Knowledge graph (KG) embeddings have shown great power in learning
representations of entities and relations for link prediction tasks. Previous
work usually embeds KGs into a single geometric space such as Euclidean space
(zero curved), hyperbolic space (negatively curved) or hyperspherical space
(positively curved) to maintain their specific geometric structures (e.g.,
chain, hierarchy and ring structures). However, the topological structure of
KGs appears to be complicated, since it may contain multiple types of geometric
structures simultaneously. Therefore, embedding KGs in a single space, no
matter the Euclidean space, hyperbolic space or hyperspheric space, cannot
capture the complex structures of KGs accurately. To overcome this challenge,
we propose Geometry Interaction knowledge graph Embeddings (GIE), which learns
spatial structures interactively between the Euclidean, hyperbolic and
hyperspherical spaces. Theoretically, our proposed GIE can capture a richer set
of relational information, model key inference patterns, and enable expressive
semantic matching across entities. Experimental results on three
well-established knowledge graph completion benchmarks show that our GIE
achieves the state-of-the-art performance with fewer parameters.

本文阐述了通过将知识图谱嵌入欧几里得空间、双曲空间和高维球面空间，提出了一种基于几何交互方法的知识图谱嵌入（GIE）。实验结果表明，与其他嵌入方法相比，GIE 在三个知识图谱数据集上的表现更加优异。