Optimizing energy-based neural network training processes with a coherent Ising machine

Abstract

While Ising machines serve as advanced physical solvers for the Ising model, thus enabling applications in combinatorial optimization problems and neural network training scenarios, their scalability for use with large-scale neural networks remains constrained by hardware connectivity limitations and suboptimal training methodologies. In this work, we leverage a coherent Ising machine (CIM) to train an energy-based neural network using equilibrium propagation, achieving performance comparable to that of existing software-based implementations. We further enhance the CIM simulation algorithm by integrating the Adam optimizer to compute the ground state of a Hopfield energy network, thereby significantly improving convergence speed and solution accuracy. Additionally, we demonstrate the scalability of our approach across deeper network architectures and convolutional operations. Our results highlight the potential for CIM dynamics to serve as a physics-inspired optical platform, distinct from classical computing, for training complex neural networks, offering a pathway toward energy-efficient implementations via analog circuits, optoelectronics, or integrated photonics. This work establishes a novel physical framework for the development of next-generation AI hardware.