# A Symbol Recognition System for Single-Line Diagrams Developed Using a Deep-Learning Approach
## 2 Related Works
### GAN Networks  
Generative adversarial networks (GANs) were first presented by [PERSON] in 2014 [48]. GAN networks are thought of as generative models that can create unique and fresh content [21]. The generator (G) and the discriminator (D) are two competing models (such as CNNs, neural networks, etc.) that make up GANs. The discriminator serves as a classifier that receives input from the generator and the training set (fake input and authentic input). The discriminator will learn how to differentiate between real input samples and fake input samples fed into the network during the training procedure. However, the generator is taught to create samples that accurately reflect the fundamental properties of the original content [49]. As depicted in Figure 2, the generator is a network that uses current data to produce new, realistic pictures. An image is created using random noise z. The generator's objective is to deceive the discriminator into believing that the fake image it produces is genuine [48]. Equation (1) is a possible way to describe this scenario. When a sample produced by the generator is discriminated against, the generator attempts to reduce the discriminator's accuracy as much as possible [50]. \[\text{min}_{\text{G}}\text{V}(\text{G})=\text{E}_{\text{z-px}(\text{z})}[\text {log}(1-\text{D}(\text{G}(\text{z}))] \tag{1}\]  
Figure 2: The generator. As seen in Figure 3, the discriminator is a network for differentiating the images. It determines whether an input image is a fake image created by the generator or a genuine image that already exists. The discriminator's job is to highlight differences between the actual image that already exists and the fake image produced by the generator. Equation (2) is a possible way to describe this. Minimizing the difference between the real data distribution px and the artificial data distribution px(z) is the main goal of GAN training. When discriminating a real sample, the discriminator seeks to optimize accuracy (D(x)), and when separating fake samples from real samples it seeks to maximize \(1-\text{D}(\text{G})\)[50]. \[\text{max}_{\text{D}}\text{V}(\text{D})=\text{E}_{\text{z-px(z)}}[\text{logD(x )}]+\text{E}_{\text{z-px(z)}}[\text{log}(1-\text{D}(\text{G}(\text{z}))] \tag{2}\]  
The GAN network architecture is depicted in Figure 4, which includes the generator and discriminator. The generator in a GAN is responsible for producing fictitious pictures. To determine which picture is real and which is fake, the discriminator uses either a fake image created by the generator or an already existing real image. The generator and discriminator will evolve in an adversarial manner after thousands of iterations. As a consequence, the generator will be able to produce pictures that resemble actual pictures. This can be stated using the goal function of the GAN (Equation (3)). The discriminator seeks to increase the V value, while the generator seeks to reduce the V value [51]. \[\text{min}_{\text{G}}\text{max}_{\text{D}}\text{V}(\text{D},\text{G})=\text{E }_{\text{z-px(z)}}[\text{logD(x)}]+\text{E}_{\text{z-px(z)}}[\text{log}(1- \text{D}(\text{G}(\text{z}))] \tag{3}\]  
To enhance the overall performance of GANs, numerous study projects have been focused on various GAN variants. BigGAN models were developed by [PERSON] et al. [52] to accomplish the task of producing distinctive images with high resolution from various datasets. The ImageNet dataset's challenging samples as well as high-resolution images can  
Figure 4: Generative adversarial networks. Figure 3: The discriminator. both be processed by the image identification algorithm. An alternative generator design dubbed StyleGAN was proposed by [PERSON] et al. [53]. The style of the generated image can be dynamically changed based on the most recent data in all convolutional layers thanks to a newly introduced architecture for the generator that the authors created.