🤖 AI Summary
This work addresses the challenge of efficiently solving NP-hard Ising and Max-Cut problems, where conventional methods struggle due to the complex, non-convex energy landscapes. The authors propose a data-driven iterative dynamical system that parameterizes spin update rules via a shared node-level multilayer perceptron and trains it using zeroth-order optimization to circumvent gradient instability associated with backpropagation. Remarkably, with an extremely low number of parameters, the learned dynamics automatically exhibit momentum-like behavior and time-varying scheduling mechanisms, substantially enhancing search efficiency. Evaluated on standard Ising and combinatorial optimization benchmarks, the method achieves solution quality and convergence speed comparable to state-of-the-art learning-based approaches and classical Ising machine heuristics.
📝 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.