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Graph invariant learning (GIL) has been an effective approach to discovering the invariant relationships between graph data and its labels for different graph learning tasks under various distribution shifts. Many recent endeavors of GIL focus on extracting the invariant subgraph from the input graph for prediction as a regularization strategy to improve the generalization performance of graph learning. Despite their success, such methods also have various limitations in obtaining their invariant subgraphs. In this paper, we provide in-depth analyses of the drawbacks of existing works and propose corresponding principles of our invariant subgraph extraction: 1) the sparsity, to filter out the variant features, 2) the softness, for a broader solution space, and 3) the differentiability, for a soundly end-to-end optimization. To meet these principles in one shot, we leverage the Optimal Transport (OT) theory and propose a novel graph attention mechanism called Graph Sinkhorn Attention (GSINA). This novel approach serves as a powerful regularization method for GIL tasks. By GSINA, we are able to obtain meaningful, differentiable invariant subgraphs with controllable sparsity and softness. Moreover, GSINA is a general graph learning framework that could handle GIL tasks of multiple data grain levels. Extensive experiments on both synthetic and real-world datasets validate the superiority of our GSINA, which outperforms the state-of-the-art GIL methods by large margins on both graph-level tasks and node-level tasks. Our code is publicly available at \url{https://github.com/dingfangyu/GSINA}. |
