# Integrated Photonic Neural Networks for Equalizing Optical Communication Signals: A Review
## 1 Introduction  
New digital technologies have enabled extraordinary advances in various scientific and technological fields in the last two decades [1, 2, 3, 4, 5]. In particular, the accelerated exponential growth of an extensive amount of data requires enormous computational resources, with machine learning techniques widely employed to process all these data [6]. In this scenario, the generation and processing of data happen continuously at every moment, often powered by some artificial intelligence algorithm [7]. Indeed, classical artificial intelligence models (those operating in the electronic domain) have been the subject of strong academicinterest in recent years, with use in healthcare [8], autonomous vehicles [9], agriculture [10], machine fault diagnosis [11], intrusion detection systems [12], Internet of Things [13], fundamental physics studies [14], education [15], battery management systems [16], speech recognition [17], optical communications [18], among other fields. For the scenario of optical signal equalization that is the focus of this review, classical machine learning techniques in the last two decades have been widely employed for this purpose since artificial intelligence algorithms can reverse the channel propagation function and thus mitigate distortions caused in the transmitted signals. Such investigations include complex-valued minimal radial basis function neural networks [19], feedforward neural networks [20], reservoir computing [21; 22], multi-layer perceptron networks [23], long short-term memory recurrent neural networks [24], recurrent neural networks [25], bidirectional long short-term memory neural networks [26], adaptive Bayesian neural networks [27], among several other neural network architectures [28; 29; 30]. Specifically, multi-layer perceptron equalizers generally perform better than decision feedback-based equalizers. However, they have limitations in determining local minima [31; 32] and present slow convergence. On the other hand, complex and Chebyshev neural networks have proven efficient in equalizing quadrature amplitude modulation signals, with faster convergence ability [33; 34]. Moreover, it is a well-known fact that recurrent neural networks outperform feedforward neural networks [28]. In this perspective, end-to-end artificial intelligence architectures have also been investigated [35]. Despite the aspects mentioned above, the major drawback of classical artificial intelligence models employed in signal equalization is their high computational complexity, requiring extensive training [30; 36]. In this scenario, investigations into the impact of the complexity of neural networks employed for the equalization of optical communication signals have also been conducted, showing a worsening in performance when the complexity of the neural network is reduced [26; 37; 38]. In recent years, compression strategy investigations to optimize the hyperparameters of classical artificial intelligence algorithms to minimize their complexity have been extensively performed. These compression approaches include pruning, which consists of removing all parameters (neurons, layers, and parts of the neural network structure) that do not seriously influence the neural network's performance [39; 40; 41; 42; 43; 44; 45; 46; 47]; weight clustering, that reduces the number of effective weights [48; 49; 50]; and quantization, employed to minimize the bit width of the numbers in arithmetic operations [51; 52; 53; 54; 55]. In particular, [PERSON] et al. experimentally demonstrated the multi-layer perceptron neural network, which applies pruning and quantization approaches for signal equalization with reduced memory and complexity [56]. Despite all these efforts over the last few years to reduce the computational complexity of classical neural networks, the performance-complexity trade-off remains an open problem, in which processing large amounts of data using classical artificial intelligence models requires high computational resources [30; 57].