Task-driven Heterophilic Graph Structure Learning

TL;DR

This paper introduces FgGSL, a novel end-to-end framework that learns both homophilic and heterophilic graph structures using spectral filtering and label-based loss, improving GNN performance on heterophilic graphs.

Contribution

It proposes a frequency-guided graph structure learning method that jointly infers complementary graph structures and provides robustness guarantees, advancing heterophilic graph learning.

Findings

FgGSL outperforms state-of-the-art GNNs on six heterophilic benchmarks.

The method effectively combines frequency information with supervised topology inference.

The framework demonstrates stability and robustness under graph perturbations.

Abstract

Graph neural networks (GNNs) often struggle to learn discriminative node representations for heterophilic graphs, where connected nodes tend to have dissimilar labels and feature similarity provides weak structural cues. We propose frequency-guided graph structure learning (FgGSL), an end-to-end graph inference framework that jointly learns homophilic and heterophilic graph structures along with a spectral encoder. FgGSL employs a learnable, symmetric, feature-driven masking function to infer said complementary graphs, which are processed using pre-designed low- and high-pass graph filter banks. A label-based structural loss explicitly promotes the recovery of homophilic and heterophilic edges, enabling task-driven graph structure learning. We derive stability bounds for the structural loss and establish robustness guarantees for the filter banks under graph perturbations. Experiments on six heterophilic benchmarks demonstrate that FgGSL consistently outperforms state-of-the-art GNNs and graph rewiring methods, highlighting the benefits of combining frequency information with supervised topology inference.