Neural Ising Machines via Unrolling and Zeroth-Order Training
This provides a data-driven heuristic for combinatorial optimization problems, though it is incremental relative to existing learning-based and classical methods.
The paper tackles NP-hard Ising and Max-Cut optimization by learning a compact neural network update rule for iterative dynamics, achieving competitive solution quality and time-to-solution on standard benchmarks.
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.