# Learning on Graphs with Out-of-Distribution Nodes

arXiv: https://arxiv.org/abs/2308.06714 · HTML: https://mlsanity.com/paper/2308.06714/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 38 references that are in the map.
- First posted on arXiv 13 Aug 2023.

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

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [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)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning](https://mlsanity.com/paper/1704.03976/) (2017)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instances](https://mlsanity.com/paper/2007.08176/) (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)
- [SSD: A Unified Framework for Self-Supervised Outlier Detection](https://mlsanity.com/paper/2103.12051/) (2021)
- [Wiki-CS: A Wikipedia-Based Benchmark for Graph Neural Networks](https://mlsanity.com/paper/2007.02901/) (2020)
- [Out-of-Distribution Detection Using an Ensemble of Self Supervised Leave-out Classifiers](https://mlsanity.com/paper/1809.03576/) (2018)
- [From Local Structures to Size Generalization in Graph Neural Networks](https://mlsanity.com/paper/2010.08853/) (2020)
- [Characteristic Functions on Graphs: Birds of a Feather, from Statistical Descriptors to Parametric Models](https://mlsanity.com/paper/2005.07959/) (2020)
- [Unsupervised Out-of-Distribution Detection by Maximum Classifier Discrepancy](https://mlsanity.com/paper/1908.04951/) (2019)
- [Multi-Stage Self-Supervised Learning for Graph Convolutional Networks on Graphs with Few Labels](https://mlsanity.com/paper/1902.11038/) (2019)
- [Uncertainty Aware Semi-Supervised Learning on Graph Data](https://mlsanity.com/paper/2010.12783/) (2020)
- [Be Confident! Towards Trustworthy Graph Neural Networks via Confidence Calibration](https://mlsanity.com/paper/2109.14285/) (2021)
- [Size-Invariant Graph Representations for Graph Classification Extrapolations](https://mlsanity.com/paper/2103.05045/) (2021)
- [Multi-Task Curriculum Framework for Open-Set Semi-Supervised Learning](https://mlsanity.com/paper/2007.11330/) (2020)
- [NRGNN: Learning a Label Noise-Resistant Graph Neural Network on Sparsely and Noisily Labeled Graphs](https://mlsanity.com/paper/2106.04714/) (2021)
- [OpenMatch: Open-set Consistency Regularization for Semi-supervised Learning with Outliers](https://mlsanity.com/paper/2105.14148/) (2021)
- [Entropic Out-of-Distribution Detection](https://mlsanity.com/paper/1908.05569/) (2019)

## Built on by (most cited first, 29 of 29)

- [A Survey of Graph Neural Networks in Real world: Imbalance, Noise, Privacy and OOD Challenges](https://mlsanity.com/paper/2403.04468/) (2024)
- [Uncertainty in Graph Neural Networks: A Survey](https://mlsanity.com/paper/2403.07185/) (2024)
- [GraphMETRO: Mitigating Complex Graph Distribution Shifts via Mixture of Aligned Experts](https://mlsanity.com/paper/2312.04693/) (2023)
- [GOODAT: Towards Test-time Graph Out-of-Distribution Detection](https://mlsanity.com/paper/2401.06176/) (2024)
- [A Survey of Deep Graph Learning under Distribution Shifts: from Graph Out-of-Distribution Generalization to Adaptation](https://mlsanity.com/paper/2410.19265/) (2024)
- [Reconsidering Faithfulness in Regular, Self-Explainable and Domain Invariant GNNs](https://mlsanity.com/paper/2406.15156/) (2024)
- [GOLD: Graph Out-of-Distribution Detection via Implicit Adversarial Latent Generation](https://mlsanity.com/paper/2502.05780/) (2025)
- [Bridged-GNN: Knowledge Bridge Learning for Effective Knowledge Transfer](https://mlsanity.com/paper/2308.09499/) (2023)
- [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)
- [Multitask Active Learning for Graph Anomaly Detection](https://mlsanity.com/paper/2401.13210/) (2024)
- [Few-Shot Graph Out-of-Distribution Detection with LLMs](https://mlsanity.com/paper/2503.22097/) (2025)
- [Graph Synthetic Out-of-Distribution Exposure with Large Language Models](https://mlsanity.com/paper/2504.21198/) (2025)
- [Open-World Lifelong Graph Learning](https://mlsanity.com/paper/2310.12565/) (2023)
- [Unveiling Mode Connectivity in Graph Neural Networks](https://mlsanity.com/paper/2502.12608/) (2025)
- [Text Meets Topology: Rethinking Out-of-distribution Detection in Text-Rich Networks](https://mlsanity.com/paper/2508.17690/) (2025)
- [DELTA: Dual Consistency Delving with Topological Uncertainty for Active Graph Domain Adaptation](https://mlsanity.com/paper/2409.08946/) (2024)
- [GLIP-OOD: Zero-Shot Graph OOD Detection with Graph Foundation Model](https://mlsanity.com/paper/2504.21186/) (2025)
- [Introducing New Node Prediction in Graph Mining: Predicting All Links from Isolated Nodes with Graph Neural Networks](https://mlsanity.com/paper/2401.05468/) (2024)
- [Open-World Semi-Supervised Learning for Node Classification](https://mlsanity.com/paper/2403.11483/) (2024)
- [Harnessing Feature Resonance under Arbitrary Target Alignment for Out-of-Distribution Node Detection](https://mlsanity.com/paper/2502.16076/) (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)
- [HKTGNN: Hierarchical Knowledge Transferable Graph Neural Network-based Supply Chain Risk Assessment](https://mlsanity.com/paper/2311.04244/) (2023)
- [G-OSR: A Comprehensive Benchmark for Graph Open-Set Recognition](https://mlsanity.com/paper/2503.00476/) (2025)
- [Out-of-Distribution Detection in Heterogeneous Graphs via Energy Propagation](https://mlsanity.com/paper/2505.03774/) (2025)
- [Towards Robust Artificial Intelligence: Self-Supervised Learning Approach for Out-of-Distribution Detection](https://mlsanity.com/paper/2510.12713/) (2025)

## Abstract (arXiv)

Graph Neural Networks (GNNs) are state-of-the-art models for performing prediction tasks on graphs. While existing GNNs have shown great performance on various tasks related to graphs, little attention has been paid to the scenario where out-of-distribution (OOD) nodes exist in the graph during training and inference. Borrowing the concept from CV and NLP, we define OOD nodes as nodes with labels unseen from the training set. Since a lot of networks are automatically constructed by programs, real-world graphs are often noisy and may contain nodes from unknown distributions. In this work, we define the problem of graph learning with out-of-distribution nodes. Specifically, we aim to accomplish two tasks: 1) detect nodes which do not belong to the known distribution and 2) classify the remaining nodes to be one of the known classes. We demonstrate that the connection patterns in graphs are informative for outlier detection, and propose Out-of-Distribution Graph Attention Network (OODGAT), a novel GNN model which explicitly models the interaction between different kinds of nodes and separate inliers from outliers during feature propagation. Extensive experiments show that OODGAT outperforms existing outlier detection methods by a large margin, while being better or comparable in terms of in-distribution classification.