Beyond Binary: Improving Signed Message Passing in Graph Neural Networks for Multi-Class Graphs

Graph Neural Networks (GNNs) exhibit satisfactory performance on homophilic networks, where most edges connect two nodes with the same label. However, their effectiveness diminishes as the graphs become heterophilic (low homophily), prompting the exploration of various message-passing schemes. In particular, assigning negative weights to heterophilic edges (signed propagation) for message-passing has gained significant attention, and some studies theoretically confirm its effectiveness. Nevertheless, prior theorems assume binary classification scenarios, which may not hold well for graphs with multiple classes. To solve this limitation, we offer new theoretical insights into GNNs in multi-class environments and identify the drawbacks of employing signed propagation from two perspectives: message-passing and parameter update. We found that signed propagation without considering feature distribution can degrade the separability of dissimilar neighbors, which also increases prediction uncertainty (e.g., conflicting evidence) that can cause instability. To address these limitations, we introduce two novel calibration strategies aiming to improve discrimination power while reducing entropy in predictions. Through theoretical and extensive experimental analysis, we demonstrate that the proposed schemes enhance the performance of both signed and general message-passing neural networks (Choi et al. 2023).