# Evidential Spectrum-Aware Contrastive Learning for OOD Detection in Dynamic Graphs

arXiv: https://arxiv.org/abs/2506.07417 · HTML: https://mlsanity.com/paper/2506.07417/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 42 references that are in the map.
- First posted on arXiv 9 Jun 2025.

## Builds on (most cited first, 21 of 21)

- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (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)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [A Survey of Autonomous Driving: Common Practices and Emerging Technologies](https://mlsanity.com/paper/1906.05113/) (2019)
- [Anti-Money Laundering in Bitcoin: Experimenting with Graph Convolutional Networks for Financial Forensics](https://mlsanity.com/paper/1908.02591/) (2019)
- [Uncertainty Aware Semi-Supervised Learning on Graph Data](https://mlsanity.com/paper/2010.12783/) (2020)
- [Energy-based Out-of-Distribution Detection for Graph Neural Networks](https://mlsanity.com/paper/2302.02914/) (2023)
- [A Survey on Graph Representation Learning Methods](https://mlsanity.com/paper/2204.01855/) (2022)
- [Anomaly Detection in Dynamic Graphs via Transformer](https://mlsanity.com/paper/2106.09876/) (2021)
- [Uncertainty Estimation by Fisher Information-based Evidential Deep Learning](https://mlsanity.com/paper/2303.02045/) (2023)
- [GOOD-D: On Unsupervised Graph Out-Of-Distribution Detection](https://mlsanity.com/paper/2211.04208/) (2022)
- [Revisiting Graph Contrastive Learning from the Perspective of Graph Spectrum](https://mlsanity.com/paper/2210.02330/) (2022)
- [Attributed Network Embedding for Learning in a Dynamic Environment](https://mlsanity.com/paper/1706.01860/) (2017)
- [Uncertainty Estimation by Density Aware Evidential Deep Learning](https://mlsanity.com/paper/2409.08754/) (2024)
- [SLADE: Detecting Dynamic Anomalies in Edge Streams without Labels via Self-Supervised Learning](https://mlsanity.com/paper/2402.11933/) (2024)
- [Learnable Spectral Wavelets on Dynamic Graphs to Capture Global Interactions](https://mlsanity.com/paper/2211.11979/) (2022)

## Abstract (arXiv)

Recently, Out-of-distribution (OOD) detection in dynamic graphs, which aims to identify whether incoming data deviates from the distribution of the in-distribution (ID) training set, has garnered considerable attention in security-sensitive fields. Current OOD detection paradigms primarily focus on static graphs and confront two critical challenges: i) high bias and high variance caused by single-point estimation, which makes the predictions sensitive to randomness in the data; ii) score homogenization resulting from the lack of OOD training data, where the model only learns ID-specific patterns, resulting in overall low OOD scores and a narrow score gap between ID and OOD data. To tackle these issues, we first investigate OOD detection in dynamic graphs through the lens of Evidential Deep Learning (EDL). Specifically, we propose EviSEC, an innovative and effective OOD detector via Evidential Spectrum-awarE Contrastive Learning. We design an evidential neural network to redefine the output as the posterior Dirichlet distribution, explaining the randomness of inputs through the uncertainty of distribution, which is overlooked by single-point estimation. Moreover, spectrum-aware augmentation module generates OOD approximations to identify patterns with high OOD scores, thereby widening the score gap between ID and OOD data and mitigating score homogenization. Extensive experiments on real-world datasets demonstrate that EviSAC effectively detects OOD samples in dynamic graphs.