# Scaling Up Thermodynamic AI Models

arXiv: https://arxiv.org/abs/2607.00170 · HTML: https://mlsanity.com/paper/2607.00170/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 23 references that are in the map.
- First posted on arXiv 30 Jun 2026.

## Builds on (most cited first, 10 of 10)

- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [Rigging the Lottery: Making All Tickets Winners](https://mlsanity.com/paper/1911.11134/) (2019)
- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Inverse statistical problems: from the inverse Ising problem to data science](https://mlsanity.com/paper/1702.01522/) (2017)
- [Training Deep Boltzmann Networks with Sparse Ising Machines](https://mlsanity.com/paper/2303.10728/) (2023)
- [Revise Saturated Activation Functions](https://mlsanity.com/paper/1602.05980/) (2016)
- [An efficient probabilistic hardware architecture for diffusion-like models](https://mlsanity.com/paper/2510.23972/) (2025)
- [Analyzing Parametric Oscillator Ising Machines through the Kuramoto Lens](https://mlsanity.com/paper/2510.24416/) (2025)
- [Scaling Equilibrium Propagation to Deeper Neural Network Architectures](https://mlsanity.com/paper/2509.26003/) (2025)
- [Correspondence Between Ising Machines and Neural Networks](https://mlsanity.com/paper/2511.00746/) (2025)

## Abstract (arXiv)

Thermodynamic computing devices based on the Ising model show great promise for low-power AI inference and edge computing, but scalable methods for training large models for such hardware remain limited. Prior theory shows that the time-averaged behavior of high-temperature Gibbs-sampled Ising systems can implement feed-forward neural inference. We turn this theoretical correspondence into a scalable and purely backpropagation-based algorithm for training deep convolutional networks for thermodynamic inference on Ising machine hardware. Our image classification models achieve accuracies of 94.9% on CIFAR-10 and 76.0% on CIFAR-100 under binary Gibbs sampling. We then develop and experimentally validate a mathematical theory relating inference cost to accuracy and controlling autocorrelation times. Subsequently, we calculate asymptotic results showing that inference cost is bounded by a well-controlled tradeoff with performance and exhibit algorithms for computing optimal inference schedules. Finally, we discuss implications for hardware development and the future of high-temperature thermodynamic AI models.