# Bounded and Uniform Energy-based Out-of-distribution Detection for Graphs

arXiv: https://arxiv.org/abs/2504.13429 · HTML: https://mlsanity.com/paper/2504.13429/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 40 references that are in the map.
- First posted on arXiv 18 Apr 2025.

## Builds on (most cited first, 30 of 31)

- [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)
- [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)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Towards Open Set Deep Networks](https://mlsanity.com/paper/1511.06233/) (2015)
- [ReAct: Out-of-distribution Detection With Rectified Activations](https://mlsanity.com/paper/2111.12797/) (2021)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [SelectiveNet: A Deep Neural Network with an Integrated Reject Option](https://mlsanity.com/paper/1901.09192/) (2019)
- [On the Importance of Gradients for Detecting Distributional Shifts in the Wild](https://mlsanity.com/paper/2110.00218/) (2021)
- [Point-GNN: Graph Neural Network for 3D Object Detection in a Point Cloud](https://mlsanity.com/paper/2003.01251/) (2020)
- [Mitigating Neural Network Overconfidence with Logit Normalization](https://mlsanity.com/paper/2205.09310/) (2022)
- [Handling Distribution Shifts on Graphs: An Invariance Perspective](https://mlsanity.com/paper/2202.02466/) (2022)
- [ATOM: Robustifying Out-of-distribution Detection Using Outlier Mining](https://mlsanity.com/paper/2006.15207/) (2020)
- [POEM: Out-of-Distribution Detection with Posterior Sampling](https://mlsanity.com/paper/2206.13687/) (2022)
- [Uncertainty Aware Semi-Supervised Learning on Graph Data](https://mlsanity.com/paper/2010.12783/) (2020)
- [Graph Posterior Network: Bayesian Predictive Uncertainty for Node Classification](https://mlsanity.com/paper/2110.14012/) (2021)
- [Energy-based Out-of-Distribution Detection for Graph Neural Networks](https://mlsanity.com/paper/2302.02914/) (2023)
- [Open-set Label Noise Can Improve Robustness Against Inherent Label Noise](https://mlsanity.com/paper/2106.10891/) (2021)
- [Detecting Corrupted Labels Without Training a Model to Predict](https://mlsanity.com/paper/2110.06283/) (2021)
- [Discriminative out-of-distribution detection for semantic segmentation](https://mlsanity.com/paper/1808.07703/) (2018)
- [Learning to Extrapolate Knowledge: Transductive Few-shot Out-of-Graph Link Prediction](https://mlsanity.com/paper/2006.06648/) (2020)

## Built on by (most cited first, 6 of 6)

- [Text Meets Topology: Rethinking Out-of-distribution Detection in Text-Rich Networks](https://mlsanity.com/paper/2508.17690/) (2025)
- [When LLMs meet open-world graph learning: a new perspective for unlabeled data uncertainty](https://mlsanity.com/paper/2505.13989/) (2025)
- [Coarse-to-Fine Open-Set Graph Node Classification with Large Language Models](https://mlsanity.com/paper/2512.16244/) (2025)
- [LLM-Enhanced Energy Contrastive Learning for Out-of-Distribution Detection in Text-Attributed Graphs](https://mlsanity.com/paper/2603.20293/) (2026)
- [What Information Matters? Graph Out-of-Distribution Detection via Tri-Component Information Decomposition](https://mlsanity.com/paper/2605.13032/) (2026)
- [Learning Graphs through Continuous Information Entropy Fields](https://mlsanity.com/paper/2606.22895/) (2026)

## Abstract (arXiv)

Given the critical role of graphs in real-world applications and their high-security requirements, improving the ability of graph neural networks (GNNs) to detect out-of-distribution (OOD) data is an urgent research problem. The recent work GNNSAFE proposes a framework based on the aggregation of negative energy scores that significantly improves the performance of GNNs to detect node-level OOD data. However, our study finds that score aggregation among nodes is susceptible to extreme values due to the unboundedness of the negative energy scores and logit shifts, which severely limits the accuracy of GNNs in detecting node-level OOD data. In this paper, we propose NODESAFE: reducing the generation of extreme scores of nodes by adding two optimization terms that make the negative energy scores bounded and mitigate the logit shift. Experimental results show that our approach dramatically improves the ability of GNNs to detect OOD data at the node level, e.g., in detecting OOD data induced by Structure Manipulation, the metric of FPR95 (lower is better) in scenarios without (with) OOD data exposure are reduced from the current SOTA by 28.4% (22.7%).