Exploring Adaptive Structure Learning for Heterophilic Graphs

TL;DR

This paper introduces a structure learning approach to improve GCN performance on heterophilic graphs by rewiring edges to capture long-range dependencies, addressing limitations of traditional message-passing methods.

Contribution

The proposed method parameterizes the adjacency matrix to enable shallow GCNs to learn non-local connections, enhancing their ability to handle heterophilic graph structures.

Findings

Improves long-range dependency capturing in GCNs.

Addresses oversmoothing in shallow GCNs.

Performance varies depending on graph structure.

Abstract

Graph Convolutional Networks (GCNs) gained traction for graph representation learning, with recent attention on improving performance on heterophilic graphs for various real-world applications. The localized feature aggregation in a typical message-passing paradigm hinders the capturing of long-range dependencies between non-local nodes of the same class. The inherent connectivity structure in heterophilic graphs often conflicts with information sharing between distant nodes of same class. We propose structure learning to rewire edges in shallow GCNs itself to avoid performance degradation in downstream discriminative tasks due to oversmoothing. Parameterizing the adjacency matrix to learn connections between non-local nodes and extend the hop span of shallow GCNs facilitates the capturing of long-range dependencies. However, our method is not generalizable across heterophilic graphs and performs inconsistently on node classification task contingent to the graph structure.