# Sampling from Bayesian Neural Network Posteriors with Symmetric Minibatch Splitting Langevin Dynamics

Source: [Sampling from Bayesian Neural Network Posteriors with Symmetric Minibatch Splitting Langevin Dynamics](<https://www.sota2.com/research/paper/68fa5d1a1e209131ce9d7298>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:56:13.857Z

Authors: Daniel Paulin, Peter A. Whalley, Neil K. Chada, Benedict Leimkuhler

Published: 2024-10-14T13:47:02.000Z

## Abstract

We propose a scalable kinetic Langevin dynamics algorithm for sampling parameter spaces of big data and AI applications. Our scheme combines a symmetric forward/backward sweep over minibatches with a symmetric discretization of Langevin dynamics. For a particular Langevin splitting method (UBU), we show that the resulting Symmetric Minibatch Splitting-UBU (SMS-UBU) integrator has bias $O(h^2 d^{1/2})$ in dimension $d\>0$ with stepsize $h\>0$, despite only using one minibatch per iteration, thus providing excellent control of the sampling bias as a function of the stepsize. We apply the algorithm to explore local modes of the posterior distribution of Bayesian neural networks (BNNs) and evaluate the calibration performance of the posterior predictive probabilities for neural networks with convolutional neural network architectures for classification problems on three different datasets (Fashion-MNIST, Celeb-A and chest X-ray). Our results indicate that BNNs sampled with SMS-UBU can offer significantly better calibration performance compared to standard methods of training and stochastic weight averaging.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Uncertainty Quantification on CIFAR-10](<https://www.sota2.com/research/sota/uncertainty-quantification-on-cifar-10.md>): Uncertainty Quantification; CIFAR-10; V-ID: 0.5608.

- [Uncertainty Quantification on FashionMNIST (using V-ID, V-OOD, MI metrics)](<https://www.sota2.com/research/sota/uncertainty-quantification-on-fashionmnist-using-v-id-v-ood-mi-metrics.md>): Uncertainty Quantification; FashionMNIST; V-ID: 90.03.

- [Uncertainty Quantification on CIFAR-100](<https://www.sota2.com/research/sota/uncertainty-quantification-on-cifar-100.md>): Uncertainty Quantification; CIFAR-100; V-ID: 0.291.

- [Uncertainty Quantification on SVHN](<https://www.sota2.com/research/sota/uncertainty-quantification-on-svhn.md>): Uncertainty Quantification; SVHN; V-ID Score: 51.36.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2410.19780>)

[PDF](<https://arxiv.org/pdf/2410.19780.pdf>)