Numerous recent research on graph neural networks (GNNs) has focused on formulating GNN architectures as an optimization problem with the smoothness assumption. However, in node classification tasks, the smoothing effect induced by GNNs tends to assimilate representations and over-homogenize labels of connected nodes, leading to adverse effects such as over-smoothing and misclassification. In this paper, we propose a novel bilevel optimization framework for GNNs inspired by the notion of Bregman distance. We demonstrate that the GNN layer proposed accordingly can effectively mitigate the over-smoothing issue by introducing a mechanism reminiscent of the "skip connection". We validate our theoretical results through comprehensive empirical studies in which Bregman-enhanced GNNs outperform their original counterparts in both homophilic and heterophilic graphs. Furthermore, our experiments also show that Bregman GNNs can produce more robust learning accuracy even when the number of layers is high, suggesting the effectiveness of the proposed method in alleviating the over-smoothing issue.

翻译：近年来，大量关于图神经网络（GNN）的研究致力于将GNN架构建模为基于平滑性假设的优化问题。然而，在节点分类任务中，GNN引发的平滑效应倾向于同化连接节点的表示并过度同质化其标签，从而导致过平滑和误分类等不利影响。受Bregman距离概念的启发，本文提出了一种新颖的双层优化框架用于GNN。我们证明，相应提出的GNN层通过引入类似“跳跃连接”的机制，能够有效缓解过平滑问题。通过全面的实证研究，我们验证了理论结果：在同类图和异类图中，增强型Bregman GNN性能均优于原始模型。此外，实验还表明，即使层数较高时，Bregman GNN仍能实现更稳健的学习精度，表明所提方法在缓解过平滑问题上的有效性。