🤖 AI Summary
Existing low-order spectral graph neural networks suffer from insufficient spectral selectivity, while high-order models face challenges in optimization and high computational complexity. This work proposes DCQ-GNN, which introduces explicit convex-concave quadratic curvature into spectral GNN design for the first time. By constructing adaptive convex-concave quadratic filter banks, the method enhances spectral selectivity through complementary curvature while preserving second-order structural information. A node-adaptive gating mechanism further enables structure-aware spectral responses. DCQ-GNN achieves spectral selectivity comparable to high-order models at a lower computational cost, while ensuring optimization stability and robustness. Experiments show that DCQ-GNN achieves the best average ranking across ten datasets—tied for first on heterophilic graphs and second on homophilic graphs—and exhibits significantly less performance degradation under strong structural perturbations compared to existing baselines.
📝 Abstract
Spectral graph neural networks (GNNs) interpret message passing as frequency-selective filtering. While low-order spectral filters are efficient, their limited selectivity often leads to weak attenuation outside the passband, whereas high-order alternatives introduce optimization challenges. We propose DCQ-GNN, a spectral GNN based on a compact bank of adaptive convex--concave quadratic filters. By restricting the filter order to two while explicitly exploiting complementary curvature, DCQ-GNN improves spectral selectivity as quantified by Dirichlet energy and entropy measures without resorting to high-order polynomial expansions. The model fuses filter outputs through a node-adaptive gating mechanism to enable node-wise structure-aware spectral selection. We provide a formal spectral analysis grounded in Dirichlet energy attenuation, von Neumann entropy, and curvature polarity, and derive explicit characterizations of filter behavior across varying levels of homophily and structural perturbations. Extensive benchmarks on 10 datasets show that DCQ-GNN ties for the top average rank (3.0) on heterophilic graphs and obtains the second-best rank (4.2) on homophilic graphs, remaining competitive with representative high-order polynomial spectral filters. Furthermore, under strong structural perturbations, DCQ-GNN exhibits substantially smaller performance degradation compared to both first-order and high-order baselines. These results demonstrate that curvature-aware quadratic banks provide a robust and efficient alternative to high-order spectral models while preserving optimization stability and computational efficiency.