# Uncertainty Propagation through Trained Deep Neural Networks Using Factor Graphs

arXiv: https://arxiv.org/abs/2312.05946 · HTML: https://mlsanity.com/paper/2312.05946/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 20 references that are in the map.
- First posted on arXiv 10 Dec 2023.

## Builds on (most cited first, 8 of 8)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Ensemble Distribution Distillation](https://mlsanity.com/paper/1905.00076/) (2019)
- [Lightweight Probabilistic Deep Networks](https://mlsanity.com/paper/1805.11327/) (2018)
- [TLIO: Tight Learned Inertial Odometry](https://mlsanity.com/paper/2007.01867/) (2020)
- [M2DGR: A Multi-sensor and Multi-scenario SLAM Dataset for Ground Robots](https://mlsanity.com/paper/2112.13659/) (2021)
- [Uncertainty Propagation in Deep Neural Networks Using Extended Kalman Filtering](https://mlsanity.com/paper/1809.06009/) (2018)

## Abstract (arXiv)

Predictive uncertainty estimation remains a challenging problem precluding the use of deep neural networks as subsystems within safety-critical applications. Aleatoric uncertainty is a component of predictive uncertainty that cannot be reduced through model improvements. Uncertainty propagation seeks to estimate aleatoric uncertainty by propagating input uncertainties to network predictions. Existing uncertainty propagation techniques use one-way information flows, propagating uncertainties layer-by-layer or across the entire neural network while relying either on sampling or analytical techniques for propagation. Motivated by the complex information flows within deep neural networks (e.g. skip connections), we developed and evaluated a novel approach by posing uncertainty propagation as a non-linear optimization problem using factor graphs. We observed statistically significant improvements in performance over prior work when using factor graphs across most of our experiments that included three datasets and two neural network architectures. Our implementation balances the benefits of sampling and analytical propagation techniques, which we believe, is a key factor in achieving performance improvements.