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Revisiting the Message Passing in Heterophilous Graph Neural Networks

Zhuonan Zheng, Yuanchen Bei, Sheng Zhou, Yao Ma, Ming Gu, HongJia XU, Chengyu Lai, Jiawei Chen, Jiajun Bu

TL;DR

This work investigates why message passing can still be effective on heterophilous graphs and introduces a unified heterophilous message-passing (HTMP) framework that generalizes how multiple neighborhoods are aggregated, combined, and fused. It identifies the compatibility matrix (CM) among classes as the core driver of MP effectiveness, and argues that real-world incomplete/noisy semantic neighborhoods limit CM exploitation. To address this, the authors propose CMGNN, a CM-aware GNN that explicitly leverages and enhances CM through supplementary messages derived from prototype-based neighborhoods, guided by a discriminative CM loss. A new, fair benchmark with 10 datasets and 13 baselines demonstrates that HTMP and CMGNN achieve state-of-the-art results on diverse heterophily regimes, offering practical improvements for semi-supervised node classification on heterophilous graphs. The work also provides design guidelines and visualization tools to advance research in heterophilous GNNs.

Abstract

Graph Neural Networks (GNNs) have demonstrated strong performance in graph mining tasks due to their message-passing mechanism, which is aligned with the homophily assumption that adjacent nodes exhibit similar behaviors. However, in many real-world graphs, connected nodes may display contrasting behaviors, termed as heterophilous patterns, which has attracted increased interest in heterophilous GNNs (HTGNNs). Although the message-passing mechanism seems unsuitable for heterophilous graphs due to the propagation of class-irrelevant information, it is still widely used in many existing HTGNNs and consistently achieves notable success. This raises the question: why does message passing remain effective on heterophilous graphs? To answer this question, in this paper, we revisit the message-passing mechanisms in heterophilous graph neural networks and reformulate them into a unified heterophilious message-passing (HTMP) mechanism. Based on HTMP and empirical analysis, we reveal that the success of message passing in existing HTGNNs is attributed to implicitly enhancing the compatibility matrix among classes. Moreover, we argue that the full potential of the compatibility matrix is not completely achieved due to the existence of incomplete and noisy semantic neighborhoods in real-world heterophilous graphs. To bridge this gap, we introduce a new approach named CMGNN, which operates within the HTMP mechanism to explicitly leverage and improve the compatibility matrix. A thorough evaluation involving 10 benchmark datasets and comparative analysis against 13 well-established baselines highlights the superior performance of the HTMP mechanism and CMGNN method.

Revisiting the Message Passing in Heterophilous Graph Neural Networks

TL;DR

This work investigates why message passing can still be effective on heterophilous graphs and introduces a unified heterophilous message-passing (HTMP) framework that generalizes how multiple neighborhoods are aggregated, combined, and fused. It identifies the compatibility matrix (CM) among classes as the core driver of MP effectiveness, and argues that real-world incomplete/noisy semantic neighborhoods limit CM exploitation. To address this, the authors propose CMGNN, a CM-aware GNN that explicitly leverages and enhances CM through supplementary messages derived from prototype-based neighborhoods, guided by a discriminative CM loss. A new, fair benchmark with 10 datasets and 13 baselines demonstrates that HTMP and CMGNN achieve state-of-the-art results on diverse heterophily regimes, offering practical improvements for semi-supervised node classification on heterophilous graphs. The work also provides design guidelines and visualization tools to advance research in heterophilous GNNs.

Abstract

Graph Neural Networks (GNNs) have demonstrated strong performance in graph mining tasks due to their message-passing mechanism, which is aligned with the homophily assumption that adjacent nodes exhibit similar behaviors. However, in many real-world graphs, connected nodes may display contrasting behaviors, termed as heterophilous patterns, which has attracted increased interest in heterophilous GNNs (HTGNNs). Although the message-passing mechanism seems unsuitable for heterophilous graphs due to the propagation of class-irrelevant information, it is still widely used in many existing HTGNNs and consistently achieves notable success. This raises the question: why does message passing remain effective on heterophilous graphs? To answer this question, in this paper, we revisit the message-passing mechanisms in heterophilous graph neural networks and reformulate them into a unified heterophilious message-passing (HTMP) mechanism. Based on HTMP and empirical analysis, we reveal that the success of message passing in existing HTGNNs is attributed to implicitly enhancing the compatibility matrix among classes. Moreover, we argue that the full potential of the compatibility matrix is not completely achieved due to the existence of incomplete and noisy semantic neighborhoods in real-world heterophilous graphs. To bridge this gap, we introduce a new approach named CMGNN, which operates within the HTMP mechanism to explicitly leverage and improve the compatibility matrix. A thorough evaluation involving 10 benchmark datasets and comparative analysis against 13 well-established baselines highlights the superior performance of the HTMP mechanism and CMGNN method.
Paper Structure (55 sections, 45 equations, 5 figures, 9 tables)

This paper contains 55 sections, 45 equations, 5 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Revisiting Message Passing in Heterophilous GNNs.
  4. Why Does Message Passing Still Remain Effective in Heterophilous Graphs?
  5. Method
  6. Message Passing in CMGNN.
  7. Compatibility Matrix Estimation.
  8. Objective Function.
  9. Benchmarks and Experiments
  10. New Benchmark
  11. Drawbacks of Existing Datasets.
  12. Newly Organized Datasets.
  13. Baseline Methods.
  14. Main Results
  15. Ablation Study
  16. ...and 40 more sections

Figures (5)

  • Figure 1: Visualizations of the compatibility matrix and the example of distribution overlap.
  • Figure 2: The visualization of observed (Obs) and estimated (Est) compatibility matrixes.
  • Figure 3: The visualization of compatibility matrix on synthetic graphs.
  • Figure 4: The visualization of compatibility matrix on Amazon-Ratings.
  • Figure 5: The visualization of real and estimated CMs on other datasets.

Theorems & Definitions (1)

  • Definition 1