## 6 Experiments
### Category Coverage on Complex Dataset
Remarkably, the SoftGAN exhibits a noticeably superior coverage, surpassing even the performance of random sampling on real data. To provide a quantitative perspective, the StyleGAN2 encompasses 958 distinct ImageNet categories, with a shortfall of 42 categories. In stark contrast, the SoftGAN only misses 4 categories. Additionally, we assess the quantitative metric pertaining to the category distribution within the real and generated samples:  
\[ \begin{split} p_{i}&=\frac{n_{i}}{N}\\ H&=-\sum_{i=1}^{C}I(p_{i}\
eq 0)p_{i}\log p_{i} \end{split}  \tag{11}\]  
where \(N\) represents the sample size of 50,000, \(C\) denotes the total number of categories (1000) and \(n_{i}\) corresponds to the count of samples in the \(i\)th category. This approach evaluates the information entropy of the sample distribution, with larger values indicating greater diversity. Notably, for random sampling of real samples, the information entropy measures 6.89, suggesting a distribution close to uniform. In the case of generated samples, StyleGAN2 yields an information entropy of 6.17, while the SoftGAN registers an information entropy of 6.69. The comparison reveals that the SoftGAN generates samples with a broader coverage and increased diversity in comparison to StyleGAN2. \begin{table}
\begin{tabular}{l l l l l l} \hline
**Generator** & **Output Shape** & **Parameters** & **Discriminator** & **Output Shape** & **Parameters** \\ \hline mapping.fc0 & [32, 512] & 262,656 & b256.fromrgb & [32, 64, 256, 256] & 256 \\ mapping.fc1 & [32, 512] & 262,656 & b256.skip & [32, 128, 128, 128] & 8192 \\ synthesis.b4.conv1 & [32, 512, 4, 4] & 2,622,465 & b256.conv0 & [32, 64, 256, 256] & 36,928 \\ synthesis.b4.torgb & [32, 34, 4] & 264,195 & b256.conv1 & [32, 128, 128, 128] & 73,856 \\ synthesis.b4.0 & [32, 512, 4, 4] & 8192 & b128.skip & [32, 256, 64, 64] & 32,768 \\ synthesis.b8.conv0 & [32, 512, 8, 8] & 2,622,465 & b128.conv0 & [32, 128, 128] & 147,584 \\ synthesis.b8.conv1 & [32, 512, 8, 8] & 2,622,465 & b128.conv1 & [32, 256, 64, 64] & 295,168 \\ synthesis.b8.torgb & [32, 3, 8, 8] & 2,64,195 & b64.skip & [32, 512, 32, 32] & 131,072 \\ synthesis.b16.conv0 & [32, 512, 16, 16] & 2,622,465 & b64.conv0 & [32, 256, 64, 64] & 590,080 \\ synthesis.b16.conv1 & [32, 512, 16, 16] & 2,622,465 & b64.conv1 & [32, 512, 32, 32] & 131,160 \\ synthesis.b16.torgb & [32, 3, 16, 16] & 264,195 & b32.skip & [32, 512, 16, 16] & 262,144 \\ synthesis.b32.conv0 & [32, 512, 32, 32] & 2,622,465 & b32.conv1 & [32, 512, 32, 32] & 2,359,808 \\ synthesis.b32.conv1 & [32, 512, 32, 32] & 2,622,465 & b32.conv1 & [32, 512, 16, 16] & 235,9808 \\ synthesis.b32.torgb & [32, 3, 32, 23] & 264,195 & b16.skip & [32, 512, 8, 8] & 262,144 \\ synthesis.b64.conv0 & [32, 256, 64, 64] & 1,442,561 & b16.conv0 & [32, 512, 16, 16] & 235,9808 \\ synthesis.b64.conv1 & [32, 256, 64, 64] & 721,409 & b16.conv1 & [32, 512, 8, 8] & 2359,808 \\ synthesis.b64.torgb & [32, 3, 64, 64] & 132,099 & b8.skip & [32, 512, 4, 4] & 262,144 \\ synthesis.b128.conv0 & [32, 128, 128, 128] & 213,249 & b8.conv1 & [32, 512, 8, 8] & 2359,808 \\ synthesis.b128.conv1 & [32, 128, 128] & 213,249 & b8.conv1 & [32, 512, 4, 4] & 2359,808 \\ synthesis.b128.torgb & [32, 32, 128, 128] & 66,051 & b4.conv & [32, 512, 4, 4] & 2364,416 \\ synthesis.b256.conv0 & [32, 45, 256, 256] & 139,457 & b4.fc & [32, 512] & 4,194,816 \\ synthesis.b256.conv1 & [32, 64, 256, 256] & 69,761 & b4.out & [32, 1] & 513 \\ synthesis.b256.torgb & [32, 3, 256, 256] & 33,027 & & & & \\ \hline Total: & & & & & & \\ \hline \multicolumn{5}{c}{23,191,522} & \multicolumn{5}{c}{24,001,089} \\ \hline \end{tabular}
\end{table} 
Table 5: The architectural design of the generator and discriminator utilized in SoftGAN and StyleGAN2 for the ImageNet [41] generation task. Moreover, it is pertinent to underscore that in contrast to the random sampling of real shuffled data, both StyleGAN2 and the SoftGAN exhibit non-uniformity in their randomly generated outputs. A discernible discrepancy arises in the intensity of square coloring across categories.