Graph neural networks (GNNs) have become compelling models designed to perform learning and inference on graph-structured data. However, little work has been done to understand the fundamental limitations of GNNs for scaling to larger graphs and generalizing to out-of-distribution (OOD) inputs. In this paper, we use a random graph generator to systematically investigate how the graph size and structural properties affect the predictive performance of GNNs. We present specific evidence that the average node degree is a key feature in determining whether GNNs can generalize to unseen graphs, and that the use of multiple node update functions can improve the generalization performance of GNNs when dealing with graphs of multimodal degree distributions. Accordingly, we propose a multi-module GNN framework that allows the network to adapt flexibly to new graphs by generalizing a single canonical nonlinear transformation over aggregated inputs. Our results show that the multi-module GNNs improve the OOD generalization on a variety of inference tasks in the direction of diverse structural features.

翻译：图神经网络（GNNs）已成为一种旨在对图结构数据进行学习和推理的引人注目的模型。然而，目前很少有研究致力于理解GNNs在扩展至更大图以及泛化到分布外（OOD）输入时的基本局限性。在本文中，我们使用随机图生成器系统性地研究了图的大小和结构特性如何影响GNNs的预测性能。我们提供了具体证据表明，平均节点度是决定GNNs能否泛化到未见图的关键特征，并且当处理具有多模态度分布的图时，使用多个节点更新函数可以提高GNNs的泛化性能。据此，我们提出了一种多模块GNN框架，该框架通过对聚合输入进行单一规范非线性变换的泛化，使网络能够灵活地适应新图。我们的结果表明，在多样化结构特征的方向上，多模块GNNs提升了多种推理任务上的OOD泛化能力。