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（GNNs）通过从相邻节点收集信息，在异质性图上表现不佳。为解决该问题，研究者提出了多种方案，其中在异质性边上传播符号信息引起了广泛关注。近期有工作提供了理论分析，表明符号传播在二分类场景下总能提升性能。然而，我们注意到先前的分析与多分类基准数据集不完全吻合。本文针对多分类场景提出了对符号传播的新理解，并指出了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，符号传播会降低类别可分性；（2）参数更新：训练过程中符号邻居的预测不确定性（如冲突证据）会增大，从而影响算法稳定性。基于上述发现，我们提出了两种改进多分类图符号传播的新策略。该方案通过结合校准机制在降低不确定性的同时保证鲁棒性。我们在六个基准图数据集上的大量实验验证了所提定理的有效性。