# Dropout as a Bayesian Approximation: Appendix

arXiv: https://arxiv.org/abs/1506.02157 · HTML: https://mlsanity.com/paper/1506.02157/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2015.

## Built on by (most cited first, 14 of 14)

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- [Probabilistic Neural Network to Quantify Uncertainty of Wind Power Estimation](https://mlsanity.com/paper/2106.04656/) (2021)
- [Real-time Detection of Anomalies in Multivariate Time Series of Astronomical Data](https://mlsanity.com/paper/2112.08415/) (2021)
- [Self-Normalized Density Map (SNDM) for Counting Microbiological Objects](https://mlsanity.com/paper/2203.09474/) (2022)
- [Deep learning for diffusion in porous media](https://mlsanity.com/paper/2304.02104/) (2023)
- [Defensive Perception: Estimation and Monitoring of Neural Network Performance under Deployment](https://mlsanity.com/paper/2308.06299/) (2023)
- [Explainable Image Classification with Reduced Overconfidence for Tissue Characterisation](https://mlsanity.com/paper/2507.23709/) (2025)
- [Linear Fitness Subspace in Protein Language Models Enables Sample-Efficient Directed Evolution](https://mlsanity.com/paper/2610.07607/) (2026)

## Abstract (arXiv)

We show that a neural network with arbitrary depth and non-linearities, with dropout applied before every weight layer, is mathematically equivalent to an approximation to a well known Bayesian model. This interpretation might offer an explanation to some of dropout's key properties, such as its robustness to over-fitting. Our interpretation allows us to reason about uncertainty in deep learning, and allows the introduction of the Bayesian machinery into existing deep learning frameworks in a principled way. This document is an appendix for the main paper "Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning" by Gal and Ghahramani, 2015.