  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.
