TopoAttn-Nets: Topological Attention in Graph Representation Learning

Abstract

Topological characteristics of graphs, that is, properties that are invariant under continuous transformations, have recently emerged as a new alternative form of graph descriptors which tend boost performance of graph neural networks (GNNs) on a wide range of graph learning tasks, from node classification to link prediction. Furthermore, GNNs coupled with such topological information tend to be more robust to attacks and perturbations. However, all prevailing topological methods for GNNs consider a scenario of a fixed learning approach and do not allow for distinguishing between topological noise and topological signatures of the graph which might be the most valuable for the current learning task. To exploit the inherent task-specific topological graph descriptors, we propose a new versatile framework known as Topological Attention Neural Networks (TopoAttn-Nets) (Our code is available at https://github.com/TopoAttn-Nets/TopoAttn-Nets.git ). As the first meta-representation of topological knowledge, TopoAttn-Nets employs the attention operation on both local and global data properties and offers their geometric augmentation. We derive theoretical guarantees of the proposed topological learning framework and evaluate TopoAttn-Nets in conjunction with graph classification. TopoAttn-Nets delivers the highest accuracy, outperforming 26 state-of-the-art classifiers on benchmark datasets.