## 4 Results and Discussion
### RQ2: What Are the Key Search Spaces Explored in NAS-GAN?
#### 4.2.2 Cell-Based Space
The overall search space is defined as the combinatorial product of the candidate channel numbers for all layers, yielding a large--but highly structured--domain. This formulation enables fine-grained architectural optimization: the method can automatically determine which layers are more amenable to aggressive channel reduction without significantly degrading performance. In a similar vein, DAMGAN's [42] search space is crafted to facilitate the efficient discovery of high-performance generator architectures through a differentiable approach enhanced by attention mechanisms. The search space is built upon a generator supernet organized into a series of cells, each containing multiple interconnected nodes. For each pair of nodes, the candidate operations are divided into two distinct groups. In connections emanating from the input node, the search space includes upsampling operations such as nearest-neighbor sampling, bilinear interpolation sampling, and transposed convolution. For all other inter-node connections, the search space comprises convolutional operations, including standard convolutions with kernel sizes of \(1\times 1\), \(3\times 3\), and \(5\times 5\), as well as depthwise separable convolutions with kernel sizes of \(3\times 3\), \(5\times 5\), and \(7\times 7\). Uniquely, DAMGAN integrates two attention mechanisms--up-attention (UA) and down-attention (DA)--between each pair of nodes. UA selectively filters and forwards the most salient feature maps to the candidate operations, while DA evaluates and assigns importance weights to the outputs of these operations. This dual-attention strategy not only refines the selection process by effectively mapping the significance of each operation but also broadens the search space to encompass the dynamic interplay between feature selection and operation efficacy, ultimately leading to more robust and computationally efficient architecture discovery. The cell-based approach seems to be favored in NAS-GAN research, likely due to its ability to reduce the search space size while still allowing for complex architectures. This approach can lead to more efficient searches and potentially better scalability. In addition to the above-discussed search spaces, hybrid approaches have also been explored. EvoGAN [25] defines a comprehensive search space that spans both architectural and training parameters. In this framework, the entire network specification--including the generator and discriminator topologies--is encoded as lists that capture discrete decisions (e.g., number of hidden layers, activation functions, weight initialization methods) as well as continuous parameters such as loss functions and update (synchronization) frequencies. Specialized mutation operators (e.g., layer_change, activ_change, latent_change) enable the GA to explore this vast and flexible space, which scales up to 784 variables and permits the discovery of transferable architectures. Similarly, the Bi-GAN framework [26] partitions the search space into discrete and continuous components. The discrete component governs fixed architectural decisions--such as the number of layers, the choice of activation functions, and binary options like dropout, batch normalization, and pooling--while the continuous component, refined via the Bi-GAN, optimizes parameter values such as the number of neurons in fully-connected layers and the number of filters in convolutional layers. This hybrid design enables a more nuanced exploration of the architectural design space by balancing rigid candidate sets with flexible parameter tuning. One key limitation is the lack of clarity in reporting search space sizes. Many papers fail to provide detailed implementation information, making it difficult to calculate or infer the exact dimensions of the search space. This ambiguity hinders direct comparisons between different approaches and impedes our understanding of the relative efficiency of various methods.