New GNN Filter Improves Spectral Selectivity and Robustness

Researchers have developed a novel spectral graph neural network (GNN) called DCQ-GNN, which addresses limitations of existing spectral filters. Traditional low-order filters often lack sufficient selectivity, while high-order alternatives introduce optimization challenges. DCQ-GNN employs a compact bank of adaptive convex-concave quadratic filters, restricting the filter order to two while leveraging complementary curvature. This approach significantly improves spectral selectivity, as measured by Dirichlet energy and entropy, without resorting to complex high-order polynomial expansions. The model also incorporates a node-adaptive gating mechanism to fuse filter outputs, enabling structure-aware spectral selection at the node level. Extensive benchmarks across ten datasets demonstrate that DCQ-GNN performs exceptionally well on heterophilic graphs and remains competitive on homophilic graphs, outperforming many baselines, particularly in scenarios with strong structural perturbations.