Box Embeddings for Knowledge Base Completion

Knowledge bases (KBs) are highly prominent in modern computing applications, and typically include hundreds of millions of facts. However, these KBs are very incomplete, which has motivated the task of knowledge base completion (KBC). A promising approach for KBC is to embed knowledge into latent spaces and make predictions from learned embeddings. However, existing approaches suffer from several limitations: Some models are not sufficiently expressive, and most are only designed to represent binary facts, and thus do not apply to general facts of higher arity. Moreover, existing models have limited support for capturing and/or incorporating prominent inference patterns, which are key to more principled completion. In this talk, we present a spatio-translational embedding model, called BoxE, that simultaneously addresses all the earlier limitations. BoxE embeds entities as points, and relations as a set of hyper-rectangles (or boxes), which spatially characterize basic logical properties. This seemingly simple abstraction yields a fully expressive model offering a natural encoding for many desired logical properties. BoxE can both capture and inject rules from rich classes of rule languages, going well beyond individual inference patterns, and naturally applies to higher-arity KBs. We will discuss all these theoretical properties, and also present a detailed experimental analysis, where we show that BoxE achieves state-of-the-art performance, both on standard benchmark knowledge graphs and on more general KBs.