Neural Ising Machines via Unrolling and Zeroth-Order Training

• URL: http://arxiv.org/abs/2602.00302v1
• Date: Fri, 30 Jan 2026 20:51:51 GMT
• Title: Neural Ising Machines via Unrolling and Zeroth-Order Training
• Authors: Sam Reifenstein, Timothee Leleu,
• Abstract summary: We propose a data-driven for NP-hard Ising and Max-Cut optimization that learns the update rule of an iterative dynamical system.<n>We call this approach a long neural network parameterized Issing machine (NPIM)
• Score: 3.5808917363708743
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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