It has been discovered that Graph Convolutional Networks (GCNs) encounter a remarkable drop in performance when multiple layers are piled up. The main factor that accounts for why deep GCNs fail lies in over-smoothing, which isolates the network output from the input with the increase of network depth, weakening expressivity and trainability. In this paper, we start by investigating refined measures upon DropEdge -- an existing simple yet effective technique to relieve over-smoothing. We term our method as DropEdge++ for its two structure-aware samplers in contrast to DropEdge: layer-dependent sampler and feature-dependent sampler. Regarding the layer-dependent sampler, we interestingly find that increasingly sampling edges from the bottom layer yields superior performance than the decreasing counterpart as well as DropEdge. We theoretically reveal this phenomenon with Mean-Edge-Number (MEN), a metric closely related to over-smoothing. For the feature-dependent sampler, we associate the edge sampling probability with the feature similarity of node pairs, and prove that it further correlates the convergence subspace of the output layer with the input features. Extensive experiments on several node classification benchmarks, including both full- and semi- supervised tasks, illustrate the efficacy of DropEdge++ and its compatibility with a variety of backbones by achieving generally better performance over DropEdge and the no-drop version.

翻译：研究发现，图卷积网络在堆叠多层时会出现性能显著下降的现象。导致深度GCN失效的核心因素在于过平滑问题——随着网络深度增加，模型输出与输入之间的关联逐渐弱化，从而削弱了表达能力和可训练性。本文首先对现有缓解过平滑的简易有效方法DropEdge进行了精细改进研究。我们将所提方法命名为DropEdge++，其创新之处在于提出两种结构感知采样器：层级依赖采样器与特征依赖采样器。对于层级依赖采样器，我们有趣地发现，相较于递减采样策略及原始DropEdge，从底层递增采样边能取得更优性能。通过引入与过平滑密切相关的平均边数指标，我们从理论上揭示了这一现象的内在机理。针对特征依赖采样器，我们将边采样概率与节点对的特征相似度相关联，并证明该方法能进一步使输出层的收敛子空间与输入特征产生关联。在多个节点分类基准任务（涵盖全监督与半监督场景）上的大量实验表明，DropEdge++相较于DropEdge及无丢弃版本，能在多种骨干网络上取得普遍更优的性能，充分验证了其有效性及兼容性。