Path Neural Networks: Expressive and Accurate Graph Neural Networks
This work addresses a fundamental limitation in GNNs for graph-structured data, offering improved expressiveness that could benefit applications in domains like social networks or bioinformatics, though it is an incremental advance over existing methods.
The paper tackles the limited expressive power of standard graph neural networks (GNNs), which are no more powerful than the 1-WL algorithm, by proposing Path Neural Networks (PathNNs) that aggregate paths from nodes; it proves that PathNNs are strictly more powerful than 1-WL and can distinguish graphs that 1-WL cannot, with variants outperforming baselines on graph classification and regression tasks.
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.