Ultrahyperbolic Knowledge Graph Embeddings
This work addresses the limitation of homogeneous geometries in knowledge graph embeddings for AI applications, offering a more accurate representation of real-world heterogeneous structures, though it is incremental as it builds on existing hyperbolic methods.
The paper tackled the problem of representing heterogeneous topological structures in knowledge graphs, which include multiple hierarchies and non-hierarchical parts, by proposing Ultrahyperbolic KG Embeddings (UltraE) that use an ultrahyperbolic manifold to interleave hyperbolic and spherical geometries, resulting in outperformance over previous Euclidean- and hyperbolic-based approaches on three standard KGs.
Recent knowledge graph (KG) embeddings have been advanced by hyperbolic geometry due to its superior capability for representing hierarchies. The topological structures of real-world KGs, however, are rather heterogeneous, i.e., a KG is composed of multiple distinct hierarchies and non-hierarchical graph structures. Therefore, a homogeneous (either Euclidean or hyperbolic) geometry is not sufficient for fairly representing such heterogeneous structures. To capture the topological heterogeneity of KGs, we present an ultrahyperbolic KG embedding (UltraE) in an ultrahyperbolic (or pseudo-Riemannian) manifold that seamlessly interleaves hyperbolic and spherical manifolds. In particular, we model each relation as a pseudo-orthogonal transformation that preserves the pseudo-Riemannian bilinear form. The pseudo-orthogonal transformation is decomposed into various operators (i.e., circular rotations, reflections and hyperbolic rotations), allowing for simultaneously modeling heterogeneous structures as well as complex relational patterns. Experimental results on three standard KGs show that UltraE outperforms previous Euclidean- and hyperbolic-based approaches.