Aleksandar Pavlović

Bruno F. Lourenço, Hesham Morgan, Ana Ozaki et al.

Knowledge base (KB) embeddings aim at combining the capability of classical knowledge graph embeddings to generalize the information present in facts, the ABox, with conceptual knowledge represented in an ontology language, the TBox. Several authors have recently explored the idea of mapping concepts to convex regions in a vector space. This is useful to represent hierarchies, typically present in TBoxes, since more general concepts can be mapped to larger regions, containing those regions associated with more specific concepts. However, the power of convexity is rarely leveraged during the actual learning tasks. Here, we introduce BoxLitE, a KB embedding model for DL-Lite$^{\mathcal{H}}$ that allows for convex optimization. We show that for any satisfiable DL-Lite$^{\mathcal{H}}$ KB, there is a BoxLitE embedding that is a weakly faithful model. As a proof of concept, we show how to formulate the KB embedding task as a convex optimization problem and how to obtain embeddings with such desirable faithfulness properties.

Aleksandar Pavlović, Emanuel Sallinger

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.

Aleksandar Pavlovic, Emanuel Sallinger, Steven Schockaert

Knowledge graph (KG) embedding methods learn geometric representations of entities and relations to predict plausible missing knowledge. These representations are typically assumed to capture rule-like inference patterns. However, our theoretical understanding of which inference patterns can be captured remains limited. Ideally, KG embedding methods should be expressive enough such that for any set of rules, there exist relation embeddings that exactly capture these rules. This principle has been studied within the framework of region-based embeddings, but existing models are severely limited in the kinds of rule bases that can be captured. We argue that this stems from the fact that entity embeddings are only compared in a coordinate-wise fashion. As an alternative, we propose RESHUFFLE, a simple model based on ordering constraints that can faithfully capture a much larger class of rule bases than existing approaches. Most notably, RESHUFFLE can capture bounded inference w.r.t. arbitrary sets of closed path rules. The entity embeddings in our framework can be learned by a Graph Neural Network (GNN), which effectively acts as a differentiable rule base.