Photonic-aware neural networks

Photonics-based neural networks promise to outperform electronic counterparts, accelerating neural network computations while reducing power consumption and footprint. However, these solutions suffer from physical layer constraints arising from the underlying analog photonic hardware, impacting the resolution of computations (in terms of effective number of bits), requiring the use of positive-valued inputs, and imposing limitations in the fan-in and in the size of convolutional kernels. To abstract these constraints, in this paper we introduce the concept of Photonic-Aware Neural Network (PANN) architectures, i.e., deep neural network models aware of the photonic hardware constraints. Then, we devise PANN training schemes resorting to quantization strategies aimed to obtain the required neural network parameters in the fixed-point domain, compliant with the limited resolution of the underlying hardware. We finally carry out extensive simulations exploiting PANNs in image classification tasks on well-known datasets (MNIST, Fashion-MNIST, and Cifar-10) with varying bitwidths (i.e., 2, 4, and 6 bits). We consider two kernel sizes and two pooling schemes for each PANN model, exploiting 2×2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\times 2$$\end{document} and 3×3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3\times 3$$\end{document} convolutional kernels, and max and average pooling, the latter more amenable to an optical implementation. 3×3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3\times 3$$\end{document} kernels perform better than 2×2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\times 2$$\end{document} counterparts, while max and average pooling provide comparable results, with the latter performing better on MNIST and Cifar-10. The accuracy degradation due to the photonic hardware constraints is quite limited, especially on MNIST and Fashion-MNIST, demonstrating the feasibility of PANN approaches on computer vision tasks.