Polynomial graph filters have been widely used as guiding principles in the design of Graph Neural Networks (GNNs). Recently, the adaptive learning of the polynomial graph filters has demonstrated promising performance for modeling graph signals on both homophilic and heterophilic graphs, owning to their flexibility and expressiveness. In this work, we conduct a novel preliminary study to explore the potential and limitations of polynomial graph filter learning approaches, revealing a severe overfitting issue. To improve the effectiveness of polynomial graph filters, we propose Auto-Polynomial, a novel and general automated polynomial graph filter learning framework that efficiently learns better filters capable of adapting to various complex graph signals. Comprehensive experiments and ablation studies demonstrate significant and consistent performance improvements on both homophilic and heterophilic graphs across multiple learning settings considering various labeling ratios, which unleashes the potential of polynomial filter learning.

翻译：多项式图滤波器已被广泛用作图神经网络设计中的指导原则。近年来，多项式图滤波器的自适应学习因其灵活性与表达能力，在同质性图与异质性图上建模图信号方面展现出令人瞩目的性能。本研究开展了一项新颖的初步探索，旨在揭示多项式图滤波器学习方法的潜力与局限性，并发现其存在严重的过拟合问题。为提升多项式图滤波器的有效性，我们提出Auto-Polynomial——一种新颖且通用的自动化多项式图滤波器学习框架，能够高效学习出适应各类复杂图信号的更优滤波器。全面的实验与消融研究表明，在同质性图与异质性图上，考虑不同标注比例的多学习设置下均取得了显著且一致的性能提升，从而释放了多项式滤波器学习的潜力。