Neural networks (NN) have demonstrated remarkable capabilities in various tasks, but their computation-intensive nature demands faster and more energy-efficient hardware implementations. Optics-based platforms, using technologies such as silicon photonics and spatial light modulators, offer promising avenues for achieving this goal. However, training multiple trainable layers in tandem with these physical systems poses challenges, as they are difficult to fully characterize and describe with differentiable functions, hindering the use of error backpropagation algorithm. The recently introduced Forward-Forward Algorithm (FFA) eliminates the need for perfect characterization of the learning system and shows promise for efficient training with large numbers of programmable parameters. The FFA does not require backpropagating an error signal to update the weights, rather the weights are updated by only sending information in one direction. The local loss function for each set of trainable weights enables low-power analog hardware implementations without resorting to metaheuristic algorithms or reinforcement learning. In this paper, we present an experiment utilizing multimode nonlinear wave propagation in an optical fiber demonstrating the feasibility of the FFA approach using an optical system. The results show that incorporating optical transforms in multilayer NN architectures trained with the FFA, can lead to performance improvements, even with a relatively small number of trainable weights. The proposed method offers a new path to the challenge of training optical NNs and provides insights into leveraging physical transformations for enhancing NN performance.

翻译：神经网络在各类任务中展现出卓越能力，但其计算密集型特性要求更快速、更节能的硬件实现。基于光学平台（如硅光子学与空间光调制器技术）为实现这一目标提供了有希望的途径。然而，在这些物理系统中串联训练多层可训练层存在挑战，因为它们难以被完全表征并可用可微函数描述，从而阻碍了误差反向传播算法的应用。最新提出的前向-前向算法消除了对学习系统完美表征的需求，并展现出在大规模可编程参数下高效训练的潜力。该算法无需通过反向传播误差信号来更新权重，仅通过单向信息传递即可实现权重更新。每层可训练权重的局部损失函数使得无需借助元启发式算法或强化学习即可实现低功耗模拟硬件实现。本文通过利用光纤中多模非线性波传播的实验，验证了基于光学系统实施前向-前向算法的可行性。结果表明，在采用前向-前向算法训练的多层神经网络架构中引入光学变换，即便在可训练权重数量相对较少的情况下，也能带来性能提升。该方法为光学神经网络训练难题提供了新路径，并为利用物理变换增强神经网络性能提供了洞见。