# Analog Bayesian neural networks are insensitive to the shape of the weight distribution

arXiv: https://arxiv.org/abs/2501.05564 · HTML: https://mlsanity.com/paper/2501.05564/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 27 references that are in the map.
- First posted on arXiv 9 Jan 2025.

## Builds on (most cited first, 6 of 6)

- [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)
- [Age Progression/Regression by Conditional Adversarial Autoencoder](https://mlsanity.com/paper/1702.08423/) (2017)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [To Trust Or Not To Trust A Classifier](https://mlsanity.com/paper/1805.11783/) (2018)
- [VIBNN: Hardware Acceleration of Bayesian Neural Networks](https://mlsanity.com/paper/1802.00822/) (2018)

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

- [Quantum Tunneling-Aware Machine Learning: Physics-Derived Noise Models for Robust Deployment](https://mlsanity.com/paper/2606.00741/) (2026)

## Abstract (arXiv)

Recent work has demonstrated that Bayesian neural networks (BNN's) trained with mean field variational inference (MFVI) can be implemented in analog hardware, promising orders of magnitude energy savings compared to the standard digital implementations. However, while Gaussians are typically used as the variational distribution in MFVI, it is difficult to precisely control the shape of the noise distributions produced by sampling analog devices. This paper introduces a method for MFVI training using real device noise as the variational distribution. Furthermore, we demonstrate empirically that the predictive distributions from BNN's with the same weight means and variances converge to the same distribution, regardless of the shape of the variational distribution. This result suggests that analog device designers do not need to consider the shape of the device noise distribution when hardware-implementing BNNs performing MFVI.