Remedying Coarsening-Based GNN Training under Heterophily via Adaptive Complementary Enhancement

2026-07-23

AI Summary

Existing graph coarsening methods suffer significant performance degradation on heterophilic graphs due to the loss of critical structural and feature information. This work proposes ACE (Adaptive Complementary Enhancement), a plug-and-play, model-agnostic strategy that mitigates this issue by learning a projector to reconstruct node features, incorporating an anisotropic structural regularizer to capture local heterophily, and adaptively weighting the primary coarsening loss and a global auxiliary loss via homoscedastic uncertainty. ACE is the first approach to systematically address information loss in heterophilic graph coarsening, achieving consistent performance gains across multiple heterophilic benchmarks while maintaining competitive results on homophilic graphs—all with minimal computational overhead.

Abstract

Coarsening-based training for graph neural networks (GNNs), i.e.\ training on coarsened graphs rather than the original large ones, has become a promising direction for scaling GNNs to massive graphs. However, prior work has been evaluated almost exclusively on \textit{homophilic} graphs, leaving the more challenging \textit{heterophilic} settings underexplored. We show, both empirically and theoretically, that existing coarsening-based training methods suffer significant performance degradation on heterophilic graphs due to inevitable loss of graph information during coarsening. To address this, we propose {\bf A}daptive {\bf C}omplementary {\bf E}nhancement, a plug-and-play, model-agnostic strategy that reintegrates the information discarded in coarsening: ACE learns a projector for re-constructing original node features and applies \textit{anisotropic structural regularization} to embed local heterophily. We further adopt \textit{homoscedastic uncertainty weighting} to adaptively balance the combined training objective of primary coarsened-graph training loss and full-graph auxiliary loss with augmented node features re-constructed by the heterophily-aware projector. Extensive experiments show that ACE drives consistent gains on heterophilic benchmarks while preserving competitive results on homophilic graphs with minimal computational overhead. Code is available at the GitHub repository: https://github.com/vasile-paskardlgm/ACE.

Problem

• graph coarsening
• heterophily
• graph neural networks
• information loss
• scalability

Innovation

• heterophily
• graph coarsening
• adaptive complementary enhancement
• anisotropic regularization
• homoscedastic uncertainty weighting