Faithful Differentiable Reasoning with Reshuffled Region-based Embeddings

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.