In the semi-supervised setting where labeled data are largely limited, it remains to be a big challenge for message passing based graph neural networks (GNNs) to learn feature representations for the nodes with the same class label that is distributed discontinuously over the graph. To resolve the discontinuous information transmission problem, we propose a control principle to supervise representation learning by leveraging the prototypes (i.e., class centers) of labeled data. Treating graph learning as a discrete dynamic process and the prototypes of labeled data as "desired" class representations, we borrow the pinning control idea from automatic control theory to design learning feedback controllers for the feature learning process, attempting to minimize the differences between message passing derived features and the class prototypes in every round so as to generate class-relevant features. Specifically, we equip every node with an optimal controller in each round through learning the matching relationships between nodes and the class prototypes, enabling nodes to rectify the aggregated information from incompatible neighbors in a graph with strong heterophily. Our experiments demonstrate that the proposed PCGCN model achieves better performances than deep GNNs and other competitive heterophily-oriented methods, especially when the graph has very few labels and strong heterophily.

翻译：在半监督场景下，当标注数据极为有限时，基于消息传递的图神经网络（GNN）难以学习图上同类标签节点（这些节点分布不连续）的特征表示。为解决这种不连续信息传递问题，我们提出了一种控制原理，通过利用标注数据的原型（即类别中心）来监督表示学习。将图学习视为离散动态过程，并将标注数据的原型视为"期望"的类别表示，我们借鉴自动控制理论中的牵制控制思想，为特征学习过程设计学习反馈控制器，旨在最小化每轮消息传递所得特征与类别原型之间的差异，从而生成类别相关特征。具体而言，我们通过学习节点与类别原型之间的匹配关系，为每个节点配备每轮最优控制器，使节点能够在强异配性图中纠正来自不兼容邻居的聚合信息。实验表明，所提出的PCGCN模型在性能上优于深度GNN及其他竞争性异配导向方法，尤其在标签极少且异配性强的图场景中表现更为突出。