Graph representation learning has now become the de facto standard when
handling graph-structured data, with the framework of message-passing graph
neural networks (MPNN) being the most prevailing algorithmic tool. Despite its
popularity, the family of MPNNs suffers from several drawbacks such as
transparency and expressivity. Recently, the idea of designing neural models on
graphs using the theory of graph kernels has emerged as a more transparent as
well as sometimes more expressive alternative to MPNNs known as kernel graph
neural networks (KGNNs). Developments on KGNNs are currently a nascent field of
research, leaving several challenges from algorithmic design and adaptation to
other learning paradigms such as self-supervised learning. In this paper, we
improve the design and learning of KGNNs. Firstly, we extend the algorithmic
formulation of KGNNs by allowing a more flexible graph-level similarity
definition that encompasses former proposals like random walk graph kernel, as
well as providing a smoother optimization objective that alleviates the need of
introducing combinatorial learning procedures. Secondly, we enhance KGNNs
through the lens of self-supervision via developing a novel
structure-preserving graph data augmentation method called latent graph
augmentation (LGA). Finally, we perform extensive empirical evaluations to
demonstrate the efficacy of our proposed mechanisms. Experimental results over
benchmark datasets suggest that our proposed model achieves competitive
performance that is comparable to or sometimes outperforming state-of-the-art
graph representation learning frameworks with or without self-supervision on
graph classification tasks. Comparisons against other previously established
graph data augmentation methods verify that the proposed LGA augmentation
scheme captures better semantics of graph-level invariance.

我们改进了核图神经网络 (KGNNs) 的设计与学习，通过扩展其算法形式并引入自我监督方法，提出了一种更灵活且结构保持的图数据增强方法 (latent graph augmentation)，实验证明我们的模型在图分类任务上达到了与先进方法相媲美甚至优于其的竞争性性能。

自监督与核图神经模型相遇：从架构到增强

Self-supervision meets kernel graph neural models: From architecture to  augmentations

Graph kernels are historically the most widely-used technique for graph
classification tasks. However, these methods suffer from limited performance
because of the hand-crafted combinatorial features of graphs. In recent years,
graph neural networks (GNNs) have become the state-of-the-art method in
downstream graph-related tasks due to their superior performance. Most GNNs are
based on Message Passing Neural Network (MPNN) frameworks. However, recent
studies show that MPNNs can not exceed the power of the Weisfeiler-Lehman (WL)
algorithm in graph isomorphism test. To address the limitations of existing
graph kernel and GNN methods, in this paper, we propose a novel GNN framework,
termed \textit{Kernel Graph Neural Networks} (KerGNNs), which integrates graph
kernels into the message passing process of GNNs. Inspired by convolution
filters in convolutional neural networks (CNNs), KerGNNs adopt trainable hidden
graphs as graph filters which are combined with subgraphs to update node
embeddings using graph kernels. In addition, we show that MPNNs can be viewed
as special cases of KerGNNs. We apply KerGNNs to multiple graph-related tasks
and use cross-validation to make fair comparisons with benchmarks. We show that
our method achieves competitive performance compared with existing
state-of-the-art methods, demonstrating the potential to increase the
representation ability of GNNs. We also show that the trained graph filters in
KerGNNs can reveal the local graph structures of the dataset, which
significantly improves the model interpretability compared with conventional
GNN models.

本文提出了一种新的 GNN 框架，称为 “核图神经网络”，将图核函数集成到 GNN 的消息传递过程中，通过卷积滤波器使用可训练图作为图过滤器与子图相结合来更新节点嵌入，并显示 MPNN 可以视为 KerGNN 的特殊情况，该方法在多个图相关任务中表现出具有竞争力的性能，并提高了模型可解释性与传统 GNN 模型相比。