Pseudo-Riemannian Embedding Models for Multi-Relational Graph Representations

TL;DR

This paper extends pseudo-Riemannian graph embedding models to multi-relational networks, introducing spacetime submanifolds and interpolation techniques, and validates their effectiveness in link prediction tasks across knowledge graphs and biological data.

Contribution

It generalizes pseudo-Riemannian embeddings to multi-relational graphs and introduces a novel view of relations as spacetime submanifolds, with interpolation between models.

Findings

Effective in link prediction for knowledge graphs

Applicable to biological knowledge discovery

Demonstrates advantages of pseudo-Riemannian models

Abstract

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.