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In recent years, a plethora of spectral graph neural networks (GNN) methodshave utilized polynomial basis with learnable coefficients to achieve top-tierperformances on many node-level tasks. Although various kinds of polynomialbases have been explored, each such method adopts a fixed polynomial basiswhich might not be the optimal choice for the given graph. Besides, we identifythe so-called over-passing issue of these methods and show that it is somewhatrooted 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, withLearnable OrthoNormal bases and prove that regularizing coefficients becomesequivalent to regularizing the norm of learned filter function now. We conductextensive experiments on diverse graph datasets to evaluate the fitting andgeneralization capability of LON-GNN, where the results imply its superiority.

LON-GNN: Spectral GNNs with Learnable Orthonormal Basis