# Thermodynamic Bayesian Inference

arXiv: https://arxiv.org/abs/2410.01793 · HTML: https://mlsanity.com/paper/2410.01793/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 56 references that are in the map.
- First posted on arXiv 2 Oct 2024.

## Builds on (most cited first, 21 of 21)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [A Tutorial on Thompson Sampling](https://mlsanity.com/paper/1707.02038/) (2017)
- [Variational Continual Learning](https://mlsanity.com/paper/1710.10628/) (2017)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices](https://mlsanity.com/paper/1903.08568/) (2019)
- [Measuring Sample Quality with Stein's Method](https://mlsanity.com/paper/1506.03039/) (2015)
- [Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI](https://mlsanity.com/paper/2402.00809/) (2024)
- [Bayesian Workflow](https://mlsanity.com/paper/2011.01808/) (2020)
- [Massively Parallel Probabilistic Computing with Sparse Ising Machines](https://mlsanity.com/paper/2110.02481/) (2021)
- [Thermodynamic Computing System for AI Applications](https://mlsanity.com/paper/2312.04836/) (2023)
- [Thermodynamic AI and the fluctuation frontier](https://mlsanity.com/paper/2302.06584/) (2023)
- [Thermodynamic Computing](https://mlsanity.com/paper/1911.01968/) (2019)
- [Scalable Bayesian Learning with posteriors](https://mlsanity.com/paper/2406.00104/) (2024)
- [Thermodynamic Neural Network](https://mlsanity.com/paper/1906.01678/) (2019)
- [Ensemble Kalman Inversion for General Likelihoods](https://mlsanity.com/paper/2110.03034/) (2021)
- [Thermodynamic Computing via Autonomous Quantum Thermal Machines](https://mlsanity.com/paper/2308.15905/) (2023)
- [Thermodynamic Natural Gradient Descent](https://mlsanity.com/paper/2405.13817/) (2024)
- [Matrix Multiplication in Quadratic Time and Energy? Towards a Fine-Grained Energy-Centric Church-Turing Thesis](https://mlsanity.com/paper/2311.16342/) (2023)

## Built on by (most cited first, 2 of 2)

- [A Blueprint for Equilibrium-Based Differentiable Continuous-Variable Thermodynamic Computing](https://mlsanity.com/paper/2607.16183/) (2026)
- [Thermodynamic cost of inference and learning in physical neural networks](https://mlsanity.com/paper/2503.09980/) (2025)

## Abstract (arXiv)

A fully Bayesian treatment of complicated predictive models (such as deep neural networks) would enable rigorous uncertainty quantification and the automation of higher-level tasks including model selection. However, the intractability of sampling Bayesian posteriors over many parameters inhibits the use of Bayesian methods where they are most needed. Thermodynamic computing has emerged as a paradigm for accelerating operations used in machine learning, such as matrix inversion, and is based on the mapping of Langevin equations to the dynamics of noisy physical systems. Hence, it is natural to consider the implementation of Langevin sampling algorithms on thermodynamic devices. In this work we propose electronic analog devices that sample from Bayesian posteriors by realizing Langevin dynamics physically. Circuit designs are given for sampling the posterior of a Gaussian-Gaussian model and for Bayesian logistic regression, and are validated by simulations. It is shown, under reasonable assumptions, that the Bayesian posteriors for these models can be sampled in time scaling with ln(d), where d is dimension. For the Gaussian-Gaussian model, the energy cost is shown to scale with  d ln(d). These results highlight the potential for fast, energy-efficient Bayesian inference using thermodynamic computing.