Learning the Graph and the Embedding Together: Classifier-Independent Rewiring for Heterophilic Node Classification

2026-09-26

AI Summary

This study addresses the significant performance degradation of Graph Neural Networks on heterophilic graphs and the difficulty of existing rewiring methods in decoupling topological contributions from downstream classifiers. To overcome these limitations, this work proposes an affinity-guided rewiring framework that jointly learns graph structure and node embeddings via EM-style alternating optimization. By integrating modularity objectives, pseudo-label homophily, and contrastive learning, the method generates structural representations independent of downstream classifiers while supporting a fully unsupervised variant. This research reveals the complementary mechanisms between graph structure and embeddings. Extensive experiments across six benchmarks demonstrate an average accuracy improvement of 5.8% and a fourfold reduction in variance across different classifiers, effectively enhancing both homophily and robustness for downstream tasks.

Abstract

Graph neural networks lose much of their advantage on heterophilic graphs, where connected nodes often carry different labels. Graph rewiring is a popular remedy, but rewiring methods are usually evaluated with a single classifier, which makes it hard to tell whether the gains come from the new topology or from that particular pairing. We propose an affinity-guided rewiring method that estimates the graph and the node representation together. It alternates, in the spirit of expectation maximisation, between training a lightweight graph neural network on the current graph and re-weighting candidate edges under a modularity objective with a pseudo-label homophily term. Candidate edges come from a compact pool scored by a contrastively learned node similarity and a neighbourhood-distribution affinity. The method returns two classifier-independent outputs: a rewired graph and a node embedding learned on it. Across six heterophilic benchmarks and five downstream classifiers, it improves accuracy over the original graph with normalised features in 23 of 30 classifier-dataset combinations, with a mean gain of 5.8 points, and reduces the accuracy spread between classifiers about fourfold. A controlled ablation shows that the two outputs are each useful and play complementary roles: the embedding contributes most of the accuracy gain, while the rewired graph makes different classifiers agree. A fully unsupervised variant, which uses no labels during rewiring, retains most of the improvement. The rewired graphs are also more homophilic and improve label propagation and community detection.

Problem

• heterophilic graphs
• graph rewiring
• classifier-independent
• graph neural networks
• node classification

Innovation

• Graph Rewiring
• Heterophilic Graphs
• Expectation Maximisation
• Contrastive Learning
• Classifier-Independent