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Message-passing Graph Neural Networks (GNNs), which collect information fromadjacent nodes achieve dismal performance on heterophilic graphs. Variousschemes have been proposed to solve this problem, and propagating signedinformation on heterophilic edges has gained great attention. Recently, someworks provided theoretical analysis that signed propagation always leads toperformance improvement under a binary class scenario. However, we notice thatprior analyses do not align well with multi-class benchmark datasets. Thispaper provides a new understanding of signed propagation for multi-classscenarios and points out two drawbacks in terms of message-passing andparameter update: (1) Message-passing: if two nodes belong to different classesbut have a high similarity, signed propagation can decrease the separability.(2) Parameter update: the prediction uncertainty (e.g., conflict evidence) ofsigned neighbors increases during training, which can impede the stability ofthe algorithm. Based on the observation, we introduce two novel strategies forimproving signed propagation under multi-class graphs. The proposed schemecombines calibration to secure robustness while reducing uncertainty. We showthe efficacy of our theorem through extensive experiments on six benchmarkgraph datasets.

Improving Signed Propagation for Graph Neural Networks in Multi-Class Environments