Hyperbolic Generative Adversarial Network
This work addresses image generation for hierarchical data, but it is incremental as it adapts existing GAN methods to hyperbolic spaces.
The paper tackled the problem of generating hierarchical image data by proposing hyperbolic neural networks integrated into GAN architectures (HGAN, HCGAN, HWGAN), achieving better Inception Score and Fréchet Inception Distance results on MNIST compared to Euclidean counterparts.
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 Fréchet 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.