# Individual and Structural Graph Information Bottlenecks for Out-of-Distribution Generalization

arXiv: https://arxiv.org/abs/2306.15902 · HTML: https://mlsanity.com/paper/2306.15902/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 76 references that are in the map.
- First posted on arXiv 28 Jun 2023.

## Builds on (most cited first, 30 of 49)

- [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)
- [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)
- [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)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [Towards Out-Of-Distribution Generalization: A Survey](https://mlsanity.com/paper/2108.13624/) (2021)
- [Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.06607/) (2021)
- [Central Moment Discrepancy (CMD) for Domain-Invariant Representation Learning](https://mlsanity.com/paper/1702.08811/) (2017)
- [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)
- [Graph Information Bottleneck](https://mlsanity.com/paper/2010.12811/) (2020)
- [Handling Distribution Shifts on Graphs: An Invariance Perspective](https://mlsanity.com/paper/2202.02466/) (2022)
- [Invariant Rationalization](https://mlsanity.com/paper/2003.09772/) (2020)
- [DeepInf: Social Influence Prediction with Deep Learning](https://mlsanity.com/paper/1807.05560/) (2018)
- [From Local Structures to Size Generalization in Graph Neural Networks](https://mlsanity.com/paper/2010.08853/) (2020)
- [Graph Information Bottleneck for Subgraph Recognition](https://mlsanity.com/paper/2010.05563/) (2020)
- [Generalization in Reinforcement Learning with Selective Noise Injection and Information Bottleneck](https://mlsanity.com/paper/1910.12911/) (2019)

## Built on by (most cited first, 15 of 15)

- [Graph Foundation Models: Concepts, Opportunities and Challenges](https://mlsanity.com/paper/2310.11829/) (2023)
- [VQGraph: Rethinking Graph Representation Space for Bridging GNNs and MLPs](https://mlsanity.com/paper/2308.02117/) (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)
- [Safety in Graph Machine Learning: Threats and Safeguards](https://mlsanity.com/paper/2405.11034/) (2024)
- [Disentangled Representation Learning with Transmitted Information Bottleneck](https://mlsanity.com/paper/2311.01686/) (2023)
- [Large Language Models Meet Graph Neural Networks: A Perspective of Graph Mining](https://mlsanity.com/paper/2412.19211/) (2024)
- [Generative Risk Minimization for Out-of-Distribution Generalization on Graphs](https://mlsanity.com/paper/2502.07968/) (2025)
- [Sparse Causal Discovery with Generative Intervention for Unsupervised Graph Domain Adaptation](https://mlsanity.com/paper/2507.07621/) (2025)
- [Improving Graph Out-of-distribution Generalization Beyond Causality](https://mlsanity.com/paper/2407.10204/) (2024)
- [BotTrans: A Multi-Source Graph Domain Adaptation Approach for Social Bot Detection](https://mlsanity.com/paper/2506.13795/) (2025)
- [What Information Matters? Graph Out-of-Distribution Detection via Tri-Component Information Decomposition](https://mlsanity.com/paper/2605.13032/) (2026)
- [NodeNAS: Node-Specific Graph Neural Architecture Search for Out-of-Distribution Generalization](https://mlsanity.com/paper/2503.02448/) (2025)
- [General OOD Detection via Model-aware and Subspace-aware Variable Priority](https://mlsanity.com/paper/2512.13003/) (2025)
- [EdgeMask-DG*: Learning Domain-Invariant Graph Structures via Adversarial Edge Masking](https://mlsanity.com/paper/2602.05571/) (2026)

## Abstract (arXiv)

Out-of-distribution (OOD) graph generalization are critical for many real-world applications. Existing methods neglect to discard spurious or noisy features of inputs, which are irrelevant to the label. Besides, they mainly conduct instance-level class-invariant graph learning and fail to utilize the structural class relationships between graph instances. In this work, we endeavor to address these issues in a unified framework, dubbed Individual and Structural Graph Information Bottlenecks (IS-GIB). To remove class spurious feature caused by distribution shifts, we propose Individual Graph Information Bottleneck (I-GIB) which discards irrelevant information by minimizing the mutual information between the input graph and its embeddings. To leverage the structural intra- and inter-domain correlations, we propose Structural Graph Information Bottleneck (S-GIB). Specifically for a batch of graphs with multiple domains, S-GIB first computes the pair-wise input-input, embedding-embedding, and label-label correlations. Then it minimizes the mutual information between input graph and embedding pairs while maximizing the mutual information between embedding and label pairs. The critical insight of S-GIB is to simultaneously discard spurious features and learn invariant features from a high-order perspective by maintaining class relationships under multiple distributional shifts. Notably, we unify the proposed I-GIB and S-GIB to form our complementary framework IS-GIB. Extensive experiments conducted on both node- and graph-level tasks consistently demonstrate the superior generalization ability of IS-GIB. The code is available at https://github.com/YangLing0818/GraphOOD.