Unifying Homophily and Heterophily for Spectral Graph Neural Networks via Triple Filter Ensembles

Polynomial-based learnable spectral graph neural networks (GNNs) utilize polynomial to approximate graph convolutions and have achieved impressive performance on graphs. Nevertheless, there are three progressive problems to be solved. Some models use polynomials with better approximation for approximating filters, yet perform worse on real-world graphs. Carefully crafted graph learning methods, sophisticated polynomial approximations, and refined coefficient constraints leaded to overfitting, which diminishes the generalization of the models. How to design a model that retains the ability of polynomial-based spectral GNNs to approximate filters while it possesses higher generalization and performance?