# Integrated Photonic Neural Networks for Equalizing Optical Communication Signals: A Review
## 4 Building Blocks of Photonic Neural Networks  
To build all-optical photonic neural network structures, robust training algorithms still need to be developed in which weight adjustments are performed optically without the need for electro-optical conversions. This requires implementing the building blocks of photonic neural networks by optically connecting neurons, exploiting optical effects such as diffraction, refraction, interference, and scattering to precisely manipulate the amplitude, phase, and direction of light in integrated photonic circuits. One of the fundamental building blocks of photonic neural networks is activation functions, which are responsible for introducing nonlinearity to the neural network's response [89]. All-optical nonlinear activation functions are critical for the expansion of optical computing and optical neural networks, which have the potential to provide significant speed and efficiency advantages over their electronic counterparts. This nonlinearity allows the network to learn and model complex relationships between inputs and outputs [99]. It is worth noting that without activation functions, the neural network only consists of a linear combination of its inputs, which limits its ability to solve more complex problems. In this scenario, activation functions are applied to neurons in a neural network to decide whether they should be activated or inactivated based on the weighted sum of the inputs received [100]. In this direction, recent studies have already successfully demonstrated the implementation of optical activation functions employing silicon electro-optical switches and Ge-Si photoelectric detectors [101], germanium silicon hybrid asymmetric couplers [102], 2D metal carbide and nitride (MXene) materials [103], the injection-locking effect of distributed feedback laser diodes [104], the free-carrier dispersion effect [105], and semiconductor lasers [106]. For instance, Figure 4 illustrates a fully integrated photonic neural network based on an MXene-saturable absorber material with an optical nonlinearity unit. With this integrated optical structure, the classification of the modified National Institute of Standards and Technology (MNIST) database was carried out with nearly 99% accuracy, as illustrated in Figure 5, confirming the effectiveness of the use of saturable absorber materials in building all-optical nonlinear activation functions [103]. Another fundamental building block of photonic neural networks is multiplication matrices, which consist of optical structures that allow mathematical operations to be performed using light [107]. As illustrated in Figure 6, the main approaches for photonic matrix-vector multiplications (MVMs) are plane light conversion (PLC), the Mach-Zehnder interferometer (MZI), and the wavelength-division multiplexing (WDM) approach [107]. Using diffraction of light, PLC matrix-vector multiplication can be implemented, in which an input vector \(X\) is expanded and replicated via optical components, as illustrated in Figure 6a. At the end of this optical structure, the beams are combined and summed to form the output vector \(Y\), defined by the product of the transmission matrix \(W\) and the vector \(X\)[108]. Figure 6b displays the MZI multiplication matrix config  
Figure 4: Illustration of a fully integrated photonic neural network based on MXene material with an optical nonlinearity unit. Reproduced without modification from [PERSON] et al. [103], © 2023, licensed under an Attribution-Noncommercial-Noderivs International License 4.0 (CC BY-NC-ND 4.0). value decomposition and rotation submatrix decomposition methods. The WDM-based multiplication matrix depicted in Figure 6c is generally based on microring resonators [107]. For instance, [PERSON] et al. demonstrated a tiled matrix multiplication as illustrated in Figure 7 for artificial intelligence applications in integrated photonics capable of executing linear algebra operations with an accuracy of 0.636 for benign and malicious attack detection [109].