FCAD: Feature-Coupled Anisotropic Diffusion for Continuous Graph Learning

In this work, we propose a novel continuous graph neural network called FCAD (Feature-Coupled Anisotropic Diffusion) for the task of node classification on graphs. Our approach is motivated by the success of feature-coupled anisotropic diffusion PDEs in multivalued image restoration. Our method introduces a total variation regularization-inspired anisotropic term to control diffusion between nodes and incorporates a learnable parameterization for feature coupling during the diffusion process. Our model performs competitively against several GNN baselines for both heterophilous and homophilous graphs, demonstrating notable benefits for heterophilous graphs due to the learnable feature coupling.