Optimizing Energy-based Neural Network Training with Coherent Ising Machine

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.

Training a Predictive Coding Network on ImageNet using Equilibrium Propagation

Equilibrium Propagation (EP) is a physics-based training framework that has primarily been employed in energy-based models, including continuous Hopfield networks, nonlinear resistive networks and coupled phase oscillators. However, EP's practical applications have so far remained limited to relatively small-scale problems. Predictive coding networks (PCNs), another class of energy-based models rooted in computational neuroscience, are typically trained with a specialized algorithm and have likewise not yet been demonstrated at large scale. In this work, we develop an EP-based training method for PCNs which combines the centered variant of EP with a novel equilibration scheme for PCNs. Using this approach, we train a 10-layer convolutional PCN (VGG10) on full-size ImageNet, achieving 13.23\% test error rate on the top-5 classification task, close to the 12.2\% backpropagation baseline. To our knowledge, this is the first demonstration of both PCNs and EP-based training at ImageNet scale. These results significantly extend the scalability of both approaches and suggest that the primary challenges in scaling EP in other physical systems may come more from the computational properties of these systems than from inherent limitations of the EP framework.