# CMOS + stochastic nanomagnets: heterogeneous computers for probabilistic inference and learning

arXiv: https://arxiv.org/abs/2304.05949 · HTML: https://mlsanity.com/paper/2304.05949/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 82 references that are in the map.
- First posted on arXiv 12 Apr 2023.

## Builds on (most cited first, 7 of 7)

- [Massively Parallel Probabilistic Computing with Sparse Ising Machines](https://mlsanity.com/paper/2110.02481/) (2021)
- [Training Deep Boltzmann Networks with Sparse Ising Machines](https://mlsanity.com/paper/2303.10728/) (2023)
- [A full-stack view of probabilistic computing with p-bits: devices, architectures and algorithms](https://mlsanity.com/paper/2302.06457/) (2023)
- [Scrambled Linear Pseudorandom Number Generators](https://mlsanity.com/paper/1805.01407/) (2018)
- [High Performance Monte Carlo Simulation of Ising Model on TPU Clusters](https://mlsanity.com/paper/1903.11714/) (2019)
- [CMOS-compatible Ising and Potts Annealing Using Single Photon Avalanche Diodes](https://mlsanity.com/paper/2211.12607/) (2022)
- [Three Learning Stages and Accuracy-Efficiency Tradeoff of Restricted Boltzmann Machines](https://mlsanity.com/paper/2209.00873/) (2022)

## Built on by (most cited first, 11 of 11)

- [An efficient probabilistic hardware architecture for diffusion-like models](https://mlsanity.com/paper/2510.23972/) (2025)
- [Local Learning Rules for Out-of-Equilibrium Physical Generative Models](https://mlsanity.com/paper/2506.19136/) (2025)
- [A Blueprint for Equilibrium-Based Differentiable Continuous-Variable Thermodynamic Computing](https://mlsanity.com/paper/2607.16183/) (2026)
- [Sub-universal variational circuits for combinatorial optimization problems](https://mlsanity.com/paper/2308.14981/) (2023)
- [Self-Adaptive Ising Machines for Constrained Optimization](https://mlsanity.com/paper/2501.04971/) (2025)
- [Securing generative artificial intelligence with parallel magnetic tunnel junction true randomness](https://mlsanity.com/paper/2510.01598/) (2025)
- [From Independent to Correlated Diffusion: Generalized Generative Modeling with Probabilistic Computers](https://mlsanity.com/paper/2603.27996/) (2026)
- [Mean-Field Assisted Deep Boltzmann Learning with Probabilistic Computers](https://mlsanity.com/paper/2401.01996/) (2024)
- [Configurable p-Neurons Using Modular p-Bits](https://mlsanity.com/paper/2601.18943/) (2026)
- [A Tool for the Synthesis of Adaptive Probabilistic Processors Based on the Ising Model](https://mlsanity.com/paper/2606.19533/) (2026)
- [Probabilistic Algorithms for Ising Machines from Optimization to Generative AI](https://mlsanity.com/paper/2610.03972/) (2026)

## Abstract (arXiv)

Extending Moore's law by augmenting complementary-metal-oxide semiconductor (CMOS) transistors with emerging nanotechnologies (X) has become increasingly important. One important class of problems involve sampling-based Monte Carlo algorithms used in probabilistic machine learning, optimization, and quantum simulation. Here, we combine stochastic magnetic tunnel junction (sMTJ)-based probabilistic bits (p-bits) with Field Programmable Gate Arrays (FPGA) to create an energy-efficient CMOS + X (X = sMTJ) prototype. This setup shows how asynchronously driven CMOS circuits controlled by sMTJs can perform probabilistic inference and learning by leveraging the algorithmic update-order-invariance of Gibbs sampling. We show how the stochasticity of sMTJs can augment low-quality random number generators (RNG). Detailed transistor-level comparisons reveal that sMTJ-based p-bits can replace up to 10,000 CMOS transistors while dissipating two orders of magnitude less energy. Integrated versions of our approach can advance probabilistic computing involving deep Boltzmann machines and other energy-based learning algorithms with extremely high throughput and energy efficiency.