# Graph Structure and Feature Extrapolation for Out-of-Distribution Generalization

arXiv: https://arxiv.org/abs/2306.08076 · HTML: https://mlsanity.com/paper/2306.08076/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 69 of its 95 references that are in the map.
- First posted on arXiv 13 Jun 2023.

## Builds on (most cited first, 30 of 69)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [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)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Deep Visual Domain Adaptation: A Survey](https://mlsanity.com/paper/1802.03601/) (2018)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Towards Out-Of-Distribution Generalization: A Survey](https://mlsanity.com/paper/2108.13624/) (2021)
- [Explainability in Graph Neural Networks: A Taxonomic Survey](https://mlsanity.com/paper/2012.15445/) (2020)
- [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018)
- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [The Risks of Invariant Risk Minimization](https://mlsanity.com/paper/2010.05761/) (2020)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)

## Built on by (most cited first, 10 of 10)

- [Does Invariant Graph Learning via Environment Augmentation Learn Invariance?](https://mlsanity.com/paper/2310.19035/) (2023)
- [Equivariance via Minimal Frame Averaging for More Symmetries and Efficiency](https://mlsanity.com/paper/2406.07598/) (2024)
- [Deep Generative Models for Detector Signature Simulation: A Taxonomic Review](https://mlsanity.com/paper/2312.09597/) (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)
- [How Interpretable Are Interpretable Graph Neural Networks?](https://mlsanity.com/paper/2406.07955/) (2024)
- [Dissecting the Failure of Invariant Learning on Graphs](https://mlsanity.com/paper/2411.02847/) (2024)
- [Pruning Spurious Subgraphs for Graph Out-of-Distribution Generalization](https://mlsanity.com/paper/2506.05957/) (2025)
- [Invariant Graph Learning Meets Information Bottleneck for Out-of-Distribution Generalization](https://mlsanity.com/paper/2408.01697/) (2024)
- [Out-of-Distribution Generalization on Graphs via Progressive Inference](https://mlsanity.com/paper/2503.02988/) (2025)
- [Out-of-Distribution Graph Models Merging](https://mlsanity.com/paper/2506.03674/) (2025)

## Abstract (arXiv)

Out-of-distribution (OOD) generalization deals with the prevalent learning scenario where test distribution shifts from training distribution. With rising application demands and inherent complexity, graph OOD problems call for specialized solutions. While data-centric methods exhibit performance enhancements on many generic machine learning tasks, there is a notable absence of data augmentation methods tailored for graph OOD generalization. In this work, we propose to achieve graph OOD generalization with the novel design of non-Euclidean-space linear extrapolation. The proposed augmentation strategy extrapolates both structure and feature spaces to generate OOD graph data. Our design tailors OOD samples for specific shifts without corrupting underlying causal mechanisms. Theoretical analysis and empirical results evidence the effectiveness of our method in solving target shifts, showing substantial and constant improvements across various graph OOD tasks.