Pseudo-Riemannian Embedding Models for Multi-Relational Graph Representations

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.

Directed Graph Embeddings in Pseudo-Riemannian Manifolds

The inductive biases of graph representation learning algorithms are often encoded in the background geometry of their embedding space. In this paper, we show that general directed graphs can be effectively represented by an embedding model that combines three components: a pseudo-Riemannian metric structure, a non-trivial global topology, and a unique likelihood function that explicitly incorporates a preferred direction in embedding space. We demonstrate the representational capabilities of this method by applying it to the task of link prediction on a series of synthetic and real directed graphs from natural language applications and biology. In particular, we show that low-dimensional cylindrical Minkowski and anti-de Sitter spacetimes can produce equal or better graph representations than curved Riemannian manifolds of higher dimensions.