# Numerical Simulation of an InP Photonic Integrated Cross-Connect for Deep Neural Networks on [PERSON] Shi
## 1 Introduction  
The boost in data volume of the information transient and data storage continuously stimulates the demand for high-speed information processing [1; 2]. Artificial neural networks (ANNs) are becoming essential for feature extraction [3], image classification [4], time series prediction [5] and system optimization [6] as they are able to extract meaningful information from huge datasets more efficiently. They are also widely adopted by scientific communities to investigate bio-structure prediction [7], astronomical pattern extraction [8], nuclear fusion environment control [9], in telecommunication [10], etc. Novel neural network architectures based on non-von Neuman architectures to perform parallel computation have been demonstrated based on advanced electronics. As some examples, IBM TrueNorth [11], Neurogrid [12], SpiNNaker [13], and BrainDrop [14] are designed for spiking neural networks, while FPGA [15], EIE [16] and Google TPU [17] are fordeep neural networks. The level of energy efficiency has been reported to be in the order of a few pJ/operation. However, the computation speed is constrained by the limited bandwidth of the electrical interconnections. Photonics technology provides a promising approach for neural network implementation as it offers parallel information processing when exploiting different domains (wavelength, polarization, phase, space), resulting in ultrabroad bandwidth that outperforms the electronics, while it decouples power consumption from computational speed. Recently, an ultrafast leaky integrate-and-fire neuron with a fiber-based system has been employed for spiking processing [18]. Large-scale optical neural networks using discrete optical components and micro-optics [19] and delay-based recurrent neural networks exploiting laser dynamics [20] have been reported. However, path-dependent and phase difference make the bulky systems difficult to scale up. Today's photonic integration technology can provide mature miniaturized solutions for high-performance sophisticated integrated circuits [21; 22]. A photonic reservoir computing unit has been proposed based on time delays and semiconductor optical amplifiers (SOAs) [23] or Mach-Zehnder interferometers (MZIs) [24] for time-sequential recognition, though they are not programmable as they rely on distributed nonlinearities in the system. A photonic programable feed-forward neural network has been proposed based on a coherent approach using MZI elements [25], in which the optical neuron layer combines serval serial stages, resulting in phase noise accumulation. Micro-ring resonator-based optical neural networks with wavelength division multiplexing (WDM) operation have promised to increase interconnection bandwidth [26], however thermal crosstalk and low dynamic range complicate the weight calibration. Recently we have demonstrated the implementation of a photonic deep neural network (PDNN) via cross-connect circuits based on a broadcast-and-weight architecture, using SOAs and array waveguide gratings (AWGs) [27]. By running an image classification problem, we have demonstrated that an accuracy of up to 85.8% is possible. But, the influence of chip losses and optical crosstalk on the ultimate prediction accuracy has not been investigated yet. This is an important step to make for further improvement and scalability investigation. In this work, we introduce the cross-connect-based photonic deep neural network and we simulate the matrix multiplication unit (MMU) via the _VPIphotonics Design Suit_ (VPIphotonics, Berlin, Germany) simulation software. In particular, we benchmark the simulation results versus the experimental results to offer a solid platform for further analysis. We study the influence of the optical crosstalk, coming from the AWGs, as well as the impact of the path loss, to identify margins for further scalability per layer and energy saving.