In recent years, graph neural networks (GNNs) have emerged as a promising tool for solving machine learning problems on graphs. Most GNNs are members of the family of message passing neural networks (MPNNs). There is a close connection between these models and the Weisfeiler-Leman (WL) test of isomorphism, an algorithm that can successfully test isomorphism for a broad class of graphs. Recently, much research has focused on measuring the expressive power of GNNs. For instance, it has been shown that standard MPNNs are at most as powerful as WL in terms of distinguishing non-isomorphic graphs. However, these studies have largely ignored the distances between the representations of nodes/graphs which are of paramount importance for learning tasks. In this paper, we define a distance function between nodes which is based on the hierarchy produced by the WL algorithm, and propose a model that learns representations which preserve those distances between nodes. Since the emerging hierarchy corresponds to a tree, to learn these representations, we capitalize on recent advances in the field of hyperbolic neural networks. We empirically evaluate the proposed model on standard node and graph classification datasets where it achieves competitive performance with state-of-the-art models.

翻译：近年来，图神经网络（GNN）已成为解决图上机器学习问题的有力工具。大多数GNN属于消息传递神经网络（MPNN）家族。这些模型与用于同构检测的韦斯费勒-莱曼（WL）检验算法存在紧密联系——该算法可成功检验广泛图类的同构性。近期大量研究聚焦于衡量GNN的表达能力。例如，已有研究表明，在区分非同构图方面，标准MPNN的表达能力最多与WL算法相当。然而，这些研究很大程度上忽略了节点/图表示之间的距离——这一要素对于学习任务至关重要。本文基于WL算法生成的层次结构定义了节点间的距离函数，并提出一种能够保持节点间距离的表示学习模型。由于该层次结构对应树形结构，为学习此类表示，我们借鉴了双曲神经网络领域的最新进展。在标准节点分类和图分类数据集上的实证评估表明，所提模型取得了与现有最优模型相竞争的优异性能。