How to Train an Oscillator Ising Machine using Equilibrium Propagation

We show that Oscillator Ising Machines (OIMs) are prime candidates for use as neuromorphic machine learning processors with Equilibrium Propagation (EP) based on-chip learning. The inherent energy gradient descent dynamics of OIMs, combined with their standard CMOS implementation using existing fabrication processes, provide a natural substrate for EP learning. Our simulations confirm that OIMs satisfy the gradient-descending update property necessary for a scalable Equilibrium Propagation implementation and achieve $\sim 97.2\pm0.1\%$ test accuracy on MNIST and $\sim 88.0\pm0.1\%$ on Fashion-MNIST without requiring any significant hardware modifications. Importantly, OIMs maintain robust performance under realistic hardware constraints, including 10-bit parameter quantization, 4-bit phase measurement precision, and moderate phase noise that can potentially be beneficial with parameter optimization. These results establish OIMs as a promising platform for fast and energy-efficient neuromorphic computing, potentially enabling energy-based learning algorithms that have been previously constrained by computational limitations.