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

arXiv: https://arxiv.org/abs/2510.20295 · HTML: https://mlsanity.com/paper/2510.20295/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 47 references that are in the map.
- First posted on arXiv 23 Oct 2025.

## Builds on (most cited first, 30 of 34)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [Parameterized Explainer for Graph Neural Network](https://mlsanity.com/paper/2011.04573/) (2020)
- [Rationalizing Neural Predictions](https://mlsanity.com/paper/1606.04155/) (2016)
- [Discovering Invariant Rationales for Graph Neural Networks](https://mlsanity.com/paper/2201.12872/) (2022)
- [Interpretable and Generalizable Graph Learning via Stochastic Attention Mechanism](https://mlsanity.com/paper/2201.12987/) (2022)
- [Learning Causally Invariant Representations for Out-of-Distribution Generalization on Graphs](https://mlsanity.com/paper/2202.05441/) (2022)
- [GOOD: A Graph Out-of-Distribution Benchmark](https://mlsanity.com/paper/2206.08452/) (2022)
- [Invariant Causal Prediction for Nonlinear Models](https://mlsanity.com/paper/1706.08576/) (2017)
- [Debiasing Graph Neural Networks via Learning Disentangled Causal Substructure](https://mlsanity.com/paper/2209.14107/) (2022)
- [Graph Rationalization with Environment-based Augmentations](https://mlsanity.com/paper/2206.02886/) (2022)
- [Invariant Causal Prediction for Sequential Data](https://mlsanity.com/paper/1706.08058/) (2017)
- [ZIN: When and How to Learn Invariance Without Environment Partition?](https://mlsanity.com/paper/2203.05818/) (2022)
- [Implicit Regularization Towards Rank Minimization in ReLU Networks](https://mlsanity.com/paper/2201.12760/) (2022)
- [Does Invariant Graph Learning via Environment Augmentation Learn Invariance?](https://mlsanity.com/paper/2310.19035/) (2023)
- [Joint Learning of Label and Environment Causal Independence for Graph Out-of-Distribution Generalization](https://mlsanity.com/paper/2306.01103/) (2023)
- [Learning Invariant Molecular Representation in Latent Discrete Space](https://mlsanity.com/paper/2310.14170/) (2023)
- [GOODAT: Towards Test-time Graph Out-of-Distribution Detection](https://mlsanity.com/paper/2401.06176/) (2024)
- [Beyond Zero Initialization: Investigating the Impact of Non-Zero Initialization on LoRA Fine-Tuning Dynamics](https://mlsanity.com/paper/2505.23194/) (2025)
- [Empowering Graph Invariance Learning with Deep Spurious Infomax](https://mlsanity.com/paper/2407.11083/) (2024)
- [Investigating Out-of-Distribution Generalization of GNNs: An Architecture Perspective](https://mlsanity.com/paper/2402.08228/) (2024)

## Built on by (most cited first, 2 of 2)

- [Beyond Higher Rank: Token-wise Input-Output Projections for Efficient Low-Rank Adaptation](https://mlsanity.com/paper/2510.23123/) (2025)
- [Rethinking Graph Generalization through the Lens of Sharpness-Aware Minimization](https://mlsanity.com/paper/2602.08855/) (2026)

## Abstract (arXiv)

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.