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

23 October 2025
Yang Qiu
Yixiong Zou
Jun Wang
Wei Liu
Xiangyu Fu
R. Li
    OOD
ArXiv (abs)PDFHTMLGithub
Main:10 Pages
11 Figures
Bibliography:3 Pages
6 Tables
Appendix:17 Pages
Abstract

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.

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