Cycle Representation Learning for Inductive Relation Prediction

TL;DR

This paper introduces a novel algebraic topology-based method for inductive relation prediction in knowledge graphs, utilizing cycle spaces and GNNs to improve efficiency and accuracy.

Contribution

It models rules as cycles using algebraic topology, enabling efficient rule search and improved relation prediction with a new GNN framework.

Findings

Achieves state-of-the-art performance on benchmark datasets.

Efficiently searches for rules using the cycle space structure.

Outperforms previous path-based methods in accuracy and speed.

Abstract

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.