# Optimizing Energy-based Neural Network Training with Coherent Ising Machine

arXiv: https://arxiv.org/abs/2606.09117 · HTML: https://mlsanity.com/paper/2606.09117/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 60 references that are in the map.
- First posted on arXiv 8 Jun 2026.

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Carbon Emissions and Large Neural Network Training](https://mlsanity.com/paper/2104.10350/) (2021)
- [All-Optical Machine Learning Using Diffractive Deep Neural Networks](https://mlsanity.com/paper/1804.08711/) (2018)
- [Efficient Learning for Deep Quantum Neural Networks](https://mlsanity.com/paper/1902.10445/) (2019)
- [Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systems](https://mlsanity.com/paper/2104.13386/) (2021)
- [Scaling Equilibrium Propagation to Deep ConvNets by Drastically Reducing its Gradient Estimator Bias](https://mlsanity.com/paper/2006.03824/) (2020)
- [Training End-to-End Analog Neural Networks with Equilibrium Propagation](https://mlsanity.com/paper/2006.01981/) (2020)
- [Training of photonic neural networks through in situ backpropagation](https://mlsanity.com/paper/1805.09943/) (2018)
- [Experimentally realized in situ backpropagation for deep learning in nanophotonic neural networks](https://mlsanity.com/paper/2205.08501/) (2022)
- [Application of Quantum Annealing to Training of Deep Neural Networks](https://mlsanity.com/paper/1510.06356/) (2015)
- [Updates of Equilibrium Prop Match Gradients of Backprop Through Time in an RNN with Static Input](https://mlsanity.com/paper/1905.13633/) (2019)
- [Support vector machines on the D-Wave quantum annealer](https://mlsanity.com/paper/1906.06283/) (2019)
- [Equivalence of Equilibrium Propagation and Recurrent Backpropagation](https://mlsanity.com/paper/1711.08416/) (2017)
- [Training an Ising Machine with Equilibrium Propagation](https://mlsanity.com/paper/2305.18321/) (2023)
- [Training Deep Boltzmann Networks with Sparse Ising Machines](https://mlsanity.com/paper/2303.10728/) (2023)
- [Training Coupled Phase Oscillators as a Neuromorphic Platform using Equilibrium Propagation](https://mlsanity.com/paper/2402.08579/) (2024)
- [Training Dynamical Binary Neural Networks with Equilibrium Propagation](https://mlsanity.com/paper/2103.08953/) (2021)
- [Noise-injected analog Ising machines enable ultrafast statistical sampling and machine learning](https://mlsanity.com/paper/2112.11534/) (2021)
- [Quantum-inspired annealers as Boltzmann generators for machine learning and statistical physics](https://mlsanity.com/paper/1912.08480/) (2019)
- [Low-rank combinatorial optimization and statistical learning by spatial photonic Ising machine](https://mlsanity.com/paper/2303.14993/) (2023)
- [Combinatorial optimization solving by coherent Ising machines based on spiking neural networks](https://mlsanity.com/paper/2208.07502/) (2022)
- [Training Multi-layer Neural Networks on Ising Machine](https://mlsanity.com/paper/2311.03408/) (2023)

## Abstract (arXiv)

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.