In graph neural networks (GNNs), both node features and labels are examples of graph signals, a key notion in graph signal processing (GSP). While it is common in GSP to impose signal smoothness constraints in learning and estimation tasks, it is unclear how this can be done for discrete node labels. We bridge this gap by introducing the concept of distributional graph signals. In our framework, we work with the distributions of node labels instead of their values and propose notions of smoothness and non-uniformity of such distributional graph signals. We then propose a general regularization method for GNNs that allows us to encode distributional smoothness and non-uniformity of the model output in semi-supervised node classification tasks. Numerical experiments demonstrate that our method can significantly improve the performance of most base GNN models in different problem settings.

翻译：在图神经网络（GNN）中，节点特征与标签同为图信号，这是图信号处理（GSP）中的关键概念。尽管在GSP中，对学习与估计任务施加信号平滑性约束是常见做法，但如何对离散节点标签实现这一约束尚不明确。我们通过引入分布图信号的概念弥合了这一差距。在该框架中，我们基于节点标签的分布而非其具体数值开展工作，并提出此类分布图信号的平滑性与非均匀性概念。随后，我们提出了一种适用于GNN的通用正则化方法，能够在半监督节点分类任务中编码模型输出的分布平滑性与非均匀性。数值实验表明，该方法可在不同问题设定下显著提升多数基础GNN模型的性能。