# Uncertainty Propagation in Deep Neural Network Using Active Subspace

arXiv: https://arxiv.org/abs/1903.03989 · HTML: https://mlsanity.com/paper/1903.03989/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Mar 2019.

## Built on by (most cited first, 3 of 3)

- [Propagation and Attribution of Uncertainty in Medical Imaging Pipelines](https://mlsanity.com/paper/2309.16831/) (2023)
- [Tailored Uncertainty Estimation for Deep Learning Systems](https://mlsanity.com/paper/2204.13963/) (2022)
- [Exact Upper and Lower Bounds for the Output Distribution of Neural Networks with Random Inputs](https://mlsanity.com/paper/2502.11672/) (2025)

## Abstract (arXiv)

The inputs of deep neural network (DNN) from real-world data usually come with uncertainties. Yet, it is challenging to propagate the uncertainty in the input features to the DNN predictions at a low computational cost. This work employs a gradient-based subspace method and response surface technique to accelerate the uncertainty propagation in DNN. Specifically, the active subspace method is employed to identify the most important subspace in the input features using the gradient of the DNN output to the inputs. Then the response surface within that low-dimensional subspace can be efficiently built, and the uncertainty of the prediction can be acquired by evaluating the computationally cheap response surface instead of the DNN models. In addition, the subspace can help explain the adversarial examples. The approach is demonstrated in MNIST datasets with a convolutional neural network. Code is available at: https://github.com/jiweiqi/nnsubspace.