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.

翻译：本工作将知识图谱形式化为一种新类型的图，我们称之为“双可交换属性图”。在这类图中，节点表示和成对（联合二节点）表示必须对节点编号和边属性（关系）与节点属性的置换同时具有等变性。双重置换等变的知识图谱表示开辟了知识图谱研究的新方向。我们证明，这种等变性强制了关系的结构化表示，使神经网络能够在知识图谱中执行复杂的逻辑推理任务。最后，我们提出了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的（GNN）双重置换等变神经架构。该架构在WN18RR、FB237和NELL995归纳式知识图谱补全任务中取得了最新的Hits@10测试准确率，并且据我们所知，能够精确执行现有方法无法实现的逻辑推理任务。