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, CGAN, and WGAN are tested, in what we call the HGAN, HCGAN, and HWGAN, respectively. The results are measured using the Inception Score (IS) and the Fr\'echet Inception Distance (FID) on the MNIST dataset. Depending on the configuration and space curvature, better results are achieved for each proposed hyperbolic versions than their euclidean counterpart.

Sharing electronic health records (EHRs) on a large scale may lead to privacy intrusions. Recent research has shown that risks may be mitigated by simulating EHRs through generative adversarial network (GAN) frameworks. Yet the methods developed to date are limited because they 1) focus on generating data of a single type (e.g., diagnosis codes), neglecting other data types (e.g., demographics, procedures or vital signs) and 2) do not represent constraints between features. In this paper, we introduce a method to simulate EHRs composed of multiple data types by 1) refining the GAN model, 2) accounting for feature constraints, and 3) incorporating key utility measures for such generation tasks. Our analysis with over $770,000$ EHRs from Vanderbilt University Medical Center demonstrates that the new model achieves higher performance in terms of retaining basic statistics, cross-feature correlations, latent structural properties, feature constraints and associated patterns from real data, without sacrificing privacy.