Graph Neural Networks (GNNs) have shown great promise in tasks like node and graph classification, but they often struggle to generalize, particularly to unseen or out-of-distribution (OOD) data. These challenges are exacerbated when training data is limited in size or diversity. To address these issues, we introduce a theoretical framework using Rademacher complexity to compute a regret bound on the generalization error and then characterize the effect of data augmentation. This framework informs the design of GRATIN, an efficient graph data augmentation algorithm leveraging the capability of Gaussian Mixture Models (GMMs) to approximate any distribution. Our approach not only outperforms existing augmentation techniques in terms of generalization but also offers improved time complexity, making it highly suitable for real-world applications.

Imagine you're teaching an AI to recognize different types of social or biological networks. These networks are complex. A powerful AI tool called Graph Neural Networks (GNNs) is used to learn from this kind of structured data.However, GNNs often struggle to understand networks they haven't seen before, especially if they only learned from a small or limited set of network examples. It's like teaching a child only about cats and then asking them to identify a tiger, they might struggle because it's a new animal.Our research tackles this problem. We've developed a new way to understand why GNNs struggle with new data and, more importantly, how to fix it. We use a concept called Rademacher complexity to measure how well a GNN will perform on unseen networks.This understanding helped us create a new technique called GRATIN. Think of GRATIN as a smart data generator. It creates many new, realistic-looking example networks. These new networks are subtly different from the original ones but still representative, giving the GNN much more diverse training data.GRATIN helps GNNs learn more effectively from limited data, making them much better at recognizing and classifying new, unseen networks. It also offers improved time complexity, making it highly suitable for real-world applications.