  Knowledge graph embeddings (KGE) have been validated as powerful methods for
inferring missing links in knowledge graphs (KGs) that they typically map
entities into Euclidean space and treat relations as transformations of
entities. Recently, some Euclidean KGE methods have been enhanced to model
semantic hierarchies commonly found in KGs, improving the performance of link
prediction. To embed hierarchical data, hyperbolic space has emerged as a
promising alternative to traditional Euclidean space, offering high fidelity
and lower memory consumption. Unlike Euclidean, hyperbolic space provides
countless curvatures to choose from. However, it is difficult for existing
hyperbolic KGE methods to obtain the optimal curvature settings manually,
thereby limiting their ability to effectively model semantic hierarchies. To
address this limitation, we propose a novel KGE model called
$\textbf{Hyp}$erbolic $\textbf{H}$ierarchical $\textbf{KGE}$ (HypHKGE). This
model introduces attention-based learnable curvatures for hyperbolic space,
which helps preserve rich semantic hierarchies. Furthermore, to utilize the
preserved hierarchies for inferring missing links, we define hyperbolic
hierarchical transformations based on the theory of hyperbolic geometry,
including both inter-level and intra-level modeling. Experiments demonstrate
the effectiveness of the proposed HypHKGE model on the three benchmark datasets
(WN18RR, FB15K-237, and YAGO3-10). The source code will be publicly released at
https://github.com/wjzheng96/HypHKGE.
