflow/neural-structured-learning/ tree/master/research/kg_hyp_emb (KhsG) (Balažević et al., 2019) and estimated curvature per relation (see Appendix A.2 for more details).”
A Survey on Knowledge Graphs: Representation, Acquisition, and Applications (2020, unknown): “QuatE [24] h, t ∈ H , r ∈ H h⊗ r |r| · t SACN [43] h, t ∈ R , r ∈ R g (vec (M (h, r))W ) t ConvKB [42] h, t ∈ R , r ∈ R concat (g ([h, r, t] ∗ ω)) w ConvE [54] Mh ∈ R dw×dh , t ∈ R σ (vec (σ ([Mh; Mr] ∗ ω)) W) t Mr ∈ Rdw×dh DihEdral [31] h , t ∈ R ∑L l=1 h (l)>R(l)t(l) R ∈ DK HAKE [18] hm, tm ∈ R , ”
A Survey of Knowledge Graph Reasoning on Graph Types: Static, Dynamic, and Multi-Modal (2022, methodology): “The Poincaré ball model of hyperbolic space is used in MuRP [31] for better performance in low dimensionality.”
Machine Learning on Graphs: A Model and Comprehensive Taxonomy (2020, background): “For instance, hyperbolic embeddings can represent hierarchical data with much smaller distortion than Euclidean embeddings (Sarkar, 2011) and have led to state-of-the-art results in many modern applications such as link prediction in knowledge graphs (Balazevic et al., 2019; Chami et al., 2020) and ”