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.

翻译：近年来，大量谱图神经网络方法利用具有可学习系数的多项式基，在许多节点级任务上取得了顶尖性能。尽管已有多种多项式基被探索，但每种方法都采用固定的多项式基，这未必是给定图的最优选择。此外，我们识别出这些方法中所谓的"过传递"问题，并表明该问题在一定程度上源于其缺乏原则性的正则化策略以及未归一化的基。本文首次尝试解决这两个问题。利用雅可比多项式，我们设计了一种新颖的谱图神经网络LON-GNN，其具有可学习正交基，并证明了此时对系数进行正则化等价于对学习滤波函数的范数进行正则化。我们在多样化的图数据集上进行了广泛实验，评估了LON-GNN的拟合与泛化能力，结果证明了其优越性。