Quantifying Distributional Invariance in Causal Subgraph for IRM-Free Graph Generalization

Jun Wang (iWudao Tech) · Wei Liu (Huazhong University of Science and Technology) · Ruixuan Li (Huazhong University of Science and Technology) · Yang Qiu (School of Computer Science and Technology, Huazhong University of Science and Technology) · Yixiong Zou (Huazhong University of Science and Technology) · Xiangyu Fu (Huazhong University of Science and Technology)

causal subgraph discoverycausal subgraphsdistributional shiftsdistributional variationsenvironment annotationsgraph generalization graph neural networksinvariant distribution criterioninvariant risk minimizationnorm-guided invariant distributionout-of-distribution generalizationquantitative relationshiprepresentation normstate-of-the-art methodssynthetic splits

Out-of-distribution generalization under distributional shifts remains a critical challenge for graph neural networks. Existing methods generally adopt the Invariant Risk Minimization (IRM) framework, requiring costly environment annotations or heuristically generated synthetic splits. To circumvent these limitations, in this work, we aim to develop an IRM-free method for capturing causal subgraphs. We first identify that causal subgraphs exhibit substantially smaller distributional variations than non-causal components across diverse environments, which we formalize as the Invariant Distribution Criterion and theoretically prove in this paper. Building on this criterion, we systematically uncover the quantitative relationship between distributional shift and representation norm for identifying the causal subgraph, and investigate its underlying mechanisms in depth. Finally, we propose an IRM-free method by introducing a norm-guided invariant distribution objective for causal subgraph discovery and prediction. Extensive experiments on two widely used benchmarks demonstrate that our method consistently outperforms state-of-the-art methods in graph generalization. Code is available at https://github.com/anders1123/IDG.