# GOLD: Graph Out-of-Distribution Detection via Implicit Adversarial Latent Generation

arXiv: https://arxiv.org/abs/2502.05780 · HTML: https://mlsanity.com/paper/2502.05780/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 67 of its 94 references that are in the map.
- First posted on arXiv 9 Feb 2025.

## Builds on (most cited first, 30 of 67)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [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)
- [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)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [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)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [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)
- [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)
- [VOS: Learning What You Don't Know by Virtual Outlier Synthesis](https://mlsanity.com/paper/2202.01197/) (2022)
- [Extremely Simple Activation Shaping for Out-of-Distribution Detection](https://mlsanity.com/paper/2209.09858/) (2022)
- [Input complexity and out-of-distribution detection with likelihood-based generative models](https://mlsanity.com/paper/1909.11480/) (2019)
- [Likelihood Regret: An Out-of-Distribution Detection Score For Variational Auto-encoder](https://mlsanity.com/paper/2003.02977/) (2020)
- [Learning Causally Invariant Representations for Out-of-Distribution Generalization on Graphs](https://mlsanity.com/paper/2202.05441/) (2022)
- [GOOD: A Graph Out-of-Distribution Benchmark](https://mlsanity.com/paper/2206.08452/) (2022)
- [Non-Parametric Outlier Synthesis](https://mlsanity.com/paper/2303.02966/) (2023)
- [Out-of-Distribution Detection Using an Ensemble of Self Supervised Leave-out Classifiers](https://mlsanity.com/paper/1809.03576/) (2018)
- [ATOM: Robustifying Out-of-distribution Detection Using Outlier Mining](https://mlsanity.com/paper/2006.15207/) (2020)

## Built on by (most cited first, 15 of 15)

- [Graph Synthetic Out-of-Distribution Exposure with Large Language Models](https://mlsanity.com/paper/2504.21198/) (2025)
- [Text Meets Topology: Rethinking Out-of-distribution Detection in Text-Rich Networks](https://mlsanity.com/paper/2508.17690/) (2025)
- [Uncertainty Estimation on Graphs with Structure Informed Stochastic Partial Differential Equations](https://mlsanity.com/paper/2506.06907/) (2025)
- [Can Molecular Foundation Models Know What They Don't Know? A Simple Remedy with Preference Optimization](https://mlsanity.com/paper/2509.25509/) (2025)
- [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)
- [Does Homophily Help in Robust Test-time Node Classification?](https://mlsanity.com/paper/2510.22289/) (2025)
- [Coarse-to-Fine Open-Set Graph Node Classification with Large Language Models](https://mlsanity.com/paper/2512.16244/) (2025)
- [What Information Matters? Graph Out-of-Distribution Detection via Tri-Component Information Decomposition](https://mlsanity.com/paper/2605.13032/) (2026)
- [Subgraph Generation for Generalizing on Out-of-Distribution Links](https://mlsanity.com/paper/2507.11710/) (2025)
- [ALSA: Anchors in Logit Space for Out-of-Distribution Accuracy Estimation](https://mlsanity.com/paper/2508.19613/) (2025)
- [Rethinking Graph Generalization through the Lens of Sharpness-Aware Minimization](https://mlsanity.com/paper/2602.08855/) (2026)
- [Both Topology and Text Matter: Revisiting LLM-guided Out-of-Distribution Detection on Text-attributed Graphs](https://mlsanity.com/paper/2602.11641/) (2026)
- [Spiking Graph Predictive Coding for Reliable OOD Generalization](https://mlsanity.com/paper/2602.19392/) (2026)
- [Hypergraph Neural Stochastic Diffusion: An SDE Framework for Uncertainty Estimation](https://mlsanity.com/paper/2607.07330/) (2026)

## Abstract (arXiv)

Despite graph neural networks' (GNNs) great success in modelling graph-structured data, out-of-distribution (OOD) test instances still pose a great challenge for current GNNs. One of the most effective techniques to detect OOD nodes is to expose the detector model with an additional OOD node-set, yet the extra OOD instances are often difficult to obtain in practice. Recent methods for image data address this problem using OOD data synthesis, typically relying on pre-trained generative models like Stable Diffusion. However, these approaches require vast amounts of additional data, as well as one-for-all pre-trained generative models, which are not available for graph data. Therefore, we propose the GOLD framework for graph OOD detection, an implicit adversarial learning pipeline with synthetic OOD exposure without pre-trained models. The implicit adversarial training process employs a novel alternating optimisation framework by training: (1) a latent generative model to regularly imitate the in-distribution (ID) embeddings from an evolving GNN, and (2) a GNN encoder and an OOD detector to accurately classify ID data while increasing the energy divergence between the ID embeddings and the generative model's synthetic embeddings. This novel approach implicitly transforms the synthetic embeddings into pseudo-OOD instances relative to the ID data, effectively simulating exposure to OOD scenarios without auxiliary data. Extensive OOD detection experiments are conducted on five benchmark graph datasets, verifying the superior performance of GOLD without using real OOD data compared with the state-of-the-art OOD exposure and non-exposure baselines.