Sign is Not a Remedy: Multiset-to-Multiset Message Passing for Learning on Heterophilic Graphs

TL;DR

This paper critically examines Signed Message Passing in heterophilic graph neural networks, identifies its limitations, and introduces a novel Multiset to Multiset GNN to improve performance and address these issues.

Contribution

It provides the first theoretical and empirical analysis of SMP's limitations and proposes M2M-GNN, a new message passing framework that overcomes these challenges.

Findings

M2M-GNN alleviates oversmoothing issues

It outperforms existing SMP-based methods

Theoretical analysis confirms effectiveness

Abstract

Graph Neural Networks (GNNs) have gained significant attention as a powerful modeling and inference method, especially for homophilic graph-structured data. To empower GNNs in heterophilic graphs, where adjacent nodes exhibit dissimilar labels or features, Signed Message Passing (SMP) has been widely adopted. However, there is a lack of theoretical and empirical analysis regarding the limitations of SMP. In this work, we unveil some potential pitfalls of SMP and their remedies. We first identify two limitations of SMP: undesirable representation update for multi-hop neighbors and vulnerability against oversmoothing issues. To overcome these challenges, we propose a novel message passing function called Multiset to Multiset GNN(M2M-GNN). Our theoretical analyses and extensive experiments demonstrate that M2M-GNN effectively alleviates the aforementioned limitations of SMP, yielding superior performance in comparison