Abstract
Graph Neural Networks (GNNs) are powerful tools for learning on graph-structured data, often designed with an underlying assumption of homophily—that connected nodes share similar characteristics. This assumption, however, limits their effectiveness on heterophilic datasets where connected nodes tend to differ. We introduce a novel GNN architecture, Decoupled Polynomial Graph Filter GCN (DPGF-GCN), specifically designed to operate effectively across varying levels of graph homophily. Our approach leverages learnable polynomial graph filters but uniquely decouples the learning of feature transformation weights from the hop-wise aggregation coefficients. This design enhances model expressivity for heterophilic settings while maintaining robustness on homophilic graphs and mitigating oversmoothing. We provide theoretical justification for the model's permutation equivariance and utilize graph signal processing principles to analyze the learned filters, demonstrating their adaptability. Empirical results on benchmark datasets show that DPGF-GCN achieves competitive or superior performance compared to state-of-the-art methods on both homophilic and heterophilic node classification tasks.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Recommended Citation
"Decoupled Polynomial Graph Filters for Enhanced Adaptability in GNNs", Technical Disclosure Commons, (April 30, 2025)
https://www.tdcommons.org/dpubs_series/8051