# Low-Depth Optical Neural Networks

## TL;DR

This paper introduces a low-depth optical neural network architecture called OCTOPUS, which significantly improves noise robustness and scalability for machine learning tasks by compressing circuit depth logarithmically.

## Contribution

The authors propose a novel low-depth ONN architecture that scales logarithmically with circuit depth, enhancing noise robustness and practical applicability.

## Key findings

- LD-ONN shows exponential gain in noise robustness.
- Numerical results on Letter Recognition dataset demonstrate improved stability.
- OCTOPUS architecture can be used as a linear perceptron for classification.

## Abstract

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)].