Graph neural networks (GNNs) have become a powerful tool for processing graph-structured data but still face challenges in effectively aggregating and propagating information between layers, which limits their performance. We tackle this problem with the kernel regression (KR) approach, using KR loss as the primary loss in self-supervised settings or as a regularization term in supervised settings. We show substantial performance improvements compared to state-of-the-art in both scenarios on multiple transductive and inductive node classification datasets, especially for deep networks. As opposed to mutual information (MI), KR loss is convex and easy to estimate in high-dimensional cases, even though it indirectly maximizes the MI between its inputs. Our work highlights the potential of KR to advance the field of graph representation learning and enhance the performance of GNNs. The code to reproduce our experiments is available at https://github.com/Anonymous1252022/KR_for_GNNs

翻译：图神经网络（GNNs）已成为处理图结构数据的强大工具，但在层间有效聚合与传播信息方面仍面临挑战，这限制了其性能。我们采用核回归（KR）方法解决该问题，将KR损失作为自监督场景下的主损失函数或监督场景下的正则化项。在多个直推式与归纳式节点分类数据集上的实验表明，与当前最优方法相比，我们的方案在两个场景下均实现了显著性能提升，尤其适用于深层网络。与互信息（MI）不同，KR损失具有凸性且易于在高维情况下估计，尽管它间接最大化其输入间的互信息。本工作凸显了KR推动图表示学习领域发展及提升GNNs性能的潜力。可复现实验的代码已开源：https://github.com/Anonymous1252022/KR_for_GNNs