Optics is an exciting route for the next generation of computing hardware for
machine learning, promising several orders of magnitude enhancement in both
computational speed and energy efficiency. However, to reach the full capacity
of an optical neural network it is necessary that the computing not only for
the inference, but also for the training be implemented optically. The primary
algorithm for training a neural network is backpropagation, in which the
calculation is performed in the order opposite to the information flow for
inference. While straightforward in a digital computer, optical implementation
of backpropagation has so far remained elusive, particularly because of the
conflicting requirements for the optical element that implements the nonlinear
activation function. In this work, we address this challenge for the first time
with a surprisingly simple and generic scheme. Saturable absorbers are employed
for the role of the activation units, and the required properties are achieved
through a pump-probe process, in which the forward propagating signal acts as
the pump and backward as the probe. Our approach is adaptable to various analog
platforms, materials, and network structures, and it demonstrates the
possibility of constructing neural networks entirely reliant on analog optical
processes for both training and inference tasks.

光学是下一代机器学习计算硬件的令人激动的方向，能够在计算速度和能源效率方面提供数个数量级的增强。本研究首次提出了一种简单而通用的方案，通过饱和吸收体作为激活单元，并通过泵浦 - 探测过程实现所需的性能以解决光学实现反向传播的挑战，从而展示了完全依赖于模拟光学过程进行训练和推理任务的神经网络的构建可能性。