Pseudo-Riemannian Embedding Models for Multi-Relational Graph Representations
This work provides a theoretical extension of geometric embedding methods for multi-relational graphs, with potential applications in knowledge representation and biological network analysis.
The authors generalized pseudo-Riemannian graph embedding models from single-relation to multi-relational networks, showing that encoding relations as manifold transformations works in both Riemannian and pseudo-Riemannian cases. They validated these extensions on link prediction tasks using flat Lorentzian manifolds, demonstrating applications in knowledge graph completion and biological knowledge discovery.
In this paper we generalize single-relation pseudo-Riemannian graph embedding models to multi-relational networks, and show that the typical approach of encoding relations as manifold transformations translates from the Riemannian to the pseudo-Riemannian case. In addition we construct a view of relations as separate spacetime submanifolds of multi-time manifolds, and consider an interpolation between a pseudo-Riemannian embedding model and its Wick-rotated Riemannian counterpart. We validate these extensions in the task of link prediction, focusing on flat Lorentzian manifolds, and demonstrate their use in both knowledge graph completion and knowledge discovery in a biological domain.