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，在众多节点级任务中取得了顶尖性能。尽管已有多种多项式基被探索，但每种方法均采用固定多项式基，这对于给定图未必是最优选择。此外，我们发现了这些方法所谓的"过传递"问题，并指出其根源在于缺乏规范化的正则化策略及非归一化基。本文首次尝试解决这两个问题。利用雅可比多项式，我们设计了一种名为LON-GNN的新型谱图神经网络，具有可学习正交基，并证明了此时正则化系数等价于正则化所学滤波器函数的范数。我们在多种图数据集上进行了广泛实验，以评估LON-GNN的拟合与泛化能力，结果表明其优越性。