Learning at the Speed of Physics: Equilibrium Propagation on Oscillator Ising Machines

Physical systems that naturally perform energy descent offer a direct route to accelerating machine learning. Oscillator Ising Machines (OIMs) exemplify this idea: their GHz-frequency dynamics mirror both the optimization of energy-based models (EBMs) and gradient descent on loss landscapes, while intrinsic noise corresponds to Langevin dynamics - supporting sampling as well as optimization. Equilibrium Propagation (EP) unifies these processes into descent on a single total energy landscape, enabling local learning rules without global backpropagation. We show that EP on OIMs achieves competitive accuracy ($\sim 97.2 \pm 0.1 \%$ on MNIST, $\sim 88.0 \pm 0.1 \%$ on Fashion-MNIST), while maintaining robustness under realistic hardware constraints such as parameter quantization and phase noise. These results establish OIMs as a fast, energy-efficient substrate for neuromorphic learning, and suggest that EBMs - often bottlenecked by conventional processors - may find practical realization on physical hardware whose dynamics directly perform their optimization.