# Uncertainty-Aware Graph Neural Networks: A Multi-Hop Evidence Fusion Approach

arXiv: https://arxiv.org/abs/2506.13083 · HTML: https://mlsanity.com/paper/2506.13083/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 79 references that are in the map.
- First posted on arXiv 16 Jun 2025.

## Builds on (most cited first, 30 of 54)

- [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)
- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [DeepGCNs: Can GCNs Go as Deep as CNNs?](https://mlsanity.com/paper/1904.03751/) (2019)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Towards Deeper Graph Neural Networks](https://mlsanity.com/paper/2007.09296/) (2020)
- [Graph Self-Supervised Learning: A Survey](https://mlsanity.com/paper/2103.00111/) (2021)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)
- [Addressing Failure Prediction by Learning Model Confidence](https://mlsanity.com/paper/1910.04851/) (2019)
- [Trusted Multi-View Classification with Dynamic Evidential Fusion](https://mlsanity.com/paper/2204.11423/) (2022)
- [Posterior Network: Uncertainty Estimation without OOD Samples via Density-Based Pseudo-Counts](https://mlsanity.com/paper/2006.09239/) (2020)
- [Learning to Drop: Robust Graph Neural Network via Topological Denoising](https://mlsanity.com/paper/2011.07057/) (2020)
- [Confidence-Aware Learning for Deep Neural Networks](https://mlsanity.com/paper/2007.01458/) (2020)
- [Dirichlet Energy Constrained Learning for Deep Graph Neural Networks](https://mlsanity.com/paper/2107.02392/) (2021)
- [Uncertainty Aware Semi-Supervised Learning on Graph Data](https://mlsanity.com/paper/2010.12783/) (2020)
- [Trusted Multi-View Classification](https://mlsanity.com/paper/2102.02051/) (2021)
- [Be Confident! Towards Trustworthy Graph Neural Networks via Confidence Calibration](https://mlsanity.com/paper/2109.14285/) (2021)

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

- [Assemble Your Crew: Automatic Multi-agent Communication Topology Design via Autoregressive Graph Generation](https://mlsanity.com/paper/2507.18224/) (2025)
- [OFA-MAS: One-for-All Multi-Agent System Topology Design based on Mixture-of-Experts Graph Generative Models](https://mlsanity.com/paper/2601.12996/) (2026)
- [Correcting False Alarms from Unseen: Adapting Graph Anomaly Detectors at Test Time](https://mlsanity.com/paper/2511.07023/) (2025)
- [FreeGAD: A Training-Free yet Effective Approach for Graph Anomaly Detection](https://mlsanity.com/paper/2508.10594/) (2025)
- [Explainable and Fine-Grained Safeguarding of LLM Multi-Agent Systems via Bi-Level Graph Anomaly Detection](https://mlsanity.com/paper/2512.18733/) (2025)
- [Towards One-for-All Anomaly Detection for Tabular Data](https://mlsanity.com/paper/2603.14407/) (2026)
- [FedCIGAR: A Personalized Reconstruction Approach for Federated Graph-level Anomaly Detection](https://mlsanity.com/paper/2605.09428/) (2026)
- [Towards Anomaly Detection on Relational Data](https://mlsanity.com/paper/2606.18621/) (2026)
- [Learning Fair Graph Representations with Multi-view Information Bottleneck](https://mlsanity.com/paper/2510.25096/) (2025)
- [TRE: Training-Free Hallucination Detection for Diffusion Language Models](https://mlsanity.com/paper/2607.22661/) (2026)
- [Attention Beyond Neighborhoods: Reviving Transformer for Graph Clustering](https://mlsanity.com/paper/2509.15024/) (2025)
- [Supervised Learning of Random Neural Architectures Structured by Latent Random Fields on Compact Boundaryless Multiply-Connected Manifolds](https://mlsanity.com/paper/2512.10407/) (2025)
- [UniER: A Unified Benchmark for Item-level and Path-level Exercise Recommendation](https://mlsanity.com/paper/2605.16750/) (2026)
- [MIDAS: Mutual Information Disentanglement with Uncertainty-Aware Fusion for Incomplete Multimodal Sentiment Analysis](https://mlsanity.com/paper/2608.09986/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) excel in graph representation learning by integrating graph structure and node features. Existing GNNs, unfortunately, fail to account for the uncertainty of class probabilities that vary with the depth of the model, leading to unreliable and risky predictions in real-world scenarios. To bridge the gap, in this paper, we propose a novel Evidence Fusing Graph Neural Network (EFGNN for short) to achieve trustworthy prediction, enhance node classification accuracy, and make explicit the risk of wrong predictions. In particular, we integrate the evidence theory with multi-hop propagation-based GNN architecture to quantify the prediction uncertainty of each node with the consideration of multiple receptive fields. Moreover, a parameter-free cumulative belief fusion (CBF) mechanism is developed to leverage the changes in prediction uncertainty and fuse the evidence to improve the trustworthiness of the final prediction. To effectively optimize the EFGNN model, we carefully design a joint learning objective composed of evidence cross-entropy, dissonance coefficient, and false confident penalty. The experimental results on various datasets and theoretical analyses demonstrate the effectiveness of the proposed model in terms of accuracy and trustworthiness, as well as its robustness to potential attacks. The source code of EFGNN is available at https://github.com/Shiy-Li/EFGNN.