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.

本文提出了一种新的知识图谱嵌入方法 UltraE，它使用超弦广义相对论模型天衣无缝地将双曲和球形流形交错地组织起来，使其能够同时建模异构结构和复杂的关系模式，实验结果表明，UltraE 优于之前的欧几里得和双曲嵌入方法。