# IENE: Identifying and Extrapolating the Node Environment for Out-of-Distribution Generalization on Graphs

arXiv: https://arxiv.org/abs/2406.00764 · HTML: https://mlsanity.com/paper/2406.00764/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 47 of its 63 references that are in the map.
- First posted on arXiv 2 Jun 2024.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [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)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [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)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [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)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [One pixel attack for fooling deep neural networks](https://mlsanity.com/paper/1710.08864/) (2017)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style](https://mlsanity.com/paper/2106.04619/) (2021)
- [Environment Inference for Invariant Learning](https://mlsanity.com/paper/2010.07249/) (2020)
- [The Risks of Invariant Risk Minimization](https://mlsanity.com/paper/2010.05761/) (2020)
- [No Subclass Left Behind: Fine-Grained Robustness in Coarse-Grained Classification Problems](https://mlsanity.com/paper/2011.12945/) (2020)
- [Topology Attack and Defense for Graph Neural Networks: An Optimization Perspective](https://mlsanity.com/paper/1906.04214/) (2019)
- [Invariant Risk Minimization Games](https://mlsanity.com/paper/2002.04692/) (2020)
- [Discovering Invariant Rationales for Graph Neural Networks](https://mlsanity.com/paper/2201.12872/) (2022)
- [Handling Distribution Shifts on Graphs: An Invariance Perspective](https://mlsanity.com/paper/2202.02466/) (2022)
- [A Meta-Transfer Objective for Learning to Disentangle Causal Mechanisms](https://mlsanity.com/paper/1901.10912/) (2019)
- [Learning Causally Invariant Representations for Out-of-Distribution Generalization on Graphs](https://mlsanity.com/paper/2202.05441/) (2022)
- [Convergence Analysis of Two-layer Neural Networks with ReLU Activation](https://mlsanity.com/paper/1705.09886/) (2017)
- [Invariant Rationalization](https://mlsanity.com/paper/2003.09772/) (2020)

## Abstract (arXiv)

Due to the performance degradation of graph neural networks (GNNs) under distribution shifts, the work on out-of-distribution (OOD) generalization on graphs has received widespread attention. A novel perspective involves distinguishing potential confounding biases from different environments through environmental identification, enabling the model to escape environmentally-sensitive correlations and maintain stable performance under distribution shifts. However, in graph data, confounding factors not only affect the generation process of node features but also influence the complex interaction between nodes. We observe that neglecting either aspect of them will lead to a decrease in performance. In this paper, we propose IENE, an OOD generalization method on graphs based on node-level environmental identification and extrapolation techniques. It strengthens the model's ability to extract invariance from two granularities simultaneously, leading to improved generalization. Specifically, to identify invariance in features, we utilize the disentangled information bottleneck framework to achieve mutual promotion between node-level environmental estimation and invariant feature learning. Furthermore, we extrapolate topological environments through graph augmentation techniques to identify structural invariance. We implement the conceptual method with specific algorithms and provide theoretical analysis and proofs for our approach. Extensive experimental evaluations on two synthetic and four real-world OOD datasets validate the superiority of IENE, which outperforms existing techniques and provides a flexible framework for enhancing the generalization of GNNs.