# Energy-based Out-of-Distribution Detection for Graph Neural Networks

arXiv: https://arxiv.org/abs/2302.02914 · HTML: https://mlsanity.com/paper/2302.02914/

## Key facts

- Cited by 68 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 52 references that are in the map.
- First posted on arXiv 6 Feb 2023.

## Builds on (most cited first, 30 of 36)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [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)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [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)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [ReAct: Out-of-distribution Detection With Rectified Activations](https://mlsanity.com/paper/2111.12797/) (2021)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Generalized ODIN: Detecting Out-of-distribution Image without Learning from Out-of-distribution Data](https://mlsanity.com/paper/2002.11297/) (2020)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [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)
- [Learning Confidence for Out-of-Distribution Detection in Neural Networks](https://mlsanity.com/paper/1802.04865/) (2018)
- [A Theory of Generative ConvNet](https://mlsanity.com/paper/1602.03264/) (2016)
- [Handling Distribution Shifts on Graphs: An Invariance Perspective](https://mlsanity.com/paper/2202.02466/) (2022)
- [Dark Model Adaptation: Semantic Image Segmentation from Daytime to Nighttime](https://mlsanity.com/paper/1810.02575/) (2018)
- [Uncertainty Aware Semi-Supervised Learning on Graph Data](https://mlsanity.com/paper/2010.12783/) (2020)
- [DIFFormer: Scalable (Graph) Transformers Induced by Energy Constrained Diffusion](https://mlsanity.com/paper/2301.09474/) (2023)
- [Size-Invariant Graph Representations for Graph Classification Extrapolations](https://mlsanity.com/paper/2103.05045/) (2021)
- [Graph Posterior Network: Bayesian Predictive Uncertainty for Node Classification](https://mlsanity.com/paper/2110.14012/) (2021)
- [Subgroup Generalization and Fairness of Graph Neural Networks](https://mlsanity.com/paper/2106.15535/) (2021)
- [Twitch Gamers: a Dataset for Evaluating Proximity Preserving and Structural Role-based Node Embeddings](https://mlsanity.com/paper/2101.03091/) (2021)
- [Discriminative out-of-distribution detection for semantic segmentation](https://mlsanity.com/paper/1808.07703/) (2018)

## Built on by (most cited first, 30 of 68)

- [SGFormer: Simplifying and Empowering Transformers for Large-Graph Representations](https://mlsanity.com/paper/2306.10759/) (2023)
- [Dream the Impossible: Outlier Imagination with Diffusion Models](https://mlsanity.com/paper/2309.13415/) (2023)
- [A Survey of Graph Neural Networks in Real world: Imbalance, Noise, Privacy and OOD Challenges](https://mlsanity.com/paper/2403.04468/) (2024)
- [Towards Understanding the Generalization of Graph Neural Networks](https://mlsanity.com/paper/2305.08048/) (2023)
- [How Does Unlabeled Data Provably Help Out-of-Distribution Detection?](https://mlsanity.com/paper/2402.03502/) (2024)
- [Out-of-Distribution Detection: A Task-Oriented Survey of Recent Advances](https://mlsanity.com/paper/2409.11884/) (2024)
- [Subgraph Pooling: Tackling Negative Transfer on Graphs](https://mlsanity.com/paper/2402.08907/) (2024)
- [GOLD: Graph Out-of-Distribution Detection via Implicit Adversarial Latent Generation](https://mlsanity.com/paper/2502.05780/) (2025)
- [Handling Out-of-Distribution Data: A Survey](https://mlsanity.com/paper/2507.21160/) (2025)
- [GraphGLOW: Universal and Generalizable Structure Learning for Graph Neural Networks](https://mlsanity.com/paper/2306.11264/) (2023)
- [Uncertainty for Active Learning on Graphs](https://mlsanity.com/paper/2405.01462/) (2024)
- [SeTAR: Out-of-Distribution Detection with Selective Low-Rank Approximation](https://mlsanity.com/paper/2406.12629/) (2024)
- [Can OOD Object Detectors Learn from Foundation Models?](https://mlsanity.com/paper/2409.05162/) (2024)
- [LEGO-Learn: Label-Efficient Graph Open-Set Learning](https://mlsanity.com/paper/2410.16386/) (2024)
- [Decoupled Graph Energy-based Model for Node Out-of-Distribution Detection on Heterophilic Graphs](https://mlsanity.com/paper/2502.17912/) (2025)
- [SGOOD: Substructure-enhanced Graph-Level Out-of-Distribution Detection](https://mlsanity.com/paper/2310.10237/) (2023)
- [Taming False Positives in Out-of-Distribution Detection with Human Feedback](https://mlsanity.com/paper/2404.16954/) (2024)
- [Mitigating Label Noise on Graph via Topological Sample Selection](https://mlsanity.com/paper/2403.01942/) (2024)
- [When and How Does In-Distribution Label Help Out-of-Distribution Detection?](https://mlsanity.com/paper/2405.18635/) (2024)
- [Few-Shot Graph Out-of-Distribution Detection with LLMs](https://mlsanity.com/paper/2503.22097/) (2025)
- [Bounded and Uniform Energy-based Out-of-distribution Detection for Graphs](https://mlsanity.com/paper/2504.13429/) (2025)
- [Graph Synthetic Out-of-Distribution Exposure with Large Language Models](https://mlsanity.com/paper/2504.21198/) (2025)
- [Understanding and Mitigating Under-Confidence in GNNs from the Final Layer](https://mlsanity.com/paper/2505.11335/) (2025)
- [Clarify Confused Nodes via Separated Learning](https://mlsanity.com/paper/2306.02285/) (2023)
- [Improvements on Uncertainty Quantification for Node Classification via Distance-Based Regularization](https://mlsanity.com/paper/2311.05795/) (2023)
- [GDDA: Semantic OOD Detection on Graphs under Covariate Shift via Score-Based Diffusion Models](https://mlsanity.com/paper/2410.17526/) (2024)
- [Managing the unknown: a survey on Open Set Recognition and tangential areas](https://mlsanity.com/paper/2312.08785/) (2023)
- [MLDGG: Meta-Learning for Domain Generalization on Graphs](https://mlsanity.com/paper/2411.12913/) (2024)
- [Out-of-Distribution Detection using Synthetic Data Generation](https://mlsanity.com/paper/2502.03323/) (2025)
- [An Information-Theoretic Framework for Feature Construction in Out-of-Distribution Detection](https://mlsanity.com/paper/2506.14194/) (2025)

## Abstract (arXiv)

Learning on graphs, where instance nodes are inter-connected, has become one of the central problems for deep learning, as relational structures are pervasive and induce data inter-dependence which hinders trivial adaptation of existing approaches that assume inputs to be i.i.d.~sampled. However, current models mostly focus on improving testing performance of in-distribution data and largely ignore the potential risk w.r.t. out-of-distribution (OOD) testing samples that may cause negative outcome if the prediction is overconfident on them. In this paper, we investigate the under-explored problem, OOD detection on graph-structured data, and identify a provably effective OOD discriminator based on an energy function directly extracted from graph neural networks trained with standard classification loss. This paves a way for a simple, powerful and efficient OOD detection model for GNN-based learning on graphs, which we call GNNSafe. It also has nice theoretical properties that guarantee an overall distinguishable margin between the detection scores for in-distribution and OOD samples, which, more critically, can be further strengthened by a learning-free energy belief propagation scheme. For comprehensive evaluation, we introduce new benchmark settings that evaluate the model for detecting OOD data from both synthetic and real distribution shifts (cross-domain graph shifts and temporal graph shifts). The results show that GNNSafe achieves up to 17.0% AUROC improvement over state-of-the-arts and it could serve as simple yet strong baselines in such an under-developed area.