# Credal Graph Neural Networks

arXiv: https://arxiv.org/abs/2512.02722 · HTML: https://mlsanity.com/paper/2512.02722/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 50 references that are in the map.
- First posted on arXiv 2 Dec 2025.

## Builds on (most cited first, 30 of 39)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [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)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [Evaluating Scalable Bayesian Deep Learning Methods for Robust Computer Vision](https://mlsanity.com/paper/1906.01620/) (2019)
- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [Distributionally Robust Language Modeling](https://mlsanity.com/paper/1909.02060/) (2019)
- [A Gentle Introduction to Deep Learning for Graphs](https://mlsanity.com/paper/1912.12693/) (2019)
- [Uncertainty Aware Semi-Supervised Learning on Graph Data](https://mlsanity.com/paper/2010.12783/) (2020)
- [A Deeper Look into Aleatoric and Epistemic Uncertainty Disentanglement](https://mlsanity.com/paper/2204.09308/) (2022)
- [Bayesian Graph Neural Networks with Adaptive Connection Sampling](https://mlsanity.com/paper/2006.04064/) (2020)
- [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)
- [Deep Ensembles Work, But Are They Necessary?](https://mlsanity.com/paper/2202.06985/) (2022)
- [Credal Learning Theory](https://mlsanity.com/paper/2402.00957/) (2024)
- [The Heterophilic Graph Learning Handbook: Benchmarks, Models, Theoretical Analysis, Applications and Challenges](https://mlsanity.com/paper/2407.09618/) (2024)
- [CreINNs: Credal-Set Interval Neural Networks for Uncertainty Estimation in Classification Tasks](https://mlsanity.com/paper/2401.05043/) (2024)
- [Uncertainty in Graph Neural Networks: A Survey](https://mlsanity.com/paper/2403.07185/) (2024)

## Built on by (most cited first, 2 of 2)

- [Random-Set Graph Neural Networks](https://mlsanity.com/paper/2605.11987/) (2026)
- [A formal definition and meta-model for a machine theory of mind](https://mlsanity.com/paper/2606.03471/) (2026)

## Abstract (arXiv)

Uncertainty quantification is essential for deploying reliable Graph Neural Networks (GNNs), where existing approaches primarily rely on Bayesian inference or ensembles. In this paper, we introduce the first credal graph neural networks (CGNNs), which extend credal learning to the graph domain by training GNNs to output set-valued predictions in the form of credal sets. To account for the distinctive nature of message passing in GNNs, we develop a complementary approach to credal learning that leverages different aspects of layer-wise information propagation. We assess our approach on uncertainty quantification in node classification under out-of-distribution conditions. Our analysis highlights the critical role of the graph homophily assumption in shaping the effectiveness of uncertainty estimates. Extensive experiments demonstrate that CGNNs deliver more reliable representations of epistemic uncertainty and achieve state-of-the-art performance under distributional shift on heterophilic graphs.