In the past few years, graph neural networks (GNNs) have become the de facto model of choice for graph classification. While, from the theoretical viewpoint, most GNNs can operate on graphs of any size, it is empirically observed that their classification performance degrades when they are applied on graphs with sizes that differ from those in the training data. Previous works have tried to tackle this issue in graph classification by providing the model with inductive biases derived from assumptions on the generative process of the graphs, or by requiring access to graphs from the test domain. The first strategy is tied to the use of ad-hoc models and to the quality of the assumptions made on the generative process, leaving open the question of how to improve the performance of generic GNN models in general settings. On the other hand, the second strategy can be applied to any GNN, but requires access to information that is not always easy to obtain. In this work we consider the scenario in which we only have access to the training data, and we propose a regularization strategy that can be applied to any GNN to improve its generalization capabilities from smaller to larger graphs without requiring access to the test data. Our regularization is based on the idea of simulating a shift in the size of the training graphs using coarsening techniques, and enforcing the model to be robust to such a shift. Experimental results on standard datasets show that popular GNN models, trained on the 50% smallest graphs in the dataset and tested on the 10% largest graphs, obtain performance improvements of up to 30% when trained with our regularization strategy.

本研究提出一种基于规则化策略的方法，能够在只有训练数据而没有测试数据的情况下，提高图神经网络在更大规模的图上的泛化能力，从而改善图分类的性能。实验结果表明，流行的 GNN 模型在我们的规则化策略下，在 50% 规模最小的图上进行训练，在 10% 规模最大的图上进行测试时，性能提高了达到 30%。

SizeShiftReg: 一种用于提高图神经网络尺寸泛化能力的正则化方法