# What Information Matters? Graph Out-of-Distribution Detection via Tri-Component Information Decomposition

arXiv: https://arxiv.org/abs/2605.13032 · HTML: https://mlsanity.com/paper/2605.13032/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 61 of its 84 references that are in the map.
- First posted on arXiv 13 May 2026.

## Builds on (most cited first, 30 of 61)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [ReAct: Out-of-distribution Detection With Rectified Activations](https://mlsanity.com/paper/2111.12797/) (2021)
- [Scaling Out-of-Distribution Detection for Real-World Settings](https://mlsanity.com/paper/1911.11132/) (2019)
- [Generalized ODIN: Detecting Out-of-distribution Image without Learning from Out-of-distribution Data](https://mlsanity.com/paper/2002.11297/) (2020)
- [Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samples](https://mlsanity.com/paper/1711.09325/) (2017)
- [Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problem](https://mlsanity.com/paper/1812.05720/) (2018)
- [VOS: Learning What You Don't Know by Virtual Outlier Synthesis](https://mlsanity.com/paper/2202.01197/) (2022)
- [Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.06607/) (2021)
- [Extremely Simple Activation Shaping for Out-of-Distribution Detection](https://mlsanity.com/paper/2209.09858/) (2022)
- [Learning Robust Representations via Multi-View Information Bottleneck](https://mlsanity.com/paper/2002.07017/) (2020)
- [Graph Information Bottleneck](https://mlsanity.com/paper/2010.12811/) (2020)
- [GOOD: A Graph Out-of-Distribution Benchmark](https://mlsanity.com/paper/2206.08452/) (2022)
- [Out-of-Distribution Detection Using an Ensemble of Self Supervised Leave-out Classifiers](https://mlsanity.com/paper/1809.03576/) (2018)
- [ATOM: Robustifying Out-of-distribution Detection Using Outlier Mining](https://mlsanity.com/paper/2006.15207/) (2020)
- [Can multi-label classification networks know what they don't know?](https://mlsanity.com/paper/2109.14162/) (2021)
- [Out-Of-Distribution Generalization on Graphs: A Survey](https://mlsanity.com/paper/2202.07987/) (2022)
- [Uncertainty Aware Semi-Supervised Learning on Graph Data](https://mlsanity.com/paper/2010.12783/) (2020)
- [MOOD: Multi-level Out-of-distribution Detection](https://mlsanity.com/paper/2104.14726/) (2021)
- [How Does Information Bottleneck Help Deep Learning?](https://mlsanity.com/paper/2305.18887/) (2023)
- [Graph Structure Learning with Variational Information Bottleneck](https://mlsanity.com/paper/2112.08903/) (2021)
- [Graph Posterior Network: Bayesian Predictive Uncertainty for Node Classification](https://mlsanity.com/paper/2110.14012/) (2021)

## Built on by (most cited first, 1 of 1)

- [Call Neighbours Yourself: Graph Walks with Destination-Conditioned On-Policy Self-Distillation](https://mlsanity.com/paper/2608.29588/) (2026)

## Abstract (arXiv)

Graph neural networks are widely used for node classification, but they remain vulnerable to out-of-distribution (OOD) shifts in node features and graph structure. Prior work established that methods trained with standard supervised learning (SL) objectives tend to capture spurious signals from either features and/or structure, leaving the model fragile under distributional changes. To address this, we propose TIDE, a novel and effective Tri-Component Information Decomposition framework that explicitly decomposes information into feature-specific, structure-specific and joint components. TIDE aims to preserve only the label-relevant part of the joint information while filtering out spurious feature- and structure-specific information, thereby enhancing the separation between in-distribution (ID) and OOD nodes. Beyond the framework, we provide theoretical and empirical analyses showing that an information bottleneck objective is preferable to standard SL for graph OOD detection, with higher ID confidence and a greater entropy gap between ID and OOD data. Extensive experiments across seven datasets confirm the efficacy of TIDE, achieving up to a 34% improvement in FPR95 over strong baselines while maintaining competitive ID accuracy.