  Physical neural networks (PNNs) are emerging paradigms for neural network
acceleration due to their high-bandwidth, in-propagation analogue processing.
Despite the advantages of PNN for inference, training remains a challenge. The
imperfect information of the physical transformation means the failure of
conventional gradient-based updates from backpropagation (BP). Here, we present
the asymmetrical training (AT) method, which treats the PNN structure as a grey
box. AT performs training while only knowing the last layer output and neuron
topological connectivity of a deep neural network structure, not requiring
information about the physical control-transformation mapping. We
experimentally demonstrated the AT method on deep grey-box PNNs implemented by
uncalibrated photonic integrated circuits (PICs), improving the classification
accuracy of Iris flower and modified MNIST hand-written digits from random
guessing to near theoretical maximum. We also showcased the consistently
enhanced performance of AT over BP for different datasets, including MNIST,
fashion-MNIST, and Kuzushiji-MNIST. The AT method demonstrated successful
training with minimal hardware overhead and reduced computational overhead,
serving as a robust light-weight training alternative to fully explore the
advantages of physical computation.
