  Optical neural networks are emerging as a promising type of machine learning
hardware capable of energy-efficient, parallel computation. Today's optical
neural networks are mainly developed to perform optical inference after in
silico training on digital simulators. However, various physical imperfections
that cannot be accurately modelled may lead to the notorious reality gap
between the digital simulator and the physical system. To address this
challenge, we demonstrate hybrid training of optical neural networks where the
weight matrix is trained with neuron activation functions computed optically
via forward propagation through the network. We examine the efficacy of hybrid
training with three different networks: an optical linear classifier, a hybrid
opto-electronic network, and a complex-valued optical network. We perform a
comparative study to in silico training, and our results show that hybrid
training is robust against different kinds of static noise. Our
platform-agnostic hybrid training scheme can be applied to a wide variety of
optical neural networks, and this work paves the way towards advanced
all-optical training in machine intelligence.
