Pseudo-Riemannian Embedding Models for Multi-Relational Graph Representations

Abstract

In this paper we generalize single-relation pseudo-Riemannian graph embedding modelsto multi-relational networks, and show that the typical approach of encoding relations asmanifold transformations translates from the Riemannian to the pseudo-Riemannian case.In addition we construct a view of relations as separate spacetime submanifolds of multi-timemanifolds, and consider an interpolation between a pseudo-Riemannian embedding modeland its Wick-rotated Riemannian counterpart. We validate these extensions in the task oflink prediction, focusing on flat Lorentzian manifolds, and demonstrate their use in bothknowledge graph completion and knowledge discovery in a biological domain.