# Decoupled Graph Energy-based Model for Node Out-of-Distribution Detection on Heterophilic Graphs

arXiv: https://arxiv.org/abs/2502.17912 · HTML: https://mlsanity.com/paper/2502.17912/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 55 references that are in the map.
- First posted on arXiv 25 Feb 2025.

## Builds on (most cited first, 30 of 41)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (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)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (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)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Deep Graph Contrastive Representation Learning](https://mlsanity.com/paper/2006.04131/) (2020)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Graph Representation Learning via Graphical Mutual Information Maximization](https://mlsanity.com/paper/2002.01169/) (2020)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [Finding Global Homophily in Graph Neural Networks When Meeting Heterophily](https://mlsanity.com/paper/2205.07308/) (2022)
- [Handling Distribution Shifts on Graphs: An Invariance Perspective](https://mlsanity.com/paper/2202.02466/) (2022)
- [Dark Model Adaptation: Semantic Image Segmentation from Daytime to Nighttime](https://mlsanity.com/paper/1810.02575/) (2018)
- [Uncertainty Aware Semi-Supervised Learning on Graph Data](https://mlsanity.com/paper/2010.12783/) (2020)
- [GraphEBM: Molecular Graph Generation with Energy-Based Models](https://mlsanity.com/paper/2102.00546/) (2021)
- [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)
- [A Contrastive Learning Approach for Training Variational Autoencoder Priors](https://mlsanity.com/paper/2010.02917/) (2020)

## Built on by (most cited first, 9 of 9)

- [Text Meets Topology: Rethinking Out-of-distribution Detection in Text-Rich Networks](https://mlsanity.com/paper/2508.17690/) (2025)
- [EHRAG: Bridging Semantic Gaps in Lightweight GraphRAG via Hybrid Hypergraph Construction and Retrieval](https://mlsanity.com/paper/2604.17458/) (2026)
- [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)
- [What Information Matters? Graph Out-of-Distribution Detection via Tri-Component Information Decomposition](https://mlsanity.com/paper/2605.13032/) (2026)
- [ERAlign: Energy-based Representation Alignment of GNNs and LLMs on Text-attributed Graphs](https://mlsanity.com/paper/2606.10461/) (2026)
- [Out-of-Distribution Detection in Heterogeneous Graphs via Energy Propagation](https://mlsanity.com/paper/2505.03774/) (2025)
- [Mitigating Structural Overfitting: A Distribution-Aware Rectification Framework for Missing Feature Imputation](https://mlsanity.com/paper/2512.06356/) (2025)
- [EagleNet: Energy-Aware Fine-Grained Relationship Learning Network for Text-Video Retrieval](https://mlsanity.com/paper/2603.25267/) (2026)

## Abstract (arXiv)

Despite extensive research efforts focused on OOD detection on images, OOD detection on nodes in graph learning remains underexplored. The dependence among graph nodes hinders the trivial adaptation of existing approaches on images that assume inputs to be i.i.d. sampled, since many unique features and challenges specific to graphs are not considered, such as the heterophily issue. Recently, GNNSafe, which considers node dependence, adapted energy-based detection to the graph domain with state-of-the-art performance, however, it has two serious issues: 1) it derives node energy from classification logits without specifically tailored training for modeling data distribution, making it less effective at recognizing OOD data; 2) it highly relies on energy propagation, which is based on homophily assumption and will cause significant performance degradation on heterophilic graphs, where the node tends to have dissimilar distribution with its neighbors. To address the above issues, we suggest training EBMs by MLE to enhance data distribution modeling and remove energy propagation to overcome the heterophily issues. However, training EBMs via MLE requires performing MCMC sampling on both node feature and node neighbors, which is challenging due to the node interdependence and discrete graph topology. To tackle the sampling challenge, we introduce DeGEM, which decomposes the learning process into two parts: a graph encoder that leverages topology information for node representations and an energy head that operates in latent space. Extensive experiments validate that DeGEM, without OOD exposure during training, surpasses previous state-of-the-art methods, achieving an average AUROC improvement of 6.71% on homophilic graphs and 20.29% on heterophilic graphs, and even outperform methods trained with OOD exposure. Our code is available at: https://github.com/draym28/DeGEM.