  Optical neural network (ONN) is emerging as an attractive proposal for
machine-learning applications, enabling high-speed computation with low-energy
consumption. However, there are several challenges in applying ONN for
industrial applications, including the realization of activation functions and
maintaining stability. In particular, the stability of ONNs decrease with the
circuit depth, limiting the scalability of the ONNs for practical uses. Here we
demonstrate how to compress the circuit depth of ONN to scale only
logarithmically, leading to an exponential gain in terms of noise robustness.
Our low-depth (LD) ONN is based on an architecture, called Optical CompuTing Of
dot-Product UnitS (OCTOPUS), which can also be applied individually as a linear
perceptron for solving classification problems. Using the standard data set of
Letter Recognition, we present numerical evidence showing that LD-ONN can
exhibit a significant gain in noise robustness, compared with a previous ONN
proposal based on singular-value decomposition [Nature Photonics 11, 441
(2017)].
