# Partial Trace-Class Bayesian Neural Networks

arXiv: https://arxiv.org/abs/2511.01628 · HTML: https://mlsanity.com/paper/2511.01628/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 31 references that are in the map.
- First posted on arXiv 3 Nov 2025.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Gaussian Process Behaviour in Wide Deep Neural Networks](https://mlsanity.com/paper/1804.11271/) (2018)
- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [Being Bayesian, Even Just a Bit, Fixes Overconfidence in ReLU Networks](https://mlsanity.com/paper/2002.10118/) (2020)
- [Bayesian Neural Network Priors Revisited](https://mlsanity.com/paper/2102.06571/) (2021)
- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [Subspace Inference for Bayesian Deep Learning](https://mlsanity.com/paper/1907.07504/) (2019)
- [Bayesian Deep Learning via Subnetwork Inference](https://mlsanity.com/paper/2010.14689/) (2020)
- [Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI](https://mlsanity.com/paper/2402.00809/) (2024)
- [Challenges in Markov chain Monte Carlo for Bayesian neural networks](https://mlsanity.com/paper/1910.06539/) (2019)
- [On Last-Layer Algorithms for Classification: Decoupling Representation from Uncertainty Estimation](https://mlsanity.com/paper/2001.08049/) (2020)
- [Disentangling the Roles of Curation, Data-Augmentation and the Prior in the Cold Posterior Effect](https://mlsanity.com/paper/2106.06596/) (2021)
- [The Relevance of Bayesian Layer Positioning to Model Uncertainty in Deep Bayesian Active Learning](https://mlsanity.com/paper/1811.12535/) (2018)
- [Bayesian Neural Networks: Essentials](https://mlsanity.com/paper/2106.13594/) (2021)
- [Partially Stochastic Infinitely Deep Bayesian Neural Networks](https://mlsanity.com/paper/2402.03495/) (2024)
- [Trace-class Gaussian priors for Bayesian learning of neural networks with MCMC](https://mlsanity.com/paper/2012.10943/) (2020)

## Abstract (arXiv)

Bayesian neural networks (BNNs) allow rigorous uncertainty quantification in deep learning, but often come at a prohibitive computational cost. We propose three different innovative architectures of partial trace-class Bayesian neural networks (PaTraC BNNs) that enable uncertainty quantification comparable to standard BNNs but use significantly fewer Bayesian parameters. These PaTraC BNNs have computational and statistical advantages over standard Bayesian neural networks in terms of speed and memory requirements. Our proposed methodology therefore facilitates reliable, robust, and scalable uncertainty quantification in neural networks. The three architectures build on trace-class neural network priors which induce an ordering of the neural network parameters, and are thus a natural choice in our framework. In a numerical simulation study, we verify the claimed benefits, and further illustrate the performance of our proposed methodology on a real-world dataset.