Automated Polynomial Filter Learning for Graph Neural Networks

Recently, polynomial graph filter learning (PGFL) has demonstrated promising performance for modeling graph signals in Graph Neural Networks (GNNs) 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 PGFL, revealing a severe overfitting issue. To improve the effectiveness of PGFL, we propose Auto-Polynomial, a novel and general automated PGFL 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 PGFL.