# Neural Ising Machines via Unrolling and Zeroth-Order Training

arXiv: https://arxiv.org/abs/2602.00302 · HTML: https://mlsanity.com/paper/2602.00302/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 51 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Builds on (most cited first, 25 of 25)

- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem](https://mlsanity.com/paper/1906.01227/) (2019)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Erdos Goes Neural: an Unsupervised Learning Framework for Combinatorial Optimization on Graphs](https://mlsanity.com/paper/2006.10643/) (2020)
- [Combinatorial Optimization with Physics-Inspired Graph Neural Networks](https://mlsanity.com/paper/2107.01188/) (2021)
- [The Transformer Network for the Traveling Salesman Problem](https://mlsanity.com/paper/2103.03012/) (2021)
- [A Diffusion Model Framework for Unsupervised Neural Combinatorial Optimization](https://mlsanity.com/paper/2406.01661/) (2024)
- [Learning What to Defer for Maximum Independent Sets](https://mlsanity.com/paper/2006.09607/) (2020)
- [Deep Unfolding for Communications Systems: A Survey and Some New Directions](https://mlsanity.com/paper/1906.05774/) (2019)
- [Let the Flows Tell: Solving Graph Combinatorial Optimization Problems with GFlowNets](https://mlsanity.com/paper/2305.17010/) (2023)
- [Variational Annealing on Graphs for Combinatorial Optimization](https://mlsanity.com/paper/2311.14156/) (2023)
- [A Deep Reinforcement Learning Approach for Solving the Traveling Salesman Problem with Drone](https://mlsanity.com/paper/2112.12545/) (2021)
- [Backpropagation of Unrolled Solvers with Folded Optimization](https://mlsanity.com/paper/2301.12047/) (2023)
- [Graph Neural Networks and Boolean Satisfiability](https://mlsanity.com/paper/1702.03592/) (2017)
- [Learning to optimize: A tutorial for continuous and mixed-integer optimization](https://mlsanity.com/paper/2405.15251/) (2024)
- [Learning for routing: A guided review of recent developments and future directions](https://mlsanity.com/paper/2507.00218/) (2025)
- [Analog Iterative Machine (AIM): using light to solve quadratic optimization problems with mixed variables](https://mlsanity.com/paper/2304.12594/) (2023)
- [Combinatorial optimization solving by coherent Ising machines based on spiking neural networks](https://mlsanity.com/paper/2208.07502/) (2022)
- [Deep Unrolling for Nonconvex Robust Principal Component Analysis](https://mlsanity.com/paper/2307.05893/) (2023)
- [Dynamic Anisotropic Smoothing for Noisy Derivative-Free Optimization](https://mlsanity.com/paper/2405.01731/) (2024)

## Abstract (arXiv)

We propose a data-driven heuristic for NP-hard Ising and Max-Cut optimization that learns the update rule of an iterative dynamical system. The method learns a shared, node-wise update rule that maps local interaction fields to spin updates, parameterized by a compact multilayer perceptron with a small number of parameters. Training is performed using a zeroth-order optimizer, since backpropagation through long, recurrent Ising-machine dynamics leads to unstable and poorly informative gradients. We call this approach a neural network parameterized Ising machine (NPIM). Despite its low parameter count, the learned dynamics recover effective algorithmic structure, including momentum-like behavior and time-varying schedules, enabling efficient search in highly non-convex energy landscapes. Across standard Ising and neural combinatorial optimization benchmarks, NPIM achieves competitive solution quality and time-to-solution relative to recent learning-based methods and strong classical Ising-machine heuristics.