Equilibrium Propagation offers a compelling alternative to traditional machine learning for training energy-based networks. Here we demonstrate a hybrid optical-digital implementation of EP using a Spatial Photonic Ising Machine (SPIM). The SPIM exploits the gauge transformation method to optically encode both continuous neuron states and rank-1 binary trainable patterns as phase modulations via a spatial light modulator, with inference realized using a finite difference scheme. The experimental system is evaluated on the Wine classification dataset. The potential of this approach, including the use of continuous couplings and structured coupling matrices, is evaluated numerically on the more complex MNIST dataset. Our work provides a concrete pathway toward energy-efficient physical implementations of Equilibrium Propagation.

翻译：平衡传播为训练基于能量的网络提供了一种引人注目的替代传统机器学习方法。本文展示了一种利用空间光子伊辛机（SPIM）实现平衡传播的混合光-数字方案。SPIM利用规范变换方法，通过空间光调制器将连续神经元状态与秩为1的二元可训练模式编码为光学相位调制，并采用有限差分方案实现推理。实验系统在葡萄酒分类数据集上进行了评估。该方法的潜力，包括使用连续耦合和结构化耦合矩阵，在更复杂的MNIST数据集上通过数值实验进行了评估。我们的工作为平衡传播的节能物理实现提供了一条具体路径。