Various recent proposals increase the distinguishing power of Graph Neural
Networks GNNs by propagating features between $k$-tuples of vertices. The
distinguishing power of these "higher-order'' GNNs is known to be bounded by
the $k$-dimensional Weisfeiler-Leman (WL) test, yet their $\mathcal O(n^k)$
memory requirements limit their applicability. Other proposals infuse GNNs with
local higher-order graph structural information from the start, hereby
inheriting the desirable $\mathcal O(n)$ memory requirement from GNNs at the
cost of a one-time, possibly non-linear, preprocessing step. We propose local
graph parameter enabled GNNs as a framework for studying the latter kind of
approaches and precisely characterize their distinguishing power, in terms of a
variant of the WL test, and in terms of the graph structural properties that
they can take into account. Local graph parameters can be added to any GNN
architecture, and are cheap to compute. In terms of expressive power, our
proposal lies in the middle of GNNs and their higher-order counterparts.
Further, we propose several techniques to aide in choosing the right local
graph parameters. Our results connect GNNs with deep results in finite model
theory and finite variable logics. Our experimental evaluation shows that
adding local graph parameters often has a positive effect for a variety of
GNNs, datasets and graph learning tasks.

我们在研究中提出了一种基于本地图参数的 GNN 架构，该架构处于 GNN 和其高阶对应物之间的表现力水平，并提出了可帮助选择正确本地图参数的技术。 我们的结果将 GNN 与有限模型理论和有限变量逻辑的深度结果联系起来，实验评估表明添加本地图参数对各种 GNN，数据集和图形学习任务通常有积极影响。

具有局部图参数的图神经网络

Graph Neural Networks with Local Graph Parameters

Graph neural networks (GNNs) are deep learning architectures for machine
learning problems on graphs. It has recently been shown that the expressiveness
of GNNs can be characterised precisely by the combinatorial Weisfeiler-Leman
algorithms and by finite variable counting logics. The correspondence has even
led to new, higher-order GNNs corresponding to the WL algorithm in higher
dimensions.
The purpose of this paper is to explain these descriptive characterisations
of GNNs.

本文旨在阐述图神经网络的表达能力可以通过组合 Weisfeiler-Leman 算法和有限变量计数逻辑来精确描述，这种对应关系甚至导致了高阶图神经网络与高维 WL 算法的相应。