A Structure-aware Invariant Learning Framework for Node-level Graph OOD Generalization

Graph Neural Networks (GNNs) have been proven effective in modeling graph data, mostly depending on the in-distribution assumption. While in the out-of-distribution (OOD) scenarios, especially for the more challenging node-level task, the feature and structure distribution shifts between training and test nodes lead to performance degradation. To improve node-level OOD generalization, typical approaches introduce graph augmentation to enrich the training environments and conduct invariant learning to learn stable representations across various augmented environments. However, their graph augmentations emphasize diversity but neglect the preservation of invariant patterns which are fundamental to invariant learning. Moreover, most of them simply conduct the classic invariant learning objective but lack the consideration of the graph-specific structure information. Therefore, to mitigate their weakness, we propose a Structure-aware Invariant learning framework for Node-level Graph OOD generalization (SING). Specifically, we develop the invariance constraint regularization terms during the optimization of augmentations. Additionally, we define the structure embedding to elucidate the structural property and design the structure embedding alignment loss to optimize the augmentations and the invariant representations. By introducing the structure information, we further integrate the unique structural property into invariant learning, thereby boosting the invariant message-passing GNNs. The extensive experiments on the transductive GOOD benchmark and the inductive datasets empirically validate our superior OOD generalization performance to baselines.