Recently, integrated optics has gained interest as a hardware platform for implementing machine learning algorithms. Here, we introduce a method that enables highly efficient, in situ training of a photonic artificial neural network. We use the adjoint variable method to derive the photonic analogue of the backpropagation algorithm, which is the standard method for computing gradients for conventional neural networks. We further show how these gradients can be obtained exactly through intensity measurements inside the device. Beyond the training of photonic machine learning implementations, our method may also be of broad interest to experimental sensitivity analysis of photonic systems and the optimization of reconfigurable optics platforms.
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