How Universal Polynomial Bases Enhance Spectral Graph Neural Networks: Heterophily, Over-smoothing, and Over-squashing

Understand

Spectral Graph Neural Networks (GNNs), alternatively known as graph filters, have gained increasing prevalence for heterophily graphs.

• Optimal graph filters rely on Laplacian eigendecomposition for Fourier transform.
• In an attempt to avert prohibitive computations, numerous polynomial filters have been proposed.
• However, polynomials in the majority of these filters are predefined and remain fixed across different graphs, failing to accommodate the varying degrees of heterophily.