Generalizing on Diverse Shifts: A Unified Topology-Aware Reweighting Algorithm for Graphs.

Graph Neural Networks (GNNs) have achieved strong performance in node classification, yet their performance often drops when facing graph distribution shifts between training and testing nodes. Existing methods have been explored to improve generalization under such shifts. However, many of them either rely on environment annotations or do not fully use graph topology, structural noise information, and uncertainty from unlabeled nodes. To address these challenges, we propose Topology-Aware Dynamic Reweighting (TAR+), a model-agnostic framework for node classification under strict graph distribution shifts and related robustness stressors. TAR+ formulates sample reweighting as a gradient flow in graph Wasserstein space, allowing node weights to depend on both prediction difficulty and graph topology. A structure-aware Huber penalty limits the influence of nodes whose losses are inconsistent with structurally related neighbors, while prediction entropy provides node-specific proxy losses for unlabeled nodes. Graph extrapolation further exposes the model to perturbed structures and features. We further provide a free-energy interpretation of the reweighting dynamics and show that each variational step admits a local distributionally robust optimization interpretation. Experiments cover covariate and concept shifts as well as noisy supervision, heterophily, class imbalance, label scarcity, unsupervised learning, and graph anomaly detection. TAR+ achieves competitive performance across these settings, supporting the broad applicability of topology-aware reweighting across heterogeneous graph learning conditions.