The graph Laplacian regularization term is usually used in semi-supervised
representation learning to provide graph structure information for a model
$f(X)$. However, with the recent popularity of graph neural networks (GNNs),
directly encoding graph structure $A$ into a model, i.e., $f(A, X)$, has become
the more common approach. While we show that graph Laplacian regularization
brings little-to-no benefit to existing GNNs, and propose a simple but
non-trivial variant of graph Laplacian regularization, called
Propagation-regularization (P-reg), to boost the performance of existing GNN
models. We provide formal analyses to show that P-reg not only infuses extra
information (that is not captured by the traditional graph Laplacian
regularization) into GNNs, but also has the capacity equivalent to an
infinite-depth graph convolutional network. We demonstrate that P-reg can
effectively boost the performance of existing GNN models on both node-level and
graph-level tasks across many different datasets.

在图神经网络中，传统的图拉普拉斯正则化对现有 GNN 的性能提升不大，提出了一种名叫 P-reg 的图拉普拉斯正则化变体，可以有效增加信息熵，提升现有 GNN 模型在节点级和图级任务上的性能。