# OOD-GNN: Out-of-Distribution Generalized Graph Neural Network

arXiv: https://arxiv.org/abs/2112.03806 · HTML: https://mlsanity.com/paper/2112.03806/

## Key facts

- Cited by 78 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 86 references that are in the map.
- First posted on arXiv 7 Dec 2021.

## Builds on (most cited first, 30 of 47)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [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)
- [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)
- [Unsupervised Feature Learning via Non-Parametric Instance-level Discrimination](https://mlsanity.com/paper/1805.01978/) (2018)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Learning to Reweight Examples for Robust Deep Learning](https://mlsanity.com/paper/1803.09050/) (2018)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Understanding disentangling in β-VAE](https://mlsanity.com/paper/1804.03599/) (2018)
- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [Modeling polypharmacy side effects with graph convolutional networks](https://mlsanity.com/paper/1802.00543/) (2018)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [Generalization and Representational Limits of Graph Neural Networks](https://mlsanity.com/paper/2002.06157/) (2020)
- [What graph neural networks cannot learn: depth vs width](https://mlsanity.com/paper/1907.03199/) (2019)
- [Learning De-biased Representations with Biased Representations](https://mlsanity.com/paper/1910.02806/) (2019)
- [Understanding Attention and Generalization in Graph Neural Networks](https://mlsanity.com/paper/1905.02850/) (2019)
- [Measuring abstract reasoning in neural networks](https://mlsanity.com/paper/1807.04225/) (2018)
- [Deep Stable Learning for Out-Of-Distribution Generalization](https://mlsanity.com/paper/2104.07876/) (2021)
- [An Empirical Study on Robustness to Spurious Correlations using Pre-trained Language Models](https://mlsanity.com/paper/2007.06778/) (2020)
- [From Local Structures to Size Generalization in Graph Neural Networks](https://mlsanity.com/paper/2010.08853/) (2020)
- [Learning to Decompose and Disentangle Representations for Video Prediction](https://mlsanity.com/paper/1806.04166/) (2018)
- [Neural Execution of Graph Algorithms](https://mlsanity.com/paper/1910.10593/) (2019)

## Built on by (most cited first, 30 of 78)

- [GOOD: A Graph Out-of-Distribution Benchmark](https://mlsanity.com/paper/2206.08452/) (2022)
- [Disentangled Representation Learning](https://mlsanity.com/paper/2211.11695/) (2022)
- [Out-Of-Distribution Generalization on Graphs: A Survey](https://mlsanity.com/paper/2202.07987/) (2022)
- [Debiasing Graph Neural Networks via Learning Disentangled Causal Substructure](https://mlsanity.com/paper/2209.14107/) (2022)
- [A Comprehensive Survey on Deep Graph Representation Learning](https://mlsanity.com/paper/2304.05055/) (2023)
- [Graph Rationalization with Environment-based Augmentations](https://mlsanity.com/paper/2206.02886/) (2022)
- [A Survey of Graph Neural Networks in Real world: Imbalance, Noise, Privacy and OOD Challenges](https://mlsanity.com/paper/2403.04468/) (2024)
- [Deciphering Spatio-Temporal Graph Forecasting: A Causal Lens and Treatment](https://mlsanity.com/paper/2309.13378/) (2023)
- [Unleashing the Power of Graph Data Augmentation on Covariate Distribution Shift](https://mlsanity.com/paper/2211.02843/) (2022)
- [Deep Learning for Cross-Domain Data Fusion in Urban Computing: Taxonomy, Advances, and Outlook](https://mlsanity.com/paper/2402.19348/) (2024)
- [Environment-Aware Dynamic Graph Learning for Out-of-Distribution Generalization](https://mlsanity.com/paper/2311.11114/) (2023)
- [Learning Invariant Molecular Representation in Latent Discrete Space](https://mlsanity.com/paper/2310.14170/) (2023)
- [GraphMETRO: Mitigating Complex Graph Distribution Shifts via Mixture of Aligned Experts](https://mlsanity.com/paper/2312.04693/) (2023)
- [Spectral Invariant Learning for Dynamic Graphs under Distribution Shifts](https://mlsanity.com/paper/2403.05026/) (2024)
- [Graph Learning under Distribution Shifts: A Comprehensive Survey on Domain Adaptation, Out-of-distribution, and Continual Learning](https://mlsanity.com/paper/2402.16374/) (2024)
- [Near-Optimal Nonconvex-Strongly-Convex Bilevel Optimization with Fully First-Order Oracles](https://mlsanity.com/paper/2306.14853/) (2023)
- [A Survey of Deep Graph Learning under Distribution Shifts: from Graph Out-of-Distribution Generalization to Adaptation](https://mlsanity.com/paper/2410.19265/) (2024)
- [Out-of-Distribution Generalization in Time Series: A Survey](https://mlsanity.com/paper/2503.13868/) (2025)
- [Curriculum Graph Machine Learning: A Survey](https://mlsanity.com/paper/2302.02926/) (2023)
- [Shift-Robust Molecular Relational Learning with Causal Substructure](https://mlsanity.com/paper/2305.18451/) (2023)
- [Individual and Structural Graph Information Bottlenecks for Out-of-Distribution Generalization](https://mlsanity.com/paper/2306.15902/) (2023)
- [GOLD: Graph Out-of-Distribution Detection via Implicit Adversarial Latent Generation](https://mlsanity.com/paper/2502.05780/) (2025)
- [Graph Contrastive Learning with Personalized Augmentation](https://mlsanity.com/paper/2209.06560/) (2022)
- [BeMap: Balanced Message Passing for Fair Graph Neural Network](https://mlsanity.com/paper/2306.04107/) (2023)
- [Predicting the Silent Majority on Graphs: Knowledge Transferable Graph Neural Network](https://mlsanity.com/paper/2302.00873/) (2023)
- [Identifying Semantic Component for Robust Molecular Property Prediction](https://mlsanity.com/paper/2311.04837/) (2023)
- [Matcha: Mitigating Graph Structure Shifts with Test-Time Adaptation](https://mlsanity.com/paper/2410.06976/) (2024)
- [Automated Graph Machine Learning: Approaches, Libraries, Benchmarks and Directions](https://mlsanity.com/paper/2201.01288/) (2022)
- [Graph Out-of-Distribution Generalization with Controllable Data Augmentation](https://mlsanity.com/paper/2308.08344/) (2023)
- [GInX-Eval: Towards In-Distribution Evaluation of Graph Neural Network Explanations](https://mlsanity.com/paper/2309.16223/) (2023)

## Abstract (arXiv)

Graph neural networks (GNNs) have achieved impressive performance when testing and training graph data come from identical distribution. However, existing GNNs lack out-of-distribution generalization abilities so that their performance substantially degrades when there exist distribution shifts between testing and training graph data. To solve this problem, in this work, we propose an out-of-distribution generalized graph neural network (OOD-GNN) for achieving satisfactory performance on unseen testing graphs that have different distributions with training graphs. Our proposed OOD-GNN employs a novel nonlinear graph representation decorrelation method utilizing random Fourier features, which encourages the model to eliminate the statistical dependence between relevant and irrelevant graph representations through iteratively optimizing the sample graph weights and graph encoder. We further present a global weight estimator to learn weights for training graphs such that variables in graph representations are forced to be independent. The learned weights help the graph encoder to get rid of spurious correlations and, in turn, concentrate more on the true connection between learned discriminative graph representations and their ground-truth labels. We conduct extensive experiments to validate the out-of-distribution generalization abilities on two synthetic and 12 real-world datasets with distribution shifts. The results demonstrate that our proposed OOD-GNN significantly outperforms state-of-the-art baselines.