Lightweight Multi-Semantic Hierarchy-Aware Poincaré Knowledge Graph Embeddings

Hyperbolic embeddings excel in encoding hierarchical data, while Euclidean embeddings are more adept at capturing complex semantic relationships through rotation operations. However, advanced Euclidean embedding models face the problem of high dimensionality, while advanced hyperbolic embedding models struggle to accommodate multiple relations and different semantics. To address this problem, we introduce LMH-PKE, a novel model that leverages the Poincaré to embed the hierarchical structure of the relationship graph data. It captures rich semantic relationships in Euclidean and models multiple relations using learnable entity decision boundary parameters. By transforming entities embedded in hyperbolic through Möbius matrix vector multiplication and Möbius addition, and encoding multiple relations in Euclidean space using cosine functions, Our experiments demonstrate that LMH-PKE achieves state-of-the-art results in hyperbolic embedding models while maintaining low dimensional simplicity.