Task-driven Heterophilic Graph Structure Learning

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.

Figures (6)

• Figure 1: Distribution of cosine similarities of node features ${{\mathbf{x}}}$ for node pairs in the Texas (left) and Cornell (right) heterophilic datasets. Homophilic pairs (same labels) and heterophilic pairs (different labels) both exhibit overlapping distributions, implying that feature similarity alone is insufficient to recover graph structures.
• Figure 2: Illustration of a homophilic graph (left), and a heterophilic graph (right). The color of the nodes indicates their labels.
• Figure 3: FgGSL framework: Node features ${\mathbf{X}}$ generate two parameterized graph structures by masking a fully connected adjacency matrix ${\mathbf{A}}_f$ with learnable functions $S_{\theta_1}$ and $S_{\theta_2}$. The homophilic graph ${\mathbf{S}}_{Ho} \odot {\mathbf{A}}_f$ uses a low-pass filter bank, while the heterophilic graph ${\mathbf{S}}_{Ht} \odot {\mathbf{A}}_f$ employs a high-pass filter bank. Filter outputs ${\mathbf{H}}_{Ho,j}$ and ${\mathbf{H}}_{Ht,j}$ at different scales are concatenated and passed through a linear layer with softmax to produce class probabilities $\hat{{\mathbf{Y}}}$.
• Figure 4: Filter-bank frequency responses: Filters from filter bank-$L$ preserve information from the lower end of the spectrum (blue), while filters from filter bank-$H$ preserve information from the higher end of the spectrum (red).
• Figure 5: Mean accuracy of different variants of the model.

Theorems & Definitions (1)

• Proposition 1