# Out-of-Distribution Detection in Heterogeneous Graphs via Energy Propagation

arXiv: https://arxiv.org/abs/2505.03774 · HTML: https://mlsanity.com/paper/2505.03774/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 44 references that are in the map.
- First posted on arXiv 29 Apr 2025.

## Builds on (most cited first, 30 of 33)

- [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)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [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)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Heterogeneous Graph Attention Network](https://mlsanity.com/paper/1903.07293/) (2019)
- [Graph Transformer Networks](https://mlsanity.com/paper/1911.06455/) (2019)
- [Towards Out-Of-Distribution Generalization: A Survey](https://mlsanity.com/paper/2108.13624/) (2021)
- [MAGNN: Metapath Aggregated Graph Neural Network for Heterogeneous Graph Embedding](https://mlsanity.com/paper/2002.01680/) (2020)
- [Are we really making much progress? Revisiting, benchmarking, and refining heterogeneous graph neural networks](https://mlsanity.com/paper/2112.14936/) (2021)
- [A Survey on Heterogeneous Graph Embedding: Methods, Techniques, Applications and Sources](https://mlsanity.com/paper/2011.14867/) (2020)
- [DOC: Deep Open Classification of Text Documents](https://mlsanity.com/paper/1709.08716/) (2017)
- [Heterogeneous Graph Neural Networks for Malicious Account Detection](https://mlsanity.com/paper/2002.12307/) (2020)
- [Uncertainty Aware Semi-Supervised Learning on Graph Data](https://mlsanity.com/paper/2010.12783/) (2020)
- [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)
- [Simple and Efficient Heterogeneous Graph Neural Network](https://mlsanity.com/paper/2207.02547/) (2022)
- [Energy-based Out-of-Distribution Detection for Graph Neural Networks](https://mlsanity.com/paper/2302.02914/) (2023)
- [STAR-GCN: Stacked and Reconstructed Graph Convolutional Networks for Recommender Systems](https://mlsanity.com/paper/1905.13129/) (2019)
- [GOOD-D: On Unsupervised Graph Out-Of-Distribution Detection](https://mlsanity.com/paper/2211.04208/) (2022)
- [Learning on Graphs with Out-of-Distribution Nodes](https://mlsanity.com/paper/2308.06714/) (2023)
- [Open Set Action Recognition via Multi-Label Evidential Learning](https://mlsanity.com/paper/2303.12698/) (2023)
- [Supervised Algorithmic Fairness in Distribution Shifts: A Survey](https://mlsanity.com/paper/2402.01327/) (2024)
- [Rank-Based Multi-task Learning for Fair Regression](https://mlsanity.com/paper/2009.11405/) (2020)
- [Energy-based Hopfield Boosting for Out-of-Distribution Detection](https://mlsanity.com/paper/2405.08766/) (2024)
- [Decoupled Graph Energy-based Model for Node Out-of-Distribution Detection on Heterophilic Graphs](https://mlsanity.com/paper/2502.17912/) (2025)

## Abstract (arXiv)

Graph neural networks (GNNs) are proven effective in extracting complex node and structural information from graph data. While current GNNs perform well in node classification tasks within in-distribution (ID) settings, real-world scenarios often present distribution shifts, leading to the presence of out-of-distribution (OOD) nodes. OOD detection in graphs is a crucial and challenging task. Most existing research focuses on homogeneous graphs, but real-world graphs are often heterogeneous, consisting of diverse node and edge types. This heterogeneity adds complexity and enriches the informational content. To the best of our knowledge, OOD detection in heterogeneous graphs remains an underexplored area. In this context, we propose a novel methodology for OOD detection in heterogeneous graphs (OODHG) that aims to achieve two main objectives: 1) detecting OOD nodes and 2) classifying all ID nodes based on the first task's results. Specifically, we learn representations for each node in the heterogeneous graph, calculate energy values to determine whether nodes are OOD, and then classify ID nodes. To leverage the structural information of heterogeneous graphs, we introduce a meta-path-based energy propagation mechanism and an energy constraint to enhance the distinction between ID and OOD nodes. Extensive experimental findings substantiate the simplicity and effectiveness of OODHG, demonstrating its superiority over baseline models in OOD detection tasks and its accuracy in ID node classification.