  Graph Neural Networks (GNNs) are widely used for node classification tasks
but often fail to generalize when training and test nodes come from different
distributions, limiting their practicality. To overcome this, recent approaches
adopt invariant learning techniques from the out-of-distribution (OOD)
generalization field, which seek to establish stable prediction methods across
environments. However, the applicability of these invariant assumptions to
graph data remains unverified, and such methods often lack solid theoretical
support. In this work, we introduce the Topology-Aware Dynamic Reweighting
(TAR) framework, which dynamically adjusts sample weights through gradient flow
in the geometric Wasserstein space during training. Instead of relying on
strict invariance assumptions, we prove that our method is able to provide
distributional robustness, thereby enhancing the out-of-distribution
generalization performance on graph data. By leveraging the inherent graph
structure, TAR effectively addresses distribution shifts. Our framework's
superiority is demonstrated through standard testing on four graph OOD datasets
and three class-imbalanced node classification datasets, exhibiting marked
improvements over existing methods.
