# Energy-based Epistemic Uncertainty for Graph Neural Networks

arXiv: https://arxiv.org/abs/2406.04043 · HTML: https://mlsanity.com/paper/2406.04043/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2024.

## Built on by (most cited first, 14 of 14)

- [Joint Out-of-Distribution Filtering and Data Discovery Active Learning](https://mlsanity.com/paper/2503.02491/) (2025)
- [Understanding and Mitigating Under-Confidence in GNNs from the Final Layer](https://mlsanity.com/paper/2505.11335/) (2025)
- [Provable Robustness of (Graph) Neural Networks Against Data Poisoning and Backdoor Attacks](https://mlsanity.com/paper/2407.10867/) (2024)
- [Epistemic Wrapping for Uncertainty Quantification](https://mlsanity.com/paper/2505.02277/) (2025)
- [Random-Set Graph Neural Networks](https://mlsanity.com/paper/2605.11987/) (2026)
- [Uncertainty Estimation for Heterophilic Graphs Through the Lens of Information Theory](https://mlsanity.com/paper/2505.22152/) (2025)
- [Uncertainty Estimation on Graphs with Structure Informed Stochastic Partial Differential Equations](https://mlsanity.com/paper/2506.06907/) (2025)
- [Credal Graph Neural Networks](https://mlsanity.com/paper/2512.02722/) (2025)
- [On Uncertainty Calibration for Equivariant Functions](https://mlsanity.com/paper/2510.21691/) (2025)
- [Graph Energy Matching: Transport-Aligned Energy-Based Modeling for Graph Generation](https://mlsanity.com/paper/2603.23398/) (2026)
- [Softmax is not Enough (for Adaptive Conformal Classification)](https://mlsanity.com/paper/2602.19498/) (2026)
- [Learning Graphs through Continuous Information Entropy Fields](https://mlsanity.com/paper/2606.22895/) (2026)
- [Hypergraph Neural Stochastic Diffusion: An SDE Framework for Uncertainty Estimation](https://mlsanity.com/paper/2607.07330/) (2026)
- [A Unified Uncertainty Representation for Graph Neural Networks via Doubly-Spectral Stochastic Expansion](https://mlsanity.com/paper/2609.35703/) (2026)

## Abstract (arXiv)

In domains with interdependent data, such as graphs, quantifying the epistemic uncertainty of a Graph Neural Network (GNN) is challenging as uncertainty can arise at different structural scales. Existing techniques neglect this issue or only distinguish between structure-aware and structure-agnostic uncertainty without combining them into a single measure. We propose GEBM, an energy-based model (EBM) that provides high-quality uncertainty estimates by aggregating energy at different structural levels that naturally arise from graph diffusion. In contrast to logit-based EBMs, we provably induce an integrable density in the data space by regularizing the energy function. We introduce an evidential interpretation of our EBM that significantly improves the predictive robustness of the GNN. Our framework is a simple and effective post hoc method applicable to any pre-trained GNN that is sensitive to various distribution shifts. It consistently achieves the best separation of in-distribution and out-of-distribution data on 6 out of 7 anomaly types while having the best average rank over shifts on all datasets.