Convex--Concave Quadratic Spectral Filtering for Graph Neural Networks

A spectral graph neural network that relies on second-order adaptive filters rather than high-order polynomial expansions has been proposed, matching or exceeding the performance of more complex models across ten benchmark datasets while showing greater resilience to structural noise. The model, called DCQ-GNN, uses a compact bank of convex–concave quadratic filters to perform frequency-selective message passing on graph-structured data [1][2]. By restricting the filter order to two and explicitly exploiting complementary curvature, the architecture improves spectral selectivity as measured by Dirichlet energy and von Neumann entropy without resorting to high-order expansions [2]. A node-adaptive gating mechanism fuses filter outputs, enabling each node to make structure-aware spectral selections [2]. On heterophilic graphs—where connected nodes tend to have different labels—DCQ-GNN tied for the top average rank of 3.0 across the tested datasets [2]. On homophilic graphs, it achieved an average rank of 4.2, placing it second among the evaluated models [2]. The authors report that the model remained competitive with representative high-order polynomial spectral filters in both settings [2]. Under strong structural perturbations, DCQ-GNN exhibited substantially smaller performance degradation compared to both first-order and high-order baselines [2]. The formal spectral analysis accompanying the model derives explicit characterizations of filter behavior across varying levels of homophily and structural perturbation, using Dirichlet energy attenuation, von Neumann entropy, and curvature polarity as analytical tools [2]. The work was posted on arXiv, the open-access e-print repository that hosts preprints across physics, mathematics, computer science, and related fields [6]. As of November 2024, the repository receives roughly 24,000 new articles per month and has surpassed two million total submissions since its founding in 1991 [6]. Papers on arXiv are moderated but not peer-reviewed before posting [6].