Directed Graph Embeddings in Pseudo-Riemannian Manifolds
This work addresses the challenge of encoding inductive biases for directed graphs in machine learning, offering a novel geometric approach with potential applications in natural language and biology.
The authors tackled the problem of representing directed graphs by proposing an embedding model that combines pseudo-Riemannian metrics, non-trivial topology, and a directional likelihood function, achieving equal or better link prediction performance compared to higher-dimensional curved Riemannian manifolds on synthetic and real-world graphs.
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.