Optimization of MZI-Based Photonic Neural Networks via Pseudo-Real Number Theory and GridNet Architecture

Abstract

As information technology continues to evolve, the computing performance of existing electronic chipsapproaches its computational limit, and integrated photon technology has the advantages of fastcomputing speed and strong anti-interference ability. Therefore, a photon neural network algorithmbased on pseudo real number theory is proposed in the study. This method employs a Mach-Zehnderinterferometer array to construct a basic convolutional neural network, wherein the Mach-Zehnderinterferometer splitter is replaced by a directional coupler to form the fundamental unit. The studyemploys singular value decomposition for matrix multiplication calculations, performs unitary matrixdecomposition based on the rectangular decomposition principle, and utilizes pseudo-real numbertheory for weight training within the photonic neural network architecture. By extracting the real part ofcomplex optical fields, this approach enables optical systems to compute arbitrary real-valued matrices.Experiments demonstrate that on the MNIST handwritten digit dataset, the photonic neural networkconverges to a loss function value of 0.08 after 20 iterations, achieving a minimum loss function value0.02 and 0.09 lower than other algorithms respectively. Module U, housing the largest array ofMach-Zehnder interferometers, exhibits greater susceptibility to noise. The computational speed of thephotonic neural network surpasses traditional methods by six orders of magnitude. Followingoptimization, its computational speed exceeds other approaches by 13 ns and 7 ns respectively. Ablationexperiments reveals that the directional coupler module exerts the most significant influence onenhancing computational speed, while pseudo-real number theory has the greatest impact onrecognition accuracy. From this, the approach proposed by the research can effectively improve thecomputing speed of neural networks and reduce the operating costs in actual production.