  Optical neural networks (ONNs), implemented on an array of cascaded
Mach-Zehnder interferometers (MZIs), have recently been proposed as a possible
replacement for conventional deep learning hardware. They potentially offer
higher energy efficiency and computational speed when compared to their
electronic counterparts. By utilizing tunable phase shifters, one can adjust
the output of each of MZIs in order to enable emulation of arbitrary
matrix-vector multiplication. These phase shifters are central to the
programmability of ONNs, but they require large footprint and are relatively
slow. Here we propose an ONN architecture that utilizes parity-time (PT)
symmetric couplers as its building blocks. Instead of modulating phase,
gain/loss contrasts across the array are adjusted as a means to train the
network. We demonstrate that PT symmetric optical neural networks (PT-ONN) are
adequately expressive by performing the digit-recognition task on the modified
national institute of standard and technology (MNIST) dataset. Compared to
conventional ONNs, the PT-ONN achieves a comparable accuracy (67% vs. 71%)
while circumventing the problems associated with changing phase. Our approach
may lead to new and alternative avenues for fast training in chip-scale optical
neural networks.
