# Uncertainty Quantification With Noise Injection in Neural Networks: A Bayesian Perspective

arXiv: https://arxiv.org/abs/2501.12314 · HTML: https://mlsanity.com/paper/2501.12314/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 37 references that are in the map.
- First posted on arXiv 21 Jan 2025.

## Builds on (most cited first, 14 of 14)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Parametric Noise Injection: Trainable Randomness to Improve Deep Neural Network Robustness against Adversarial Attack](https://mlsanity.com/paper/1811.09310/) (2018)
- [Uncertainty in Neural Networks: Approximately Bayesian Ensembling](https://mlsanity.com/paper/1810.05546/) (2018)
- [Bayesian Uncertainty Estimation for Batch Normalized Deep Networks](https://mlsanity.com/paper/1802.06455/) (2018)
- [Training Robust Deep Neural Networks via Adversarial Noise Propagation](https://mlsanity.com/paper/1909.09034/) (2019)
- [Training-Free Uncertainty Estimation for Dense Regression: Sensitivity as a Surrogate](https://mlsanity.com/paper/1910.04858/) (2019)
- [Adaptive Sign Algorithm for Graph Signal Processing](https://mlsanity.com/paper/2201.05821/) (2022)
- [PEP: Parameter Ensembling by Perturbation](https://mlsanity.com/paper/2010.12721/) (2020)
- [Robustness Enhancement in Neural Networks with Alpha-Stable Training Noise](https://mlsanity.com/paper/2311.10803/) (2023)

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

- [Distribution-Aware Conformal Prediction: A Framework for generating efficient prediction intervals for time series](https://mlsanity.com/paper/2605.26569/) (2026)

## Abstract (arXiv)

Model uncertainty quantification involves measuring and evaluating the uncertainty linked to a model's predictions, helping assess their reliability and confidence. Noise injection is a technique used to enhance the robustness of neural networks by introducing randomness. In this paper, we establish a connection between noise injection and uncertainty quantification from a Bayesian standpoint. We theoretically demonstrate that injecting noise into the weights of a neural network is equivalent to Bayesian inference on a deep Gaussian process. Consequently, we introduce a Monte Carlo Noise Injection (MCNI) method, which involves injecting noise into the parameters during training and performing multiple forward propagations during inference to estimate the uncertainty of the prediction. Through simulation and experiments on regression and classification tasks, our method demonstrates superior performance compared to the baseline model.