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（GNN）已成为专为图结构数据学习和推理而设计的极具吸引力的模型。然而，目前鲜有工作深入探究GNN在扩展到更大图及泛化至分布外（OOD）输入时的基本局限性。本文利用随机图生成器系统性地研究了图的规模与结构属性如何影响GNN的预测性能。我们提供了具体证据，表明平均节点度是决定GNN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，采用多个节点更新函数可提升GNN的泛化性能。据此，我们提出了一种多模块GNN框架，该框架通过将单一标准非线性变换泛化应用于聚合输入，使网络能够灵活适应新图。我们的结果表明，在面向多样结构特征的各类推理任务中，多模块GNN显著提升了分布外泛化能力。