GPatcher: A Simple and Adaptive MLP Model for Alleviating Graph Heterophily

TL;DR

GPatcher is a novel adaptive MLP-based GNN that effectively handles graph heterophily by transforming node representations and combining local and global information, leading to superior node classification performance.

Contribution

The paper introduces GPatcher, a simple adaptive GNN leveraging MLP-Mixer architecture, designed to address graph heterophily with theoretical backing and practical effectiveness.

Findings

GPatcher outperforms existing GNNs on heterophilous graphs.

Theoretical analysis confirms the importance of adaptive polynomial filters.

Extensive experiments validate GPatcher's superior performance.

Abstract

While graph heterophily has been extensively studied in recent years, a fundamental research question largely remains nascent: How and to what extent will graph heterophily affect the prediction performance of graph neural networks (GNNs)? In this paper, we aim to demystify the impact of graph heterophily on GNN spectral filters. Our theoretical results show that it is essential to design adaptive polynomial filters that adapts different degrees of graph heterophily to guarantee the generalization performance of GNNs. Inspired by our theoretical findings, we propose a simple yet powerful GNN named GPatcher by leveraging the MLP-Mixer architectures. Our approach comprises two main components: (1) an adaptive patch extractor function that automatically transforms each node's non-Euclidean graph representations to Euclidean patch representations given different degrees of heterophily, and (2) an efficient patch mixer function that learns salient node representation from both the local context information and the global positional information. Through extensive experiments, the GPatcher model demonstrates outstanding performance on node classification compared with popular homophily GNNs and state-of-the-art heterophily GNNs.