Many mathematical models have been leveraged to design embeddings for representing Knowledge Graph (KG) entities and relations for link prediction and many downstream tasks. These mathematically-inspired models are not only highly scalable for inference in large KGs, but also have many explainable advantages in modeling different relation patterns that can be validated through both formal proofs and empirical results. In this paper, we make a comprehensive overview of the current state of research in KG completion. In particular, we focus on two main branches of KG embedding (KGE) design: 1) distance-based methods and 2) semantic matching-based methods. We discover the connections between recently proposed models and present an underlying trend that might help researchers invent novel and more effective models. Next, we delve into CompoundE and CompoundE3D, which draw inspiration from 2D and 3D affine operations, respectively. They encompass a broad spectrum of techniques including distance-based and semantic-based methods. We will also discuss an emerging approach for KG completion which leverages pre-trained language models (PLMs) and textual descriptions of entities and relations and offer insights into the integration of KGE embedding methods with PLMs for KG completion.

翻译：在知识图谱（KG）中，许多数学模型被用于设计实体和关系的嵌入表示，以支持链接预测和多种下游任务。这些基于数学启发的模型不仅在大规模KG推理中具有高度可扩展性，而且在建模不同关系模式方面具备诸多可解释优势，这些优势可通过形式化证明和实证结果得到验证。本文全面综述了知识图谱补全领域的研究现状，重点关注知识图谱嵌入（KGE）设计的两个主要分支：1）基于距离的方法，以及2）基于语义匹配的方法。我们揭示了近期提出模型之间的关联，并呈现了一种潜在趋势，这可能有助于研究者发明新颖且更有效的模型。随后，我们深入探讨了CompoundE和CompoundE3D，它们分别受二维和三维仿射操作启发，涵盖了包括基于距离和基于语义方法在内的广泛技术。此外，我们将讨论一种新兴的知识图谱补全方法，该方法利用预训练语言模型（PLM）以及实体和关系的文本描述，并为我们提供关于将KGE嵌入方法与PLM相结合以进行知识图谱补全的洞见。