# Efficient Optimization with Higher-Order Ising Machines

arXiv: https://arxiv.org/abs/2212.03426 · HTML: https://mlsanity.com/paper/2212.03426/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Dec 2022.

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

- [Training Deep Boltzmann Networks with Sparse Ising Machines](https://mlsanity.com/paper/2303.10728/) (2023)
- [Explosive neural networks via higher-order interactions in curved statistical manifolds](https://mlsanity.com/paper/2408.02326/) (2024)
- [Efficient Combinatorial Optimization via Heat Diffusion](https://mlsanity.com/paper/2403.08757/) (2024)
- [Programmable k-local Ising interactions and shallow optical Kolmogorov--Arnold networks through repeated data encounters](https://mlsanity.com/paper/2508.17440/) (2025)
- [Self-Adaptive Ising Machines for Constrained Optimization](https://mlsanity.com/paper/2501.04971/) (2025)
- [Nonlocal Monte Carlo via Reinforcement Learning](https://mlsanity.com/paper/2508.10520/) (2025)
- [Augmented Electronic Ising Machine as an Effective SAT Solver](https://mlsanity.com/paper/2305.01623/) (2023)
- [A general learning scheme for classical and quantum Ising machines](https://mlsanity.com/paper/2310.18411/) (2023)
- [Provable Accuracy Bounds for Hybrid Dynamical Optimization and Sampling](https://mlsanity.com/paper/2410.06397/) (2024)
- [Thermodynamics-Inspired Computing with Oscillatory Neural Networks for Inverse Matrix Computation](https://mlsanity.com/paper/2507.22544/) (2025)
- [Probabilistic Algorithms for Ising Machines from Optimization to Generative AI](https://mlsanity.com/paper/2610.03972/) (2026)

## Abstract (arXiv)

A prominent approach to solving combinatorial optimization problems on parallel hardware is Ising machines, i.e., hardware implementations of networks of interacting binary spin variables. Most Ising machines leverage second-order interactions although important classes of optimization problems, such as satisfiability problems, map more seamlessly to Ising networks with higher-order interactions. Here, we demonstrate that higher-order Ising machines can solve satisfiability problems more resource-efficiently in terms of the number of spin variables and their connections when compared to traditional second-order Ising machines. Further, our results show on a benchmark dataset of Boolean textitk-satisfiability problems that higher-order Ising machines implemented with coupled oscillators rapidly find solutions that are better than second-order Ising machines, thus, improving the current state-of-the-art for Ising machines.