## 3 Method
### Overall Framework of ICSO
This is attributed to SNGAN's use of spectral normalization techniques to stabilize the training process, which provide more stable gradients, highly beneficial for gradient descent-based methods like the I-FGSM used by AdvLatGAN. This consistent outstanding performance across datasets and model architectures demonstrates the high scalability of ICSO, indicating that it is not only applicable to small-scale datasets but also to large-scale datasets, and can be effectively applied to different foundational model architectures. This provides a new approach for improving latent space optimization in GAN. ### Mode Collapse

When evaluating the diversity of GANs, the 2D Gaussian mixture distribution, typically consisting of 8-Gaussian-mixture distribution and 25-Gaussian-mixture distribution, can visually demonstrate the model's mode collapse. Typically, this can be directly observed using kernel density estimation (KDE) plots, with side plots reflecting the probability distribution. To verify the effectiveness of ICSO, ICSO-GAN is compared with five classical GANs, i.e., GAN [28], NS-GAN [28], LS-GAN, E-GAN [29], and IE-GAN. For fairness, various GANs are trained using the same three-layer MLP network architecture. In particular, all images are from [15], except ICSO-GAN. As depicted in Figure 4, on two synthetic datasets, all classical GANs tend to generate some missing modes. Taking the 8-Gaussian-mixture distribution as an example, GAN produces seven modes, NS-GAN produces six modes, and LS-GAN and E-GAN produce very few modes. These results indicate that they are affected by mode collapse. In contrast, ICSO-GAN successfully learns the Gaussian mixture distribution for all modes, although some modes are weakly covered. Similar experimental results also occur in 25-Gaussian-mixture distribution. Compared with most classical GANs, ICSO-GAN has obvious advantages. This suggests that our evolutionary strategy can effectively suppress mode collapse. This is corroborated by the side plots, which show that the probability distribution of ICSO-GAN is closest to that of the target dataset. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**Baseline**} & \multicolumn{2}{c}{**AdvLatGAN**} & \multicolumn{2}{c}{**ICSO**} \\ \cline{3-8}  & & **IS** & **FID** & **IS** & **FID** & **IS** & **FID** \\ \hline \multirow{8}{*}{CIFAR-10} & DCGAN & 5.92 & 46.4 & 6.21 & 41.7 & **6.39** & **38.60** \\  & WGAN & 6.63 & 32.8 & 7.21 & 27.3 & **7.26** & **26.36** \\  & WGAN-GP & 7.47 & 24.7 & 7.60 & 22.6 & **7.81** & **20.32** \\  & SNGAN & 7.29 & 25.5 & **7.58** & **22.3** & 7.40 & 22.46 \\  & LSGAN & 5.87 & 49.3 & 6.13 & 42.8 & **6.66** & **39.10** \\  & WGAN-div & 7.43 & 23.8 & 7.81 & 20.6 & **7.87** & **19.93** \\  & ACGAN & 6.02 & 59.5 & 6.06 & 53.7 & **6.46** & **39.71** \\ \hline \multirow{8}{*}{STL-10} & DCGAN & 7.18 & 61.2 & 7.33 & 56.3 & **7.62** & **50.94** \\  & WGAN & 6.51 & 73.0 & 7.62 & 51.0 & **7.69** & **49.69** \\  & WGAN-GP & 8.86 & 37.4 & 8.90 & 34.2 & **9.04** & **32.70** \\  & SNGAN & 8.49 & 36.8 & **8.63** & **34.5** & 8.50 & 34.59 \\  & LSGAN & 7.08 & 62.9 & **7.16** & **58.5** & 6.97 & 61.56 \\  & WGAN-div & 8.82 & 37.7 & 9.00 & 32.0 & **9.09** & **31.91** \\ \hline \multirow{2}{*}{LSUN-64} & WGAN-GP & - & 14.0 & - & 12.4 & **2.63** & **10.39** \\  & SNGAN & - & 11.9 & - & 9.9 & **2.44** & **9.72** \\ \hline \multirow{2}{*}{LSUN-128} & WGAN-GP & - & 14.1 & - & 12.5 & **2.81** & **12.29** \\  & SNGAN & - & 16.0 & - & 14.2 & **3.22** & **14.11** \\ \hline \multirow{2}{*}{CelebA-64} & WGAN-GP & - & 19.8 & - & 18.9 & 3.06 & **17.96** \\  & SNGAN & - & 19.5 & - & **18.2** & 2.73 & 18.38 \\ \hline \multirow{2}{*}{CelebA-128} & WGAN-GP & - & 25.2 & - & 22.3 & **7.89** & **22.30** \\  & SNGAN & - & 22.9 & - & 22.4 & **7.91** & **22.21** \\ \hline \multirow{2}{*}{ImageNet} & WGAN-GP & - & 78.1 & - & 73.6 & **9.81** & **71.50** \\  & SNGAN & - & 98.3 & - & 79.0 & **8.81** & **78.40** \\ \hline \hline \end{tabular}
\end{table}