Knowledge graphs are inherently incomplete. Therefore substantial research has been directed toward knowledge graph completion (KGC), i.e., predicting missing triples from the information represented in the knowledge graph (KG). KG embedding models (KGEs) have yielded promising results for KGC, yet any current KGE is incapable of: (1) fully capturing vital inference patterns (e.g., composition), (2) capturing prominent patterns jointly (e.g., hierarchy and composition), and (3) providing an intuitive interpretation of captured patterns. In this work, we propose ExpressivE, a fully expressive spatio-functional KGE that solves all these challenges simultaneously. ExpressivE embeds pairs of entities as points and relations as hyper-parallelograms in the virtual triple space $\mathbb{R}^{2d}$. This model design allows ExpressivE not only to capture a rich set of inference patterns jointly but additionally to display any supported inference pattern through the spatial relation of hyper-parallelograms, offering an intuitive and consistent geometric interpretation of ExpressivE embeddings and their captured patterns. Experimental results on standard KGC benchmarks reveal that ExpressivE is competitive with state-of-the-art KGEs and even significantly outperforms them on WN18RR.

翻译：知识图谱本质上是不完整的。因此，大量研究致力于知识图谱补全（KGC），即根据知识图谱（KG）中表示的信息预测缺失的三元组。知识图谱嵌入模型（KGEs）在KGC方面取得了有前景的结果，然而当前任何KGE模型都无法同时实现：（1）完全捕获关键的推理模式（如组合）、（2）联合捕获显著模式（如层次结构和组合）、以及（3）提供对捕获模式的直观解释。本文提出ExpressivE，一种完全表达的时空功能KGE模型，能够同时解决所有这些挑战。ExpressivE在虚拟三元组空间$\mathbb{R}^{2d}$中将实体对编码为点，关系编码为超平行四边形。这种模型设计不仅使ExpressivE能够联合捕获丰富的推理模式集合，还能通过超平行四边形的空间关系展示任何支持的推理模式，为ExpressivE嵌入及其捕获的模式提供直观且一致的几何解释。在标准KGC基准上的实验结果表明，ExpressivE与最先进的KGE模型具有竞争力，并在WN18RR上显著优于它们。