Link prediction with physics-inspired graph neural networks

The message-passing mechanism underlying Graph Neural Networks (GNNs) is not naturally suited for heterophilic datasets, where adjacent nodes often have different labels. Most solutions to this problem remain confined to the task of node classification. In this article, we focus on the valuable task of link prediction under heterophily, an interesting problem for recommendation systems, social network analysis, and other applications. GNNs like GRAFF have improved node classification under heterophily by incorporating physics biases in the architecture. Similarly, we propose GRAFF-LP, an extension of GRAFF for link prediction. We show that GRAFF-LP effectively discriminates existing from non-existing edges by learning implicitly to separate the edge gradients. Based on this information, we propose a new readout function inspired by physics. Remarkably, this new function not only enhances the performance of GRAFF-LP but also improves that of other baseline models, leading us to reconsider how every link prediction experiment has been conducted so far. Finally, we provide evidence that even simple GNNs did not experience greater difficulty in predicting heterophilic links compared to homophilic ones. This leads us to believe in the necessity for heterophily measures specifically tailored for link prediction, distinct from those used in node classification. The code and appendix are available at https://github.com/difra100/Link_Prediction_with_PIGNN_IJCNN.