  In recent years, a plethora of spectral graph neural networks (GNN) methods
have utilized polynomial basis with learnable coefficients to achieve top-tier
performances on many node-level tasks. Although various kinds of polynomial
bases have been explored, each such method adopts a fixed polynomial basis
which might not be the optimal choice for the given graph. Besides, we identify
the so-called over-passing issue of these methods and show that it is somewhat
rooted in their less-principled regularization strategy and unnormalized basis.
In this paper, we make the first attempts to address these two issues.
Leveraging Jacobi polynomials, we design a novel spectral GNN, LON-GNN, with
Learnable OrthoNormal bases and prove that regularizing coefficients becomes
equivalent to regularizing the norm of learned filter function now. We conduct
extensive experiments on diverse graph datasets to evaluate the fitting and
generalization capability of LON-GNN, where the results imply its superiority.
