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

2025-10-23

AI Summary

Graph Neural Networks (GNNs) face a critical bottleneck in out-of-distribution generalization: identifying causal subgraphs requires environment annotations, and existing Invariant Risk Minimization (IRM) approaches rely on costly environment partitioning or heuristic splitting. This paper proposes an IRM-free framework that, for the first time, establishes a quantitative relationship between representation norm and distributional shift, thereby defining a novel distribution-invariance criterion independent of environment labels. Building upon this, we design a norm-guided invariant distribution objective that jointly leverages theoretical analysis and self-supervision to discover causal subgraphs. Our method achieves significant improvements over state-of-the-art methods on two mainstream graph benchmarks, demonstrating superior cross-environment stability and structural generalization robustness. The core contribution lies in eliminating the need for environment annotations and unifying the characterization of distribution-invariant graph representations both theoretically and algorithmically.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Develop IRM-free method for causal subgraph discovery
• Quantify distributional shift relationship with representation norm
• Improve graph generalization without environment annotations

Innovation

• IRM-free method for causal subgraph discovery
• Norm-guided invariant distribution objective introduced
• Quantitative relationship between distributional shift and norm