# Does Invariant Graph Learning via Environment Augmentation Learn Invariance?

arXiv: https://arxiv.org/abs/2310.19035 · HTML: https://mlsanity.com/paper/2310.19035/

## Key facts

- Cited by 42 papers in the map (data through 14 Oct 2026).
- Builds on 71 of its 92 references that are in the map.
- First posted on arXiv 29 Oct 2023.

## Builds on (most cited first, 30 of 71)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Just Train Twice: Improving Group Robustness without Training Group Information](https://mlsanity.com/paper/2107.09044/) (2021)
- [Parameterized Explainer for Graph Neural Network](https://mlsanity.com/paper/2011.04573/) (2020)
- [Explainability in Graph Neural Networks: A Taxonomic Survey](https://mlsanity.com/paper/2012.15445/) (2020)
- [AllenNLP: A Deep Semantic Natural Language Processing Platform](https://mlsanity.com/paper/1803.07640/) (2018)
- [Environment Inference for Invariant Learning](https://mlsanity.com/paper/2010.07249/) (2020)
- [Therapeutics Data Commons: Machine Learning Datasets and Tasks for Drug Discovery and Development](https://mlsanity.com/paper/2102.09548/) (2021)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.06607/) (2021)
- [Discovering Invariant Rationales for Graph Neural Networks](https://mlsanity.com/paper/2201.12872/) (2022)
- [Correct-N-Contrast: A Contrastive Approach for Improving Robustness to Spurious Correlations](https://mlsanity.com/paper/2203.01517/) (2022)

## Built on by (most cited first, 30 of 42)

- [Pairwise Alignment Improves Graph Domain Adaptation](https://mlsanity.com/paper/2403.01092/) (2024)
- [HIGHT: Hierarchical Graph Tokenization for Molecule-Language Alignment](https://mlsanity.com/paper/2406.14021/) (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)
- [Empowering Graph Invariance Learning with Deep Spurious Infomax](https://mlsanity.com/paper/2407.11083/) (2024)
- [How Interpretable Are Interpretable Graph Neural Networks?](https://mlsanity.com/paper/2406.07955/) (2024)
- [Neural Atoms: Propagating Long-range Interaction in Molecular Graphs through Efficient Communication Channel](https://mlsanity.com/paper/2311.01276/) (2023)
- [Raising the Bar in Graph OOD Generalization: Invariant Learning Beyond Explicit Environment Modeling](https://mlsanity.com/paper/2502.10706/) (2025)
- [BrainOOD: Out-of-distribution Generalizable Brain Network Analysis](https://mlsanity.com/paper/2502.01688/) (2025)
- [Enhancing Evolving Domain Generalization through Dynamic Latent Representations](https://mlsanity.com/paper/2401.08464/) (2024)
- [Leveraging Invariant Principle for Heterophilic Graph Structure Distribution Shifts](https://mlsanity.com/paper/2408.09490/) (2024)
- [Improving out-of-distribution generalization in graphs via hierarchical semantic environments](https://mlsanity.com/paper/2403.01773/) (2024)
- [When Graph Neural Network Meets Causality: Opportunities, Methodologies and An Outlook](https://mlsanity.com/paper/2312.12477/) (2023)
- [Subgraph Aggregation for Out-of-Distribution Generalization on Graphs](https://mlsanity.com/paper/2410.22228/) (2024)
- [Unifying Invariance and Spuriousity for Graph Out-of-Distribution via Probability of Necessity and Sufficiency](https://mlsanity.com/paper/2402.09165/) (2024)
- [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)
- [A Recipe for Causal Graph Regression: Confounding Effects Revisited](https://mlsanity.com/paper/2507.00440/) (2025)
- [Unifying Invariant and Variant Features for Graph Out-of-Distribution via Probability of Necessity and Sufficiency](https://mlsanity.com/paper/2407.15273/) (2024)
- [Invariant Graph Learning Meets Information Bottleneck for Out-of-Distribution Generalization](https://mlsanity.com/paper/2408.01697/) (2024)
- [Enhancing Distribution and Label Consistency for Graph Out-of-Distribution Generalization](https://mlsanity.com/paper/2501.04102/) (2025)
- [Generative Risk Minimization for Out-of-Distribution Generalization on Graphs](https://mlsanity.com/paper/2502.07968/) (2025)
- [Out-of-Distribution Generalization on Graphs via Progressive Inference](https://mlsanity.com/paper/2503.02988/) (2025)
- [Invariant Graph Transformer for Out-of-Distribution Generalization](https://mlsanity.com/paper/2508.00304/) (2025)
- [Quantifying Distributional Invariance in Causal Subgraph for IRM-Free Graph Generalization](https://mlsanity.com/paper/2510.20295/) (2025)
- [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)
- [Scale-aware Message Passing For Graph Node Classification](https://mlsanity.com/paper/2411.19392/) (2024)
- [Learning Invariant Graph Representations Through Redundant Information](https://mlsanity.com/paper/2512.06154/) (2025)
- [Context-aware Graph Causality Inference for Few-Shot Molecular Property Prediction](https://mlsanity.com/paper/2601.11135/) (2026)
- [Score-based Conditional Out-of-Distribution Augmentation for Graph Covariate Shift](https://mlsanity.com/paper/2410.17506/) (2024)

## Abstract (arXiv)

Invariant graph representation learning aims to learn the invariance among data from different environments for out-of-distribution generalization on graphs. As the graph environment partitions are usually expensive to obtain, augmenting the environment information has become the de facto approach. However, the usefulness of the augmented environment information has never been verified. In this work, we find that it is fundamentally impossible to learn invariant graph representations via environment augmentation without additional assumptions. Therefore, we develop a set of minimal assumptions, including variation sufficiency and variation consistency, for feasible invariant graph learning. We then propose a new framework Graph invAriant Learning Assistant (GALA). GALA incorporates an assistant model that needs to be sensitive to graph environment changes or distribution shifts. The correctness of the proxy predictions by the assistant model hence can differentiate the variations in spurious subgraphs. We show that extracting the maximally invariant subgraph to the proxy predictions provably identifies the underlying invariant subgraph for successful OOD generalization under the established minimal assumptions. Extensive experiments on datasets including DrugOOD with various graph distribution shifts confirm the effectiveness of GALA.