Automated Polynomial Filter Learning for Graph Neural Networks

TL;DR

This paper introduces Auto-Polynomial, an automated framework for learning polynomial graph filters in GNNs, addressing overfitting issues and improving performance on diverse graph types.

Contribution

The paper proposes a novel automated learning framework for polynomial graph filters, enhancing their adaptability and effectiveness in GNNs across different graph signals.

Findings

Auto-Polynomial reduces overfitting in polynomial filter learning.

Significant performance improvements on homophilic and heterophilic graphs.

Consistent gains across various experimental settings.

Abstract

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.