Neural Ising Machines via Unrolling and Zeroth-Order Training

TL;DR

This paper introduces a neural Ising machine trained with zeroth-order optimization that learns effective update rules for solving NP-hard Ising and Max-Cut problems efficiently.

Contribution

It presents a novel neural network-based approach for Ising machines that learns update rules without backpropagation through dynamics, improving solution quality and efficiency.

Findings

Achieves competitive results on standard benchmarks.

Learns momentum-like and adaptive schedules.

Operates with a small number of parameters.

Abstract

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.