Hyperbolic Hierarchical Knowledge Graph Embeddings for Link Prediction in Low Dimensions

TL;DR

Knowledge graphs exhibit hierarchical structure that is challenging to model in Euclidean spaces with low dimensionality. HypHKGE introduces attention-based learnable curvatures and hyperbolic hierarchical transformations to capture multi-level and same-level hierarchies within hyperbolic space, enabling effective low-dimensional embeddings for link prediction. The method defines semantic hierarchy representations, inter-level and intra-level transformations, and a curvature-aware scoring function, with theoretical support and extensive experiments showing consistent gains over both Euclidean and hyperbolic baselines on WN18RR, FB15K-237, and YAGO3-10. Overall, the approach advances efficient, hierarchy-aware KGEs with practical impact for scalable link prediction and knowledge inference in hierarchically structured data.

Abstract

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.

Figures (6)

• Figure 1: An example of semantic hierarchies in KGs where entities are linked through relations in the hierarchical structure.
• Figure 2: An illustration of the $log$ and the $exp$ maps. The $log$ map projects a point $\mathbf{x}\in \mathcal{M}$ to the tangent space $T_{\mathbf x}\mathcal{M}$ by moving a unit length along the geodesic, and the $exp$ map gives the reverse.
• Figure 3: Spatial curvature modeled by different approaches from the perspective of semantic hierarchy. Assume that ①, ②, ③, and ④ are the four hierarchical structures existing in KGs. MuRP Balazevic2019 embeds the full graph in hyperbolic space with the fixed curvature, i.e., ①, ②, ③, and ④ use the same curvature. AttH Chami2020 learns a curvature for each relation, i.e., ① and ② share a curvature, ③ and ④ share another curvature. In contrast, our approach considers the head entity in addition to the relations, i.e., ①, ②, ③, and ④ use unique curvature, respectively.
• Figure 4: With the embedding dimension increases, comparison of MRR of HypHKGE and EucHKGE on WN18RR.
• Figure 5: Effect of entity information on curvature under a single relation.