## 4 Results and Discussion
### RQ2: What Are the Key Search Spaces Explored in NAS-GAN?
#### 4.2.1. Entire/Chain-Structure Space  
Entire/chain-structure neural networks represent one of the simplest search spaces. In this space, an architecture can be described as a sequence of multiple layers, where the output of a layer serves as input for the next layer.  
NSGA-II DCGAN [28] presents an entire/chain -structure search space. This search space encompasses various architectural elements for both the generator and discriminator networks. For the generator, the search space includes the number of convolutional layers, the number of filters (kernels) in each layer, kernel sizes, padding settings, and activation functions. The discriminator's search space mirrors that of the generator, allowing for a symmetric exploration of network architectures. The framework employs a flexible approach, treating the number of layers as a significant parameter, thus allowing for variable-depth networks. This flexibility extends to other hyperparameters of the network structure, creating a multidimensional search space. The structural parameters are encoded as solution vectors, forming a continuous search domain.  
COEGAN [13] employs a chain-structured search space to evolve both the Generator and Discriminator networks in a GAN. This search space incorporates three types of layers: linear, convolution, and transpose convolution, each of which can have an activation function randomly selected from options like ReLU, LeakyReLU, ELU, Sigmoid, and Tanh. The convolution and transpose convolution layers vary in the number of output channels, while linear layers vary in the number of output features. The architecture evolves through mutations that can add, remove, or modify layers, with the number of layers capped at six in the experiments, although this parameter is adjustable. The search space supports dynamic calculation of parameters such as stride and kernel size for convolutional layers, based on the required output size of each layer. Designed to incrementally increase network complexity over generations, the search space is structured to safeguard novel architectures through a speciation mechanism.  
DEGAS [40] uses an entire/chain-structure search space, focusing on searching neural architectures for the Generator network efficiently. It searches for the whole network architecture globally, divided into three parts: a fixed first part with linear operation and reshape, a searchable middle part, and a fixed last part with batch normalization, ReLU, convolution and Tanh. The searchable part includes normal operations that maintain input size and up-sample operations that increase it. Normal operations encompass various combinations of batch norm, ReLU, convolutions, pooling, skip connections, and dilated convolutions. Up-sample operations include deconvolutions and nearest neighbor upsam  
Figure 3. Distribution of Search Space Types in NAS-GAN Literature.  
pling with convolutions. Connections between feature maps use Mixed Operations with these defined operations.  
The entire/chain-structure approach offers more freedom in architecture design but may lead to a larger search space, potentially increasing computational costs. DEGAS's approach of having fixed parts could help reduce the search space while still allowing for significant architectural exploration.