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.

翻译：本文首次将知识图谱（KGs）形式化定义为一种新型图结构——双可交换属性图，其中节点表示和成对（联合双节点）表示必须对节点标识符和边（及节点）属性（关系与节点特征）的置换具有等变性。双置换等变的KG表示开辟了知识图谱研究的新方向。研究表明，这种等变性施加的关系结构表示，使得神经网络能够在KG中执行复杂逻辑推理任务。最后，我们提出此类等变表示的通用蓝图，并测试了一种基于简单图神经网络（GNN）的双置换等变神经架构。该架构在WN18RRv1和NELL995v1归纳式KG补全任务中均达到100%的Hits@10测试准确率，并且能够精确执行据我们所知现有方法无法实现的逻辑推理任务。