## 4 Results and Discussion
### RQ2: What Are the Key Search Spaces Explored in NAS-GAN?
#### 4.2.2 Cell-Based Space
The search employs an evolutionary algorithm, treating the generator as an evolving supernet composed of multiple Directed Acyclic Graphs (DAGs). Each cell is represented by a DAG with N nodes, where edges between nodes are candidate operations including various convolutions (\(1\times 1,3\times 3,5\times 5\)), dilated convolutions, skip-connections, and zero operations. Upsampling options include transposed convolution \(3\times 3\), nearest neighbor, and bilinear interpolation. The evolutionary process optimizes both cell structure and operation weights simultaneously. Architectures are evaluated against a Discriminator serving as the evolutionary environment. The final generator is constructed by stacking the best-performing discovered cells. T2 IGAN's [37] search space is designed to optimize the generator architecture via a cell-based approach. The generator is modeled as a supernet comprised of multiple cells, each represented by a DAG with a fixed number of nodes (typically 4). In each cell, edges correspond to candidate operations drawn from two primary categories: conventional convolutional operations and transformer modules. The convolutional candidates include operations with kernel sizes of \(3\times 3\) and \(5\times 5\), while the transformer candidates incorporate multi-head self-attention (configured with 4 or 8 heads) followed by a position-wise feed-forward network with an expansion factor of 4 and an internal dimension of 128. Additionally, a zero operation is provided, allowing the cell to bypass an edge when beneficial. Upsampling choices within the cell-based framework include nearest neighbor and bilinear interpolation techniques to progressively scale feature maps from an initial low resolution (e.g., \(4\times 4\)) to higher resolutions. MN-NAS [35] propose a search space tailored for designing class-aware generators in conditional GANs (cGANs). The search space follows a cell-based structure, where the generator is composed of multiple cells, each containing a fixed number of nodes (e.g., 4 nodes). Each cell is designed to maintain the spatial resolution and channel dimensions of the input data, ensuring consistency throughout the network. Within each cell, edges between nodes represent candidate operations, which are selected from a set of operators that include regular convolutions (RConv) and class-modulated convolutions (CMConv). The RConv operator performs standard convolutional operations, while the CMConv operator introduces class-specific information by modulating the convolutional weights using a class-conditional vector. This modulation is achieved through a combination of affine transformations and normalization steps, allowing the network to share convolutional weights across different classes while still incorporating class-specific adjustments. The search space also includes a zero operation, which allows the network to skip certain edges when necessary, providing flexibility in architecture design. The overall architecture is constructed by stacking multiple cells, with each cell contributing to the progressive upsampling of the input latent vector to generate high-resolution images. GAN Compression's [41] search space differs from the typical cell-based approach. Instead of designing entirely new cells or motifs, GAN Compression leverages the structure of a pre-trained teacher generator and focuses on automatically reducing its redundancy by searching over channel configurations. In this framework, a \"once-for-all\" network is first trained via standard gradient descent with weight sharing; this super-network supports a wide range of sub-networks, each corresponding to a unique assignment of channel widths across the generator's layers. Each convolutional layer is allowed to choose its number of channels from a discrete set (typically multiples of 8), which reflects a trade-off between computational efficiency and hardware parallelism.