Knowledge Graph Embedding by Normalizing Flows

A key to knowledge graph embedding (KGE) is choose a proper representation space, e.g., point-wise Euclidean space and complex vector space. In this paper, we propose unified perspective of introduce uncertainty into KGE from the view group theory. Our model can incorporate existing models (i.e., generality), ensure computation tractable efficiency) enjoy expressive power random variables expressiveness). The core idea that embed entities/relations as elements symmetric group, i.e., permutations set. Permutations different sets reflect properties embedding. And operation groups easy compute. specific, show many models, point vectors, be seen group. To uncertainty, first set variables. permutation transform simple variable for greater expressiveness, called normalizing flow. We then define scoring functions by measuring similarity two flows, namely NFE. construct several instantiating prove they are able learn logical rules. Experimental results demonstrate effectiveness introducing our model. code available at https://github.com/changyi7231/NFE.