# Uncertainty-Preserving QBNNs: Multi-Level Quantization of SVI-Based Bayesian Neural Networks for Image Classification

arXiv: https://arxiv.org/abs/2512.10602 · HTML: https://mlsanity.com/paper/2512.10602/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 33 references that are in the map.
- First posted on arXiv 11 Dec 2025.

## Builds on (most cited first, 20 of 20)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [HAQ: Hardware-Aware Automated Quantization with Mixed Precision](https://mlsanity.com/paper/1811.08886/) (2018)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Deep Deterministic Uncertainty: A Simple Baseline](https://mlsanity.com/paper/2102.11582/) (2021)
- [Resource-Efficient Neural Networks for Embedded Systems](https://mlsanity.com/paper/2001.03048/) (2020)
- [On the Effects of Quantisation on Model Uncertainty in Bayesian Neural Networks](https://mlsanity.com/paper/2102.11062/) (2021)
- [Towards Hardware-Specific Automatic Compression of Neural Networks](https://mlsanity.com/paper/2212.07818/) (2022)
- [Uncertainty Reasoning with Photonic Bayesian Machines](https://mlsanity.com/paper/2512.02217/) (2025)
- [One Simple Trick to Fix Your Bayesian Neural Network](https://mlsanity.com/paper/2207.13167/) (2022)
- [Resource-Efficient and Robust Inference of Deep and Bayesian Neural Networks on Embedded and Analog Computing Platforms](https://mlsanity.com/paper/2510.24951/) (2025)

## Abstract (arXiv)

Bayesian Neural Networks (BNNs) provide principled uncertainty quantification but suffer from substantial computational and memory overhead compared to deterministic networks. While quantization techniques have successfully reduced resource requirements in standard deep learning models, their application to probabilistic models remains largely unexplored. We introduce a systematic multi-level quantization framework for Stochastic Variational Inference based BNNs that distinguishes between three quantization strategies: Variational Parameter Quantization (VPQ), Sampled Parameter Quantization (SPQ), and Joint Quantization (JQ). Our logarithmic quantization for variance parameters, and specialized activation functions to preserve the distributional structure are essential for calibrated uncertainty estimation. Through comprehensive experiments on Dirty-MNIST, we demonstrate that BNNs can be quantized down to 4-bit precision while maintaining both classification accuracy and uncertainty disentanglement. At 4 bits, Joint Quantization achieves up to 8x memory reduction compared to floating-point implementations with minimal degradation in epistemic and aleatoric uncertainty estimation. These results enable deployment of BNNs on resource-constrained edge devices and provide design guidelines for future analog "Bayesian Machines" operating at inherently low precision.