A Robust MZI-Based Optical Neural Network Using QR Decomposition

In this paper, a robust MZI-based optical neural network using QR decomposition is proposed and investigated. To construct optical linear unit, (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>+<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i>)/2 MZIs are required to achieve <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> × <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> weight matrix <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">W</i> in the case of QR decomposition, while in the case of singular value decomposition, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> MZIs are needed. A two-layer MZI-based optical neural network using QR decomposition, in which each layer comprises the 4 × 4 optical linear unit and absolute activation function, is designed to identify the first four MNIST handwritten digit images to verify the feasibility of our proposal. A validation accuracy of 81.5% is obtained in the simulation. As a proof of concept, the designed MZI-based optical neural network using QR decomposition was fabricated an SOI platform. Experimental results show that, the measured validation accuracy is 72.5%. Under the same situation, the corresponding validation accuracy of the MZI-based optical neural network using singular value decomposition is estimated to be 67.25%. Compared to MZI-based optical neural network using singular value decomposition, the presented MZI-based optical neural network using QR decomposition needs fewer MZIs and has stronger robustness. If the size of the matrix <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">W</i> increases, these advantages of the presented MZI-based optical neural network using QR decomposition will become more apparent.