ExpressivE: A Spatio-Functional Embedding For Knowledge Graph Completion

Knowledge graphs are inherently incomplete. Therefore substantial research has been directed towards knowledge graph completion (KGC), i.e., predicting missing triples from the information represented in the knowledge graph (KG). Embedding models have yielded promising results for KGC, yet any current KGC embedding model is incapable of: (1) fully capturing vital inference patterns (e.g., composition), (2) capturing prominent logical rules 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 embedding model 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 models and even significantly outperforms them on WN18RR.