LON-GNN: Spectral GNNs with Learnable Orthonormal Basis

TL;DR

LON-GNN introduces a spectral graph neural network with learnable orthonormal bases using Jacobi polynomials, addressing over-passing issues and improving performance on various graph tasks.

Contribution

This paper pioneers the use of learnable orthonormal bases in spectral GNNs with Jacobi polynomials, enhancing regularization and model flexibility.

Findings

LON-GNN outperforms existing spectral GNNs on multiple datasets.

Regularizing coefficients equates to regularizing the learned filter norm.

The method effectively addresses over-passing issues in spectral GNNs.

Abstract

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.