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 100% Hits@10 test accuracy in both the WN18RRv1 and NELL995v1 inductive KG completion tasks, and can accurately perform logical reasoning tasks that no existing methods can perform, to the best of our knowledge.