Capturing Knowledge Graphs and Rules with Octagon Embeddings

Region based knowledge graph embeddings represent relations as geometric regions. This has the advantage that the rules which are captured by the model are made explicit, making it straightforward to incorporate prior knowledge and to inspect learned models. Unfortunately, existing approaches are severely restricted in their ability to model relational composition, and hence also their ability to model rules, thus failing to deliver on the main promise of region based models. With the aim of addressing these limitations, we investigate regions which are composed of axis-aligned octagons. Such octagons are particularly easy to work with, as intersections and compositions can be straightforwardly computed, while they are still sufficiently expressive to model arbitrary knowledge graphs. Among others, we also show that our octagon embeddings can properly capture a non-trivial class of rule bases. Finally, we show that our model achieves competitive experimental results.