Graph neural networks (GNNs) have recently become the standard approach for learning with graph-structured data. Prior work has shed light into their potential, but also their limitations. Unfortunately, it was shown that standard GNNs are limited in their expressive power. These models are no more powerful than the 1-dimensional Weisfeiler-Leman (1-WL) algorithm in terms of distinguishing non-isomorphic graphs. In this paper, we propose Path Neural Networks (PathNNs), a model that updates node representations by aggregating paths emanating from nodes. We derive three different variants of the PathNN model that aggregate single shortest paths, all shortest paths and all simple paths of length up to K. We prove that two of these variants are strictly more powerful than the 1-WL algorithm, and we experimentally validate our theoretical results. We find that PathNNs can distinguish pairs of non-isomorphic graphs that are indistinguishable by 1-WL, while our most expressive PathNN variant can even distinguish between 3-WL indistinguishable graphs. The different PathNN variants are also evaluated on graph classification and graph regression datasets, where in most cases, they outperform the baseline methods.

翻译：图神经网络（GNNs）近年来已成为处理图结构数据的标准方法。先前的研究揭示了它们的潜力，但也暴露了其局限性。不幸的是，标准GNN的表达能力受限已被证实：在区分非同构图方面，这些模型的能力并不优于一维Weisfeiler-Leman（1-WL）算法。本文提出路径神经网络（PathNNs），该模型通过聚合从节点出发的路径来更新节点表示。我们推导出PathNN模型的三种变体，分别聚合单条最短路径、所有最短路径以及长度不超过K的所有简单路径。我们证明其中两种变体严格强于1-WL算法，并通过实验验证了这一理论结果。研究发现，PathNN能够区分1-WL无法区分的非同构图对，而最具表达力的PathNN变体甚至能区分3-WL无法区分的图。不同PathNN变体在图分类和图回归数据集上的评估显示，多数情况下其性能优于基线方法。