The study of Graph Neural Networks has received considerable interest in the past few years. By extending deep learning to graph-structured data, GNNs can solve a diverse set of tasks in fields including social science, chemistry, and medicine. The development of GNN architectures has largely been focused on improving empirical performance on tasks like node or graph classification. However, a line of recent work has instead sought to find GNN architectures that have desirable theoretical properties - by studying their expressive power and designing architectures that maximize this expressiveness. While there is no consensus on the best way to define the expressiveness of a GNN, it can be viewed from several well-motivated perspectives. Perhaps the most natural approach is to study the universal approximation properties of GNNs, much in the way that this has been studied extensively for MLPs. Another direction focuses on the extent to which GNNs can distinguish between different graph structures, relating this to the graph isomorphism test. Besides, a GNN's ability to compute graph properties such as graph moments has been suggested as another form of expressiveness. All of these different definitions are complementary and have yielded different recommendations for GNN architecture choices. In this paper, we would like to give an overview of the notion of "expressive power" of GNNs and provide some valuable insights regarding the design choices of GNNs.

翻译：近年来，图神经网络的研究引起了广泛关注。通过将深度学习扩展到图结构数据，GNN能够解决包括社会科学、化学和医学在内的多个领域的多样化任务。GNN架构的发展主要集中在提升节点分类或图分类等任务的实证性能上。然而，最近一系列研究转而寻求具有理想理论特性的GNN架构——通过研究其表达能力并设计最大化这种表达能力的架构。尽管对于如何定义GNN的表达能力尚未达成共识，但可以从多个具有充分动机的角度进行审视。或许最自然的途径是研究GNN的通用逼近特性，类似于多层感知机领域已被广泛研究的方式。另一方向聚焦于GNN区分不同图结构的能力，并将其与图同构测试相关联。此外，GNN计算图属性（如图矩）的能力也被视为另一种形式的表达能力。所有这些不同的定义互为补充，并为GNN架构选择提出了不同建议。在本文中，我们拟对GNN的"表达能力"概念进行综述，并就GNN的设计选择提供一些有价值的见解。