LD²: Scalable Heterophilous Graph Neural Network with Decoupled Embeddings

Heterophilous Graph Neural Network (GNN) is a family of GNNs that specializes in learning graphs under heterophily, where connected nodes tend to have different labels. Most existing heterophilous models incorporate iterative non-local computations to capture node relationships. However, these approaches have limited application to large-scale graphs due to their high computational costs and challenges in adopting minibatch schemes. In this work, we study the scalability issues of heterophilous GNN and propose a scalable model, LD², which simplifies the learning process by decoupling graph propagation and generating expressive embeddings prior to training. Theoretical analysis demonstrates that LD² achieves optimal time complexity in training, as well as a memory footprint that remains independent of the graph scale. We conduct extensive experiments to showcase that our model is capable of lightweight minibatch training on large-scale heterophilous graphs, with up to 15× speed improvement and efficient memory utilization, while maintaining comparable or better performance than the baselines. Our code is available at: https://github.com/gdmnl/LD2.