# Thermodynamic Computing System for AI Applications

arXiv: https://arxiv.org/abs/2312.04836 · HTML: https://mlsanity.com/paper/2312.04836/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 45 references that are in the map.
- First posted on arXiv 8 Dec 2023.

## Builds on (most cited first, 14 of 14)

- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [The Hardware Lottery](https://mlsanity.com/paper/2009.06489/) (2020)
- [Zeus: Understanding and Optimizing GPU Energy Consumption of DNN Training](https://mlsanity.com/paper/2208.06102/) (2022)
- [Massively Parallel Probabilistic Computing with Sparse Ising Machines](https://mlsanity.com/paper/2110.02481/) (2021)
- [Thermodynamic AI and the fluctuation frontier](https://mlsanity.com/paper/2302.06584/) (2023)
- [Thermodynamic Computing](https://mlsanity.com/paper/1911.01968/) (2019)
- [A full-stack view of probabilistic computing with p-bits: devices, architectures and algorithms](https://mlsanity.com/paper/2302.06457/) (2023)
- [Thermodynamic Neural Network](https://mlsanity.com/paper/1906.01678/) (2019)
- [High-quality Thermal Gibbs Sampling with Quantum Annealing Hardware](https://mlsanity.com/paper/2109.01690/) (2021)
- [Analog Iterative Machine (AIM): using light to solve quadratic optimization problems with mixed variables](https://mlsanity.com/paper/2304.12594/) (2023)
- [Thermodynamic Computing via Autonomous Quantum Thermal Machines](https://mlsanity.com/paper/2308.15905/) (2023)
- [Stochastic Neuromorphic Circuits for Solving MAXCUT](https://mlsanity.com/paper/2210.02588/) (2022)

## Built on by (most cited first, 16 of 16)

- [Thermodynamic Natural Gradient Descent](https://mlsanity.com/paper/2405.13817/) (2024)
- [Nonlinear thermodynamic computing out of equilibrium](https://mlsanity.com/paper/2412.17183/) (2024)
- [Local Learning Rules for Out-of-Equilibrium Physical Generative Models](https://mlsanity.com/paper/2506.19136/) (2025)
- [Training thermodynamic computers by gradient descent](https://mlsanity.com/paper/2509.15324/) (2025)
- [Thermodynamic Bayesian Inference](https://mlsanity.com/paper/2410.01793/) (2024)
- [Self-orthogonalizing attractor neural networks emerging from the free energy principle](https://mlsanity.com/paper/2505.22749/) (2025)
- [A Blueprint for Equilibrium-Based Differentiable Continuous-Variable Thermodynamic Computing](https://mlsanity.com/paper/2607.16183/) (2026)
- [The Conditions of Physical Embodiment Enable Generalization and Care](https://mlsanity.com/paper/2510.07117/) (2025)
- [Robust Stochastic Gradient Posterior Sampling with Lattice Based Discretisation](https://mlsanity.com/paper/2602.15925/) (2026)
- [Provable Accuracy Bounds for Hybrid Dynamical Optimization and Sampling](https://mlsanity.com/paper/2410.06397/) (2024)
- [Thermodynamic cost of inference and learning in physical neural networks](https://mlsanity.com/paper/2503.09980/) (2025)
- [Agentic Information Theory: Ergodicity and Intrinsic Semantics of Information Processes](https://mlsanity.com/paper/2505.19275/) (2025)
- [Thermodynamics-Inspired Computing with Oscillatory Neural Networks for Inverse Matrix Computation](https://mlsanity.com/paper/2507.22544/) (2025)
- [Learning with springs and sticks](https://mlsanity.com/paper/2508.19015/) (2025)
- [CN101 - A Digital Thermodynamic Computer for Generative AI](https://mlsanity.com/paper/2608.00754/) (2026)
- [Online local learning for generative thermodynamic computing](https://mlsanity.com/paper/2609.15439/) (2026)

## Abstract (arXiv)

Recent breakthroughs in artificial intelligence (AI) algorithms have highlighted the need for novel computing hardware in order to truly unlock the potential for AI. Physics-based hardware, such as thermodynamic computing, has the potential to provide a fast, low-power means to accelerate AI primitives, especially generative AI and probabilistic AI. In this work, we present the first continuous-variable thermodynamic computer, which we call the stochastic processing unit (SPU). Our SPU is composed of RLC circuits, as unit cells, on a printed circuit board, with 8 unit cells that are all-to-all coupled via switched capacitances. It can be used for either sampling or linear algebra primitives, and we demonstrate Gaussian sampling and matrix inversion on our hardware. The latter represents the first thermodynamic linear algebra experiment. We also illustrate the applicability of the SPU to uncertainty quantification for neural network classification. We envision that this hardware, when scaled up in size, will have significant impact on accelerating various probabilistic AI applications.