# Hierarchical Uncertainty-Aware Graph Neural Network

arXiv: https://arxiv.org/abs/2504.19820 · HTML: https://mlsanity.com/paper/2504.19820/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 67 references that are in the map.
- First posted on arXiv 28 Apr 2025.

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

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks](https://mlsanity.com/paper/1707.09564/) (2017)
- [Adversarial Attacks on Graph Neural Networks via Meta Learning](https://mlsanity.com/paper/1902.08412/) (2019)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [Deep Convolutional Networks on Graph-Structured Data](https://mlsanity.com/paper/1506.05163/) (2015)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [GNNGuard: Defending Graph Neural Networks against Adversarial Attacks](https://mlsanity.com/paper/2006.08149/) (2020)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [Learning to Drop: Robust Graph Neural Network via Topological Denoising](https://mlsanity.com/paper/2011.07057/) (2020)
- [Uncertainty Aware Semi-Supervised Learning on Graph Data](https://mlsanity.com/paper/2010.12783/) (2020)
- [Signed Graph Attention Networks](https://mlsanity.com/paper/1906.10958/) (2019)
- [GEMSEC: Graph Embedding with Self Clustering](https://mlsanity.com/paper/1802.03997/) (2018)
- [What Makes Graph Neural Networks Miscalibrated?](https://mlsanity.com/paper/2210.06391/) (2022)
- [Calibrated and Sharp Uncertainties in Deep Learning via Density Estimation](https://mlsanity.com/paper/2112.07184/) (2021)
- [PC-Conv: Unifying Homophily and Heterophily with Two-fold Filtering](https://mlsanity.com/paper/2312.14438/) (2023)
- [Graph Neural Convection-Diffusion with Heterophily](https://mlsanity.com/paper/2305.16780/) (2023)
- [Extracting Low-/High- Frequency Knowledge from Graph Neural Networks and Injecting it into MLPs: An Effective GNN-to-MLP Distillation Framework](https://mlsanity.com/paper/2305.10758/) (2023)
- [Towards Deep Attention in Graph Neural Networks: Problems and Remedies](https://mlsanity.com/paper/2306.02376/) (2023)
- [Auto-HeG: Automated Graph Neural Network on Heterophilic Graphs](https://mlsanity.com/paper/2302.12357/) (2023)

## Built on by (most cited first, 1 of 1)

- [LiveGraph: Active-Structure Neural Re-ranking for Exercise Recommendation](https://mlsanity.com/paper/2602.17036/) (2026)

## Abstract (arXiv)

Recent research on graph neural networks (GNNs) has explored mechanisms for capturing local uncertainty and exploiting graph hierarchies to mitigate data sparsity and leverage structural properties. However, the synergistic integration of these two approaches remains underexplored. This work introduces a novel architecture, the Hierarchical Uncertainty-Aware Graph Neural Network (HU-GNN), which unifies multi-scale representation learning, principled uncertainty estimation, and self-supervised embedding diversity within a single end-to-end framework. Specifically, HU-GNN adaptively forms node clusters and estimates uncertainty at multiple structural scales from individual nodes to higher levels. These uncertainty estimates guide a robust message-passing mechanism and attention weighting, effectively mitigating noise and adversarial perturbations while preserving predictive accuracy on semi-supervised classification tasks. We also offer key theoretical contributions, including a probabilistic formulation, rigorous uncertainty-calibration guarantees, and formal robustness bounds. Extensive experiments on standard benchmarks demonstrate that our model achieves state-of-the-art robustness and interpretability.