Training neural networks with end-to-end optical backpropagation

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, reaching the full capacity of an optical neural network (NN) necessitates that the computing be implemented optically not only for inference but also for training. The primary algorithm for network training is backpropagation, in which the calculation is performed in the order opposite to the information flow for inference. Although straightforward in a digital computer, the optical implementation of backpropagation has remained elusive, particularly because of the conflicting requirements for the optical element that implements the nonlinear activation function. We address this challenge for the first time, we believe, with a surprisingly simple scheme, employing saturable absorbers for the role of activation units. Our approach is adaptable to various analog platforms and materials and demonstrates the possibility of constructing NNs entirely reliant on analog optical processes for both training and inference tasks.