# Variational Neural Networks

arXiv: https://arxiv.org/abs/2207.01524 · HTML: https://mlsanity.com/paper/2207.01524/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 29 references that are in the map.
- First posted on arXiv 4 Jul 2022.

## Builds on (most cited first, 13 of 13)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Randomized Prior Functions for Deep Reinforcement Learning](https://mlsanity.com/paper/1806.03335/) (2018)
- [Epistemic Neural Networks](https://mlsanity.com/paper/2107.08924/) (2021)
- [Hypermodels for Exploration](https://mlsanity.com/paper/2006.07464/) (2020)

## Built on by (most cited first, 7 of 7)

- [Quantification of Uncertainty with Adversarial Models](https://mlsanity.com/paper/2307.03217/) (2023)
- [Bayesian Learning for Neural Networks: an algorithmic survey](https://mlsanity.com/paper/2211.11865/) (2022)
- [Layer Ensembles](https://mlsanity.com/paper/2210.04882/) (2022)
- [Uncertainty-Aware AB3DMOT by Variational 3D Object Detection](https://mlsanity.com/paper/2302.05923/) (2023)
- [Probabilistic Neural Networks (PNNs) for Modeling Aleatoric Uncertainty in Scientific Machine Learning](https://mlsanity.com/paper/2402.13945/) (2024)
- [Variational Voxel Pseudo Image Tracking](https://mlsanity.com/paper/2302.05914/) (2023)
- [Variational Graph Convolutional Neural Networks](https://mlsanity.com/paper/2507.01699/) (2025)

## Abstract (arXiv)

Bayesian Neural Networks (BNNs) provide a tool to estimate the uncertainty of a neural network by considering a distribution over weights and sampling different models for each input. In this paper, we propose a method for uncertainty estimation in neural networks which, instead of considering a distribution over weights, samples outputs of each layer from a corresponding Gaussian distribution, parametrized by the predictions of mean and variance sub-layers. In uncertainty quality estimation experiments, we show that the proposed method achieves better uncertainty quality than other single-bin Bayesian Model Averaging methods, such as Monte Carlo Dropout or Bayes By Backpropagation methods.