Recently, Hyperbolic Spaces in the context of Non-Euclidean Deep Learning have gained popularity because of their ability to represent hierarchical data. We propose that it is possible to take advantage of the hierarchical characteristic present in the images by using hyperbolic neural networks in a GAN architecture. In this study, different configurations using fully connected hyperbolic layers in the GAN, WGAN, CGAN, and the mapping network of the StyleGAN2 are tested in what we call the HGAN, HWGAN, HCGAN, and HStyleGAN, respectively. Furthermore, we test multiple values of curvature and introduce an exponential way to train it. The results are measured using the Inception Score (IS) and the Fréchet Inception Distance (FID) over the MNIST dataset and with FID over CIFAR-10. Depending on the configuration and space curvature, better results are achieved for each proposed hyperbolic version than their euclidean counterpart.
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