mlsanityData to 14 Oct 2026

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

arXiv 2504.13429 ↗First posted 18 Apr 2025cs.LG cs.AIcited by 6

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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%).

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

31 of 40 references.

References · 31

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  2. 2017Graph Attention Networkscited by 8,923
  3. 2016A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networkscited by 2,385
  4. 2020Open Graph Benchmark: Datasets for Machine Learning on Graphscited by 2,163
  5. 2018A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attackscited by 1,485
  6. 2017Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networkscited by 1,328
  7. 2020Energy-based Out-of-distribution Detectioncited by 1,299
  8. 2018Deep Anomaly Detection with Outlier Exposurecited by 942
  9. 2018Representation Learning on Graphs with Jumping Knowledge Networkscited by 877
  10. 2019Graph Neural Networks for Social Recommendationcited by 714
  11. 2022Out-of-Distribution Detection with Deep Nearest Neighborscited by 600
  12. 2018Predictive Uncertainty Estimation via Prior Networkscited by 557
19 more
  1. 2015Towards Open Set Deep Networkscited by 538
  2. 2021ReAct: Out-of-distribution Detection With Rectified Activationscited by 486
  3. 2019MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixingcited by 443
  4. 2018MolGAN: An implicit generative model for small molecular graphscited by 393
  5. 2019SelectiveNet: A Deep Neural Network with an Integrated Reject Optioncited by 350
  6. 2021On the Importance of Gradients for Detecting Distributional Shifts in the Wildcited by 339
  7. 2020Point-GNN: Graph Neural Network for 3D Object Detection in a Point Cloudcited by 335
  8. 2022Mitigating Neural Network Overconfidence with Logit Normalizationcited by 252
  9. 2022Handling Distribution Shifts on Graphs: An Invariance Perspectivecited by 164
  10. 2020ATOM: Robustifying Out-of-distribution Detection Using Outlier Miningcited by 116
  11. 2022POEM: Out-of-Distribution Detection with Posterior Samplingcited by 108
  12. 2020Uncertainty Aware Semi-Supervised Learning on Graph Datacited by 95
  13. 2021Graph Posterior Network: Bayesian Predictive Uncertainty for Node Classificationcited by 80
  14. 2023Energy-based Out-of-Distribution Detection for Graph Neural Networkscited by 68
  15. 2021Open-set Label Noise Can Improve Robustness Against Inherent Label Noisecited by 59
  16. 2021Detecting Corrupted Labels Without Training a Model to Predictcited by 58
  17. 2018Discriminative out-of-distribution detection for semantic segmentationcited by 47
  18. 2020Learning to Extrapolate Knowledge: Transductive Few-shot Out-of-Graph Link Predictioncited by 47
  19. 2022Towards OOD Detection in Graph Classification from Uncertainty Estimation Perspectivecited by 13

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 3.

6 papers.

  1. 2025Text Meets Topology: Rethinking Out-of-distribution Detection in Text-Rich Networkscited by 3
  2. 2025When LLMs meet open-world graph learning: a new perspective for unlabeled data uncertaintycited by 1
  3. 2025Coarse-to-Fine Open-Set Graph Node Classification with Large Language Modelscited by 1
  4. 2026LLM-Enhanced Energy Contrastive Learning for Out-of-Distribution Detection in Text-Attributed Graphscited by 1
  5. 2026What Information Matters? Graph Out-of-Distribution Detection via Tri-Component Information Decompositioncited by 1
  6. 2026Learning Graphs through Continuous Information Entropy Fieldscited by 0