Keywords: Inductive Relation Prediction, Topological Data Analysis, Cycle Basis, Homology
Abstract: Inductive relation prediction is an important learning task for knowledge graph completion. To predict the relation between two entities, one can use the existence of rules, namely a sequence of relations. Previous works primarily focus on searching the rules between entities. The space of rules is huge, and one has to sacrifice either efficiency or accuracy. In this paper, we consider rules as cycles and show that the space of cycles has a unique structure based on the mathematics of algebraic topology. By exploring the linear structure of the cycle space, we can improve the searching efficiency of rules. We propose to collect cycle bases that span the space of cycles. We build a novel GNN framework on the collected cycles to learn the representations of cycles, and to predict the existence/non-existence of a relation. Our method achieves state-of-the-art performance on popular benchmarks.