Beyond Low-frequency Information in Graph Convolutional Networks

TL;DR

This paper investigates the importance of high-frequency signals in graph neural networks and introduces FAGCN, a novel model that adaptively integrates signals beyond low-frequency information to improve node representations.

Contribution

The paper proposes FAGCN, a frequency adaptation GCN with a self-gating mechanism, enabling adaptive integration of diverse frequency signals in message passing.

Findings

FAGCN alleviates over-smoothing in GNNs

FAGCN outperforms state-of-the-art methods on real-world networks

Theoretical analysis explains the effectiveness of high-frequency signals

Abstract

Graph neural networks (GNNs) have been proven to be effective in various network-related tasks. Most existing GNNs usually exploit the low-frequency signals of node features, which gives rise to one fundamental question: is the low-frequency information all we need in the real world applications? In this paper, we first present an experimental investigation assessing the roles of low-frequency and high-frequency signals, where the results clearly show that exploring low-frequency signal only is distant from learning an effective node representation in different scenarios. How can we adaptively learn more information beyond low-frequency information in GNNs? A well-informed answer can help GNNs enhance the adaptability. We tackle this challenge and propose a novel Frequency Adaptation Graph Convolutional Networks (FAGCN) with a self-gating mechanism, which can adaptively integrate different signals in the process of message passing. For a deeper understanding, we theoretically analyze the roles of low-frequency signals and high-frequency signals on learning node representations, which further explains why FAGCN can perform well on different types of networks. Extensive experiments on six real-world networks validate that FAGCN not only alleviates the over-smoothing problem, but also has advantages over the state-of-the-arts.