Oversmoothing has been assumed to be the major cause of performance drop in
deep graph convolutional networks (GCNs). In this paper, we propose a new view
that deep GCNs can actually learn to anti-oversmooth during training. This work
interprets a standard GCN architecture as layerwise integration of a
Multi-layer Perceptron (MLP) and graph regularization. We analyze and conclude
that before training, the final representation of a deep GCN does over-smooth,
however, it learns anti-oversmoothing during training. Based on the conclusion,
the paper further designs a cheap but effective trick to improve GCN training.
We verify our conclusions and evaluate the trick on three citation networks and
further provide insights on neighborhood aggregation in GCNs.

本论文提出了一种新的观点，即深度图卷积网络在训练过程中可以学习抗去平滑化的能力，并设计了一种简单却有效的技巧来改善 GCN 训练，同时在三个引用网络上验证了结论并提供了 GCN 邻域聚合方面的见解。

深度图卷积网络中过度平滑化的重新审视

Revisiting Over-smoothing in Deep GCNs

Graph convolutional networks (GCNs) are powerful tools for graph-structured
data. However, they have been recently shown to be vulnerable to topological
attacks. To enhance adversarial robustness, we go beyond spectral graph theory
to robust graph theory. By challenging the classical graph Laplacian, we
propose a new convolution operator that is provably robust in the spectral
domain and is incorporated in the GCN architecture to improve expressivity and
interpretability. By extending the original graph to a sequence of graphs, we
also propose a robust training paradigm that encourages transferability across
graphs that span a range of spatial and spectral characteristics. The proposed
approaches are demonstrated in extensive experiments to simultaneously improve
performance in both benign and adversarial situations.

通过挑战经典的图形拉普拉斯算子，设计出一种可以证明在频谱域内具有鲁棒性的新卷积算子，它被纳入 GCN 体系结构中以改善其表达能力和可解释性，同时通过将原始图形扩展到一系列图形，提出了一种鲁棒的训练范式，以鼓励跨越具有一系列空间和频谱特征的图形的可转移性，这些方法在广泛的实验中得到证明，可以同时提高在良性和对抗性情况下的性能。