# Logically Synthesized, Hardware-Accelerated, Restricted Boltzmann Machines for Combinatorial Optimization and Integer Factorization

arXiv: https://arxiv.org/abs/2007.13489 · HTML: https://mlsanity.com/paper/2007.13489/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jun 2020.

## Built on by (most cited first, 4 of 4)

- [Alleviation of Temperature Variation Induced Accuracy Degradation in Ferroelectric FinFET Based Neural Network](https://mlsanity.com/paper/2103.03111/) (2021)
- [A Statistical Analysis for Per-Instance Evaluation of Stochastic Optimizers: Avoiding Unreliable Conclusions](https://mlsanity.com/paper/2503.16589/) (2025)
- [Efficient Optimization Accelerator Framework for Multistate Ising Problems](https://mlsanity.com/paper/2505.20250/) (2025)
- [Photonic restricted Boltzmann machine for content generation tasks](https://mlsanity.com/paper/2508.20472/) (2025)

## Abstract (arXiv)

The Restricted Boltzmann Machine (RBM) is a stochastic neural network capable of solving a variety of difficult tasks such as NP-Hard combinatorial optimization problems and integer factorization. The RBM architecture is also very compact; requiring very few weights and biases. This, along with its simple, parallelizable sampling algorithm for finding the ground state of such problems, makes the RBM amenable to hardware acceleration. However, training of the RBM on these problems can pose a significant challenge, as the training algorithm tends to fail for large problem sizes and efficient mappings can be hard to find. Here, we propose a method of combining RBMs together that avoids the need to train large problems in their full form. We also propose methods for making the RBM more hardware amenable, allowing the algorithm to be efficiently mapped to an FPGA-based accelerator. Using this accelerator, we are able to show hardware accelerated factorization of 16 bit numbers with high accuracy with a speed improvement of 10000x and a power improvement of 32x.