We present a method for implementing an optical neural network using only linear optical resources, namely field displacement and interferometry applied to coherent states of light. The nonlinearity required for learning in a neural network is realized via an encoding of the input into phase shifts allowing for far more straightforward experimental implementation compared to previous proposals for, and demonstrations of, $\textit{in situ}$ inference. Beyond $\textit{in situ}$ inference, the method enables $\textit{in situ}$ training by utilizing established techniques like parameter shift rules or physical backpropagation to extract gradients directly from measurements of the linear optical circuit. We also investigate the effect of photon losses and find the model to be very resilient to these.

翻译：我们提出一种仅利用线性光学资源（即相干态光场的场位移与干涉测量）实现光学神经网络的方法。神经网络学习所需的非线性通过将输入编码为相移来实现，与先前提出的及演示的$\textit{原位}$推理方案相比，该方法实验实现更为直接。除$\textit{原位}$推理外，本方法通过利用参数平移规则或物理反向传播等成熟技术，可直接从线性光学电路的测量中提取梯度，从而实现$\textit{原位}$训练。我们还研究了光子损耗的影响，发现该模型对此类损耗具有极强的鲁棒性。