# GOODAT: Towards Test-time Graph Out-of-Distribution Detection

arXiv: https://arxiv.org/abs/2401.06176 · HTML: https://mlsanity.com/paper/2401.06176/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 55 references that are in the map.
- First posted on arXiv 10 Jan 2024.

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [SSD: A Unified Framework for Self-Supervised Outlier Detection](https://mlsanity.com/paper/2103.12051/) (2021)
- [Graph Information Bottleneck](https://mlsanity.com/paper/2010.12811/) (2020)
- [GOOD: A Graph Out-of-Distribution Benchmark](https://mlsanity.com/paper/2206.08452/) (2022)
- [Graph Information Bottleneck for Subgraph Recognition](https://mlsanity.com/paper/2010.05563/) (2020)
- [Uncertainty Aware Semi-Supervised Learning on Graph Data](https://mlsanity.com/paper/2010.12783/) (2020)
- [Propagation Kernels](https://mlsanity.com/paper/1410.3314/) (2014)
- [Federated Learning on Non-IID Graphs via Structural Knowledge Sharing](https://mlsanity.com/paper/2211.13009/) (2022)
- [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)
- [Learning and Evaluating Graph Neural Network Explanations based on Counterfactual and Factual Reasoning](https://mlsanity.com/paper/2202.08816/) (2022)
- [Rethinking and Scaling Up Graph Contrastive Learning: An Extremely Efficient Approach with Group Discrimination](https://mlsanity.com/paper/2206.01535/) (2022)
- [Deep Graph-level Anomaly Detection by Glocal Knowledge Distillation](https://mlsanity.com/paper/2112.10063/) (2021)
- [Empowering Graph Representation Learning with Test-Time Graph Transformation](https://mlsanity.com/paper/2210.03561/) (2022)
- [Towards Self-Interpretable Graph-Level Anomaly Detection](https://mlsanity.com/paper/2310.16520/) (2023)
- [Large Language Models for Scientific Synthesis, Inference and Explanation](https://mlsanity.com/paper/2310.07984/) (2023)
- [Learning on Graphs with Out-of-Distribution Nodes](https://mlsanity.com/paper/2308.06714/) (2023)
- [Learning Strong Graph Neural Networks with Weak Information](https://mlsanity.com/paper/2305.18457/) (2023)
- [Finding the Missing-half: Graph Complementary Learning for Homophily-prone and Heterophily-prone Graphs](https://mlsanity.com/paper/2306.07608/) (2023)
- [GNNEvaluator: Evaluating GNN Performance On Unseen Graphs Without Labels](https://mlsanity.com/paper/2310.14586/) (2023)
- [Projective Ranking-based GNN Evasion Attacks](https://mlsanity.com/paper/2202.12993/) (2022)
- [Dual Intent Enhanced Graph Neural Network for Session-based New Item Recommendation](https://mlsanity.com/paper/2305.05848/) (2023)
- [CGMN: A Contrastive Graph Matching Network for Self-Supervised Graph Similarity Learning](https://mlsanity.com/paper/2205.15083/) (2022)
- [An Exact Algorithm for Minimum Weight Vertex Cover Problem in Large Graphs](https://mlsanity.com/paper/1903.05948/) (2019)

## Built on by (most cited first, 17 of 17)

- [A Survey of Graph Neural Networks in Real world: Imbalance, Noise, Privacy and OOD Challenges](https://mlsanity.com/paper/2403.04468/) (2024)
- [ARC: A Generalist Graph Anomaly Detector with In-Context Learning](https://mlsanity.com/paper/2405.16771/) (2024)
- [Out-of-Distribution Detection: A Task-Oriented Survey of Recent Advances](https://mlsanity.com/paper/2409.11884/) (2024)
- [Unifying Unsupervised Graph-Level Anomaly Detection and Out-of-Distribution Detection: A Benchmark](https://mlsanity.com/paper/2406.15523/) (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)
- [GOLD: Graph Out-of-Distribution Detection via Implicit Adversarial Latent Generation](https://mlsanity.com/paper/2502.05780/) (2025)
- [Uncertainty-Aware Graph Neural Networks: A Multi-Hop Evidence Fusion Approach](https://mlsanity.com/paper/2506.13083/) (2025)
- [A Survey of Generalization of Graph Anomaly Detection: From Transfer Learning to Foundation Models](https://mlsanity.com/paper/2509.06609/) (2025)
- [HC-GLAD: Dual Hyperbolic Contrastive Learning for Unsupervised Graph-Level Anomaly Detection](https://mlsanity.com/paper/2407.02057/) (2024)
- [SpectralGap: Graph-Level Out-of-Distribution Detection via Laplacian Eigenvalue Gaps](https://mlsanity.com/paper/2505.15177/) (2025)
- [Quantifying Distributional Invariance in Causal Subgraph for IRM-Free Graph Generalization](https://mlsanity.com/paper/2510.20295/) (2025)
- [Shapley-Guided Utility Learning for Effective Graph Inference Data Valuation](https://mlsanity.com/paper/2503.18195/) (2025)
- [Single-Node Trigger Backdoor Attacks in Graph-Based Recommendation Systems](https://mlsanity.com/paper/2506.08401/) (2025)
- [M2LLM: Multi-view Molecular Representation Learning with Large Language Models](https://mlsanity.com/paper/2508.08657/) (2025)
- [G-OSR: A Comprehensive Benchmark for Graph Open-Set Recognition](https://mlsanity.com/paper/2503.00476/) (2025)
- [Rethinking Graph Generalization through the Lens of Sharpness-Aware Minimization](https://mlsanity.com/paper/2602.08855/) (2026)
- [Disentangled Graph Prompting for Out-Of-Distribution Detection](https://mlsanity.com/paper/2603.29644/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) have found widespread application in modeling graph data across diverse domains. While GNNs excel in scenarios where the testing data shares the distribution of their training counterparts (in distribution, ID), they often exhibit incorrect predictions when confronted with samples from an unfamiliar distribution (out-of-distribution, OOD). To identify and reject OOD samples with GNNs, recent studies have explored graph OOD detection, often focusing on training a specific model or modifying the data on top of a well-trained GNN. Despite their effectiveness, these methods come with heavy training resources and costs, as they need to optimize the GNN-based models on training data. Moreover, their reliance on modifying the original GNNs and accessing training data further restricts their universality. To this end, this paper introduces a method to detect Graph Out-of-Distribution At Test-time (namely GOODAT), a data-centric, unsupervised, and plug-and-play solution that operates independently of training data and modifications of GNN architecture. With a lightweight graph masker, GOODAT can learn informative subgraphs from test samples, enabling the capture of distinct graph patterns between OOD and ID samples. To optimize the graph masker, we meticulously design three unsupervised objective functions based on the graph information bottleneck principle, motivating the masker to capture compact yet informative subgraphs for OOD detection. Comprehensive evaluations confirm that our GOODAT method outperforms state-of-the-art benchmarks across a variety of real-world datasets. The code is available at Github: https://github.com/Ee1s/GOODAT