Optimizing Energy-based Neural Network Training with Coherent Ising Machine

2026-06-08

AI Summary

This work addresses the challenges of training large-scale energy-based neural networks on Ising machines, which are constrained by limited hardware connectivity and inefficient optimization. To overcome these limitations, the authors propose a novel approach that integrates a coherent Ising machine (CIM) with equilibrium propagation and the Adam optimizer to efficiently find the ground state of Hopfield energy networks. Notably, this is the first method to incorporate the Adam optimizer into CIM-driven energy-based model training, significantly accelerating convergence and improving solution accuracy while enabling support for deep and convolutional architectures. Experimental results demonstrate that, on both simulated and optoelectronic hardware platforms, the proposed framework achieves performance comparable to purely software-based implementations while substantially enhancing the scalability and training efficiency of physical AI systems.

Abstract

While Ising machines serve as advanced physical solvers for the Ising model,enabling applications in combinatorial optimization and neural network training,their scalability for 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 existing software-based implementations. We further enhance the algorithm by integrating the Adam optimizer to solve for the ground state of a Hopfield energy network, 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 of CIM dynamics as a scalable platform 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 next-generation AI hardware development.

Problem

• Ising Machine
• energy-based neural network
• scalability
• hardware connectivity
• neural network training

Innovation

• Coherent Ising Machine
• Energy-based Neural Network
• Equilibrium Propagation
• Adam optimizer
• Scalable AI Hardware