# DC-MMD-GAN: A New Maximum Mean Discrepancy Generative Adversarial Network Using Divide and Conquer
## 4 Experiment
The Adam optimizer was used for all models with \(\beta_{1}=0.5\), \(\beta_{2}=0.9\). Figure 4 shows FID and KID of CelebA trained on these models. According to score curves in Figure 4, we find that curves of DC-MMD-GANs drop faster when compared to the original models. The training process of DC-MMD-GANs is faster than the original model. For example, in Figure 4a, the FID score of DC-SMMD-GAN with 8 models reaches 40 in about 6500 iterations on celebA. The FID score of original model reaches 40 in about 11,500 iterations, which is 5000 iterations more than the DC-SMMD-GANs with 8 sub-models. The FID score can reach 40 in fewer iterations as the sub-model increases (about 8500 iterations of DC-SMMD-GAN with 4 sub-models and 9500 iterations of DC-SMMD-GAN with 2 sub-models). We can get the consistent observation on other figures. Under the same number of iterations, we find that in most cases, the score of DC-MMD-GANs is better than the original models. The DC-MMD-GANs with 4 sub-models perform better than the 2-sub-models ones. The training results of DC-MMD-GANs with more sub-models are relatively better because of the more precise value of loss function. However, compared to the promotion of performance from original models to 4-sub-model DC-MMD-GANs, the improvement from 4-sub-models DC-MMD-GANs to  
8-sub-models ones is not obvious. Partly because the improvement of the tightness from 4-sub-models DC-MMD-GANs to 8-sub-models ones is not obvious, which can be also observed in Figure 1. Figures 5 and 6 shows the generated images of CelebA after 15,000 iterations. We find that under the same number of iterations, DC-MMD-GANs can generate higher quality images while parts of the images from original models are blurred. Under the limited iterations, DC-MMD-GANs can learn more detail from training images and generate more realistic images. However, the resolution of CIFAR-10 is low. It is hard to find how the DC-MMD-GANs improve the generating quality so we did not show the generated images of CIFAR-10. However, the improvement of DC-MMD-GANs can be observed in Figure 7. Figure 7 presents FID and KID of CIFAR-10 trained on these models. DC-MMD-GANs can converge faster on CIFAR-10, which is consistent with the results of training on CelebA. Figure 5: Images generated by different models trained on CelebA when the number of iterations is 15,000. DC-SMMD-GANs generate more realistic images while parts of images from the original models are blurred. Figure 6: DC-MMD-GAN generate more realistic images while parts of images from the original models are blurred. For CelebA, the GANs training time is 14.70 h in DC-SMMD-GANs and SMMD-GANs. In DC-MMD-GANs and MMD-GANs, the training time is 18.10 h. The time for auto-encoder training and conducting k-means (division task) is 1.57 h. Compared to training time of GANs, the division task can be omitted. For CIFAR-10, the training time is 0.7 h in DC-SMMD-GANs and 0.90 h in DC-MMD-GANs. The time of division task is 0.10 h, which can be omitted. The time used for auto-encoder training and k-means can be omitted because: (1) Compared to the GANs training time, division task takes a short period of time which will be shown in experiment. (2) The auto-encoder is trained once in each dataset and time of conducting k-means can be omitted. We compared the training score of 2-sub-models DC-MMD-GANs with batch size equaling to 32, 4-sub-models DC-MMD-GANs with batch size equaling to 16, 8-sub-models DC-MMD-GANs with batch size equaling to 8, and MMD-GANs with batch size equaling to 64. Figures 8 and 9 shows FID and KID of CelebA and CIFAR-10 trained on these models. According to the score curves, we find that the training score of DC-MMD-GANs is close to the MMD-GANs. Table 1 shows the training time of DC-MMD-GANs can be reduced as the number of sub-models increases compared to MMD-GANs.