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.

翻译：知识图谱嵌入（KGE）已被验证为推断知识图谱（KG）中缺失链接的有效方法，这类方法通常将实体映射到欧氏空间，并将关系视为实体的变换。近年来，部分欧氏KGE方法通过增强建模KG中常见的语义层级结构，提升了链接预测性能。为嵌入层级数据，双曲空间作为传统欧氏空间的有前景替代方案，展现出高保真度和更低内存消耗的特点。与欧氏空间不同，双曲空间提供无数曲率选项。然而，现有双曲KGE方法难以手动获取最优曲率设置，从而限制了其有效建模语义层级的能力。为解决这一局限，我们提出一种新型KGE模型——双曲层级知识图谱嵌入（HypHKGE）。该模型为双曲空间引入基于注意力机制的可学习曲率，有助于保留丰富的语义层级结构。此外，为利用保留的层级结构推断缺失链接，我们基于双曲几何理论定义了双曲层级变换，涵盖层级间与层级内建模。实验在三个基准数据集（WN18RR、FB15K-237和YAGO3-10）上验证了所提HypHKGE模型的有效性。源代码将在https://github.com/wjzheng96/HypHKGE公开。