5* Knowledge Graph Embeddings with Projective Transformations

Performing link prediction using knowledge graph embedding (KGE) models is a popular approach for knowledge graph completion. Such link predictions are performed by measuring the likelihood of links in the graph via a transformation function that maps nodes via edges into a vector space. Since the complex structure of the real world is reflected in multi-relational knowledge graphs, the transformation functions need to be able to represent this complexity. However, most of the existing transformation functions in embedding models have been designed in Euclidean geometry and only cover one or two simple transformations. Therefore, they are prone to underfitting and limited in their ability to embed complex graph structures. The area of projective geometry, however, fully covers inversion, reflection, translation, rotation, and homothety transformations. We propose a novel KGE model, which supports those transformations and subsumes other state-of-the-art models. The model has several favorable theoretical properties and outperforms existing approaches on widely used link prediction benchmarks

Faithiful Embeddings for EL++ Knowledge Bases

Recently, increasing efforts are put into learning continual representations for symbolic knowledge bases (KBs). However, these approaches either only embed the data-level knowledge (ABox) or suffer from inherent limitations when dealing with concept-level knowledge (TBox), i.e., they cannot faithfully model the logical structure present in the KBs. We present BoxEL, a geometric KB embedding approach that allows for better capturing the logical structure (i.e., ABox and TBox axioms) in the description logic EL++. BoxEL models concepts in a KB as axis-parallel boxes that are suitable for modeling concept intersection, entities as points inside boxes, and relations between concepts/entities as affine transformations. We show theoretical guarantees (soundness) of BoxEL for preserving logical structure. Namely, the learned model of BoxEL embedding with loss 0 is a (logical) model of the KB. Experimental results on (plausible) subsumption reasonings and a real-world application for protein-protein prediction show that BoxEL outperforms traditional knowledge graph embedding methods as well as state-of-the-art EL++ embedding approaches.Comment: Published in ISWC'2