Double Permutation Equivariance for Knowledge Graph Completion

This work provides a formalization of Knowledge Graphs (KGs) as a new class of graphs that we denote doubly exchangeable attributed graphs, where node and pairwise (joint 2-node) representations must be equivariant to permutations of both node ids and edge (& node) attributes (relations & node features). Double-permutation equivariant KG representations open a new research direction in KGs. We show that this equivariance imposes a structural representation of relations that allows neural networks to perform complex logical reasoning tasks in KGs. Finally, we introduce a general blueprint for such equivariant representations and test a simple GNN-based double-permutation equivariant neural architecture that achieve state-of-the-art Hits@10 test accuracy in the WN18RR, FB237 and NELL995 inductive KG completion tasks, and can accurately perform logical reasoning tasks that no existing methods can perform, to the best of our knowledge.