# Graph Information Bottleneck

arXiv: https://arxiv.org/abs/2010.12811 · HTML: https://mlsanity.com/paper/2010.12811/

## Key facts

- Cited by 168 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2020.

## Built on by (most cited first, 30 of 168)

- [NodeFormer: A Scalable Graph Structure Learning Transformer for Node Classification](https://mlsanity.com/paper/2306.08385/) (2023)
- [Adversarial Graph Augmentation to Improve Graph Contrastive Learning](https://mlsanity.com/paper/2106.05819/) (2021)
- [Interpretable and Generalizable Graph Learning via Stochastic Attention Mechanism](https://mlsanity.com/paper/2201.12987/) (2022)
- [Data Augmentation for Deep Graph Learning: A Survey](https://mlsanity.com/paper/2202.08235/) (2022)
- [InfoGCL: Information-Aware Graph Contrastive Learning](https://mlsanity.com/paper/2110.15438/) (2021)
- [Robustness of Graph Neural Networks at Scale](https://mlsanity.com/paper/2110.14038/) (2021)
- [Beltrami Flow and Neural Diffusion on Graphs](https://mlsanity.com/paper/2110.09443/) (2021)
- [Graph Structure Learning with Variational Information Bottleneck](https://mlsanity.com/paper/2112.08903/) (2021)
- [On Positional and Structural Node Features for Graph Neural Networks on Non-attributed Graphs](https://mlsanity.com/paper/2107.01495/) (2021)
- [Improving Subgraph Recognition with Variational Graph Information Bottleneck](https://mlsanity.com/paper/2112.09899/) (2021)
- [Towards Self-Interpretable Graph-Level Anomaly Detection](https://mlsanity.com/paper/2310.16520/) (2023)
- [Are Defenses for Graph Neural Networks Robust?](https://mlsanity.com/paper/2301.13694/) (2023)
- [Variational Positive-incentive Noise: How Noise Benefits Models](https://mlsanity.com/paper/2306.07651/) (2023)
- [GUARDIAN: Safeguarding LLM Multi-Agent Collaborations with Temporal Graph Modeling](https://mlsanity.com/paper/2505.19234/) (2025)
- [SE-GSL: A General and Effective Graph Structure Learning Framework through Structural Entropy Optimization](https://mlsanity.com/paper/2303.09778/) (2023)
- [TimeX++: Learning Time-Series Explanations with Information Bottleneck](https://mlsanity.com/paper/2405.09308/) (2024)
- [EIGNN: Efficient Infinite-Depth Graph Neural Networks](https://mlsanity.com/paper/2202.10720/) (2022)
- [DropMessage: Unifying Random Dropping for Graph Neural Networks](https://mlsanity.com/paper/2204.10037/) (2022)
- [Joint Learning of Label and Environment Causal Independence for Graph Out-of-Distribution Generalization](https://mlsanity.com/paper/2306.01103/) (2023)
- [Recognizing Predictive Substructures with Subgraph Information Bottleneck](https://mlsanity.com/paper/2103.11155/) (2021)
- [PAC-Bayes Information Bottleneck](https://mlsanity.com/paper/2109.14509/) (2021)
- [Bringing Your Own View: Graph Contrastive Learning without Prefabricated Data Augmentations](https://mlsanity.com/paper/2201.01702/) (2022)
- [Interpretable Geometric Deep Learning via Learnable Randomness Injection](https://mlsanity.com/paper/2210.16966/) (2022)
- [Conditional Graph Information Bottleneck for Molecular Relational Learning](https://mlsanity.com/paper/2305.01520/) (2023)
- [Graph Information Bottleneck for Remote Sensing Segmentation](https://mlsanity.com/paper/2312.02545/) (2023)
- [Interpretable Prototype-based Graph Information Bottleneck](https://mlsanity.com/paper/2310.19906/) (2023)
- [Improving Molecular Graph Neural Network Explainability with Orthonormalization and Induced Sparsity](https://mlsanity.com/paper/2105.04854/) (2021)
- [Compact Graph Structure Learning via Mutual Information Compression](https://mlsanity.com/paper/2201.05540/) (2022)
- [Self-Supervised Graph Structure Refinement for Graph Neural Networks](https://mlsanity.com/paper/2211.06545/) (2022)
- [EXGC: Bridging Efficiency and Explainability in Graph Condensation](https://mlsanity.com/paper/2402.05962/) (2024)

## Abstract (arXiv)

Representation learning of graph-structured data is challenging because both graph structure and node features carry important information. Graph Neural Networks (GNNs) provide an expressive way to fuse information from network structure and node features. However, GNNs are prone to adversarial attacks. Here we introduce Graph Information Bottleneck (GIB), an information-theoretic principle that optimally balances expressiveness and robustness of the learned representation of graph-structured data. Inheriting from the general Information Bottleneck (IB), GIB aims to learn the minimal sufficient representation for a given task by maximizing the mutual information between the representation and the target, and simultaneously constraining the mutual information between the representation and the input data. Different from the general IB, GIB regularizes the structural as well as the feature information. We design two sampling algorithms for structural regularization and instantiate the GIB principle with two new models: GIB-Cat and GIB-Bern, and demonstrate the benefits by evaluating the resilience to adversarial attacks. We show that our proposed models are more robust than state-of-the-art graph defense models. GIB-based models empirically achieve up to 31% improvement with adversarial perturbation of the graph structure as well as node features.