# Graph Invariant Learning with Subgraph Co-mixup for Out-Of-Distribution Generalization

arXiv: https://arxiv.org/abs/2312.10988 · HTML: https://mlsanity.com/paper/2312.10988/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 46 references that are in the map.
- First posted on arXiv 18 Dec 2023.

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

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Explainability in Graph Neural Networks: A Taxonomic Survey](https://mlsanity.com/paper/2012.15445/) (2020)
- [Environment Inference for Invariant Learning](https://mlsanity.com/paper/2010.07249/) (2020)
- [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)
- [A Meta-Transfer Objective for Learning to Disentangle Causal Mechanisms](https://mlsanity.com/paper/1901.10912/) (2019)
- [G-Mixup: Graph Data Augmentation for Graph Classification](https://mlsanity.com/paper/2202.07179/) (2022)
- [Remix: Rebalanced Mixup](https://mlsanity.com/paper/2007.03943/) (2020)
- [Learning Causally Invariant Representations for Out-of-Distribution Generalization on Graphs](https://mlsanity.com/paper/2202.05441/) (2022)
- [Co-Mixup: Saliency Guided Joint Mixup with Supermodular Diversity](https://mlsanity.com/paper/2102.03065/) (2021)
- [From Local Structures to Size Generalization in Graph Neural Networks](https://mlsanity.com/paper/2010.08853/) (2020)
- [Causal Attention for Interpretable and Generalizable Graph Classification](https://mlsanity.com/paper/2112.15089/) (2021)
- [Size-Invariant Graph Representations for Graph Classification Extrapolations](https://mlsanity.com/paper/2103.05045/) (2021)
- [Graph Representation Learning: A Survey](https://mlsanity.com/paper/1909.00958/) (2019)
- [Graph Rationalization with Environment-based Augmentations](https://mlsanity.com/paper/2206.02886/) (2022)
- [DrugOOD: Out-of-Distribution (OOD) Dataset Curator and Benchmark for AI-aided Drug Discovery -- A Focus on Affinity Prediction Problems with Noise Annotations](https://mlsanity.com/paper/2201.09637/) (2022)
- [Graph Transplant: Node Saliency-Guided Graph Mixup with Local Structure Preservation](https://mlsanity.com/paper/2111.05639/) (2021)

## Built on by (most cited first, 18 of 18)

- [Pairwise Alignment Improves Graph Domain Adaptation](https://mlsanity.com/paper/2403.01092/) (2024)
- [A Survey of Deep Graph Learning under Distribution Shifts: from Graph Out-of-Distribution Generalization to Adaptation](https://mlsanity.com/paper/2410.19265/) (2024)
- [Learning Invariant Representations of Graph Neural Networks via Cluster Generalization](https://mlsanity.com/paper/2403.03599/) (2024)
- [Raising the Bar in Graph OOD Generalization: Invariant Learning Beyond Explicit Environment Modeling](https://mlsanity.com/paper/2502.10706/) (2025)
- [DIVE: Subgraph Disagreement for Graph Out-of-Distribution Generalization](https://mlsanity.com/paper/2408.04400/) (2024)
- [BrainOOD: Out-of-distribution Generalizable Brain Network Analysis](https://mlsanity.com/paper/2502.01688/) (2025)
- [Dissecting the Failure of Invariant Learning on Graphs](https://mlsanity.com/paper/2411.02847/) (2024)
- [Towards Invariance to Node Identifiers in Graph Neural Networks](https://mlsanity.com/paper/2502.13660/) (2025)
- [A Survey of Out-of-distribution Generalization for Graph Machine Learning from a Causal View](https://mlsanity.com/paper/2409.09858/) (2024)
- [Pruning Spurious Subgraphs for Graph Out-of-Distribution Generalization](https://mlsanity.com/paper/2506.05957/) (2025)
- [On the Utilization of Unique Node Identifiers in Graph Neural Networks](https://mlsanity.com/paper/2411.02271/) (2024)
- [GSINA: Improving Subgraph Extraction for Graph Invariant Learning via Graph Sinkhorn Attention](https://mlsanity.com/paper/2402.07191/) (2024)
- [Improving Graph Out-of-distribution Generalization Beyond Causality](https://mlsanity.com/paper/2407.10204/) (2024)
- [GraphIFE: Rethinking Graph Imbalance Node Classification via Invariant Learning](https://mlsanity.com/paper/2509.23616/) (2025)
- [Teleporter Theory: A General and Simple Approach for Modeling Cross-World Counterfactual Causality](https://mlsanity.com/paper/2406.11501/) (2024)
- [Soft causal learning for generalized molecule property prediction: An environment perspective](https://mlsanity.com/paper/2505.06283/) (2025)
- [Out-of-Distribution Graph Models Merging](https://mlsanity.com/paper/2506.03674/) (2025)
- [Enhancing Protein Representation Learning via Manifold Restore Mixing](https://mlsanity.com/paper/2606.22307/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) have been demonstrated to perform well in graph representation learning, but always lacking in generalization capability when tackling out-of-distribution (OOD) data. Graph invariant learning methods, backed by the invariance principle among defined multiple environments, have shown effectiveness in dealing with this issue. However, existing methods heavily rely on well-predefined or accurately generated environment partitions, which are hard to be obtained in practice, leading to sub-optimal OOD generalization performances. In this paper, we propose a novel graph invariant learning method based on invariant and variant patterns co-mixup strategy, which is capable of jointly generating mixed multiple environments and capturing invariant patterns from the mixed graph data. Specifically, we first adopt a subgraph extractor to identify invariant subgraphs. Subsequently, we design one novel co-mixup strategy, i.e., jointly conducting environment Mixup and invariant Mixup. For the environment Mixup, we mix the variant environment-related subgraphs so as to generate sufficiently diverse multiple environments, which is important to guarantee the quality of the graph invariant learning. For the invariant Mixup, we mix the invariant subgraphs, further encouraging to capture invariant patterns behind graphs while getting rid of spurious correlations for OOD generalization. We demonstrate that the proposed environment Mixup and invariant Mixup can mutually promote each other. Extensive experiments on both synthetic and real-world datasets demonstrate that our method significantly outperforms state-of-the-art under various distribution shifts.