Message-passing Graph Neural Networks (GNNs), which collect information from adjacent nodes achieve dismal performance on heterophilic graphs. Various schemes have been proposed to solve this problem, and propagating signed information on heterophilic edges has gained great attention. Recently, some works provided theoretical analysis that signed propagation always leads to performance improvement under a binary class scenario. However, we notice that prior analyses do not align well with multi-class benchmark datasets. This paper provides a new understanding of signed propagation for multi-class scenarios and points out two drawbacks in terms of message-passing and parameter update: (1) Message-passing: if two nodes belong to different classes but have a high similarity, signed propagation can decrease the separability. (2) Parameter update: the prediction uncertainty (e.g., conflict evidence) of signed neighbors increases during training, which can impede the stability of the algorithm. Based on the observation, we introduce two novel strategies for improving signed propagation under multi-class graphs. The proposed scheme combines calibration to secure robustness while reducing uncertainty. We show the efficacy of our theorem through extensive experiments on six benchmark graph datasets.

翻译：消息传递图神经网络通过从相邻节点收集信息，在异配图上表现不佳。已有多种方案被提出以解决此问题，其中在异配边上传播符号信息的方法受到广泛关注。近期研究表明，在二分类场景下符号传播总能带来性能提升的理论分析。然而，我们注意到现有分析与多类基准数据集存在明显偏差。本文对多类场景下的符号传播提出了新的理解，并指出其在消息传递和参数更新方面的两个缺陷：(1) 消息传递：若两个节点属于不同类别但具有高相似性，符号传播可能降低特征可分性；(2) 参数更新：带符号邻居的预测不确定性（如冲突证据）在训练过程中增加，可能影响算法稳定性。基于此观察，我们提出了两种改进多类图符号传播的新策略。该方案通过校准机制在保证鲁棒性的同时降低不确定性。我们在六个基准图数据集上的大量实验验证了所提理论的有效性。