  In recent years, algebraic topology and its modern development, the theory of
persistent homology, has shown great potential in graph representation
learning. In this paper, based on the mathematics of algebraic topology, we
propose a novel solution for inductive relation prediction, 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 view rules as paths and primarily focus on the
searching of paths 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 benchmarks.
