图神经网络已经成为图数据处理和建模最重要的工具之一。然而，过平滑问题限制了深度图神经网络的表征能力，已经成为图神经网络结构设计以及训练过程中不可忽视的障碍，受到研究者广泛的关注。该问题指出，随着图神经网络层的堆叠，输入的图数据执行了多次节点与节点之间的信息聚合，导致处于同一图连通分量的所有节点快速收敛到同一个稳定点，降低了不同节点的判别区分度。本文首先调研了领域内对过平滑问题的研究进展，将其划分为两大类进行介绍和分析。随后，本文从解决过平滑问题的两个角度——调整模型结构和添加正则化约束——出发，提出了两种新的研究方案。在方案一中，本文提出了自适应的近邻差异度自蒸馏的训练策略，约束图神经网络输出的图表征保持与输入图接近的较高的非平滑度。该策略能够作为一种通用的训练方法，以较小的额外计算开销为代价，增强各类图神经网络模型。在方案二中，本文提出了基于图自纠正机制的图池化模型，为池化图提供池化过程中丢失信息的反馈补偿。该机制能够作为即插即用型的模型组件，提高池化图的语义丰富度，并且抑制池化图的节点表征同质化问题。本文选择了领域内多个基准数据集和多种结构不同的图神经网络作为实验对象，通过大量定性分析实验和定量验证实验确认了所提研究方案的有效性和通用性。总而言之，本文的工作内容和创新贡献点主要有：（1）提出了一个用于量化图表征向量非平滑程度的指标，并基于此构建了自适应的近邻差异度蒸馏的训练策略。该训练方式可以用来替换图网络模型的常规训练方式，有效地缓解图神经网络遇到的过平滑现象并提升模型性能。（2）提出了对图池化过程中丢失的信息进行信息补偿和反馈纠正的图自纠正机制。该机制可以提高图池化方法在图分类任务上的性能表现，并且缓解池化图表征向量高度平滑的问题，从而推动多尺度图表征集成学习模型的成功构建。（3）在3个节点分类数据集、7个图分类数据集上，采用多种结构、深度不同的图神经网络作为基线模型，开展了详实全面的实验验证和结果分析。实验结果表明，本文提出的方法为过平滑问题提供了可靠的解决方案。
Graph neural networks have become one of the most important tools for graph data processing and modeling. However, the over-smoothing problem limits the representation ability of deep graph neural networks, which has become an obstacle that cannot be ignored in the structure design and training process of graph neural networks and has received extensive attention from researchers. The problem states that, with the stacking of graph neural network layers, the input graph data performs multiple node-to-node information aggregation, leading to a rapid convergence of all nodes in the same graph connectivity component to the same stable point. It reduces the discriminative power of different nodes.In this paper, we first investigate the research progress on over-smoothing problems in the field and classify them into two categories for introduction and analysis. Subsequently, for solving the over-smoothing problem, our paper proposes two approaches from the perspectives of adjusting the model structure and adding regularization constraints. In the first method, we propose an adaptive discrepancy retaining strategy, which constrains the graph representation generated by graph neural networks to maintain a high non-smoothness that is close to the input graph. In the second method, we propose a graph pooling model based on the graph self-correction mechanism to provide feedback of lost information for the pooled graph. This mechanism can serve as a plug-and-play component to improve the semantic richness of the pooled graph and suppress the homogeneity of node representation in the pooled graph. In this paper, we select multiple benchmark datasets and various graph neural networks with different structures to conduct experiments. We have confirmed the effectiveness and generalization of the proposed methods through extensive qualitative and quantitative experiments. In summary, the main contents and contributions of this paper are as follows:(1) A metric for quantifying the degree of non-smoothness of graph representation is proposed, and an adaptive distillation strategy is constructed based on it. By replacing the original training algorithm, our approach effectively alleviates the over-smoothing phenomenon encountered by graph neural networks and improves their performance.(2) A graph self-correction mechanism for information compensation and feedback of information lost during the graph pooling process is proposed. This mechanism can improve the performance of graph pooling methods on graph classification tasks and suppress the homogeneity of the pooled graph, thus facilitating the application of the ensembled multi-scale graph learning method.(3) Detailed and comprehensive experimental verification and result analysis were carried out on three node classification datasets and seven graph classification datasets, using a variety of graph neural networks with different structures and depths as baseline models. Experimental results show that our proposed methods provide a reliable solution to the over-smoothing problem.
