Towards fully integrated photonic backpropagation training and inference using on-chip nonlinear activation and gradient functions

Gradient descent-based backpropagation training is widely used in many neural network systems. However, photonic implementation of such method is not straightforward mainly since having both the nonlinear activation function and its gradient using standard integrated photonic components is challenging. Here, we demonstrate the realization of two commonly used neural nonlinear activation functions and their gradients on a silicon photonic platform. Our method leverages the nonlinear electro-optic response of a micro-disk modulator. As a proof of concept, the experimental results are incorporated into a neural network simulation platform to classify MNIST handwritten digits dataset where we classification accuracies of more than 97\% are achieved that are on par with those of ideal nonlinearities and gradients.