Lorentzian Fully Hyperbolic Generative Adversarial Network

With the recent advance of deep learning, neural networks have been extensively used for data in non-Euclidean domains. In particular, hyperbolic neural networks have proved successful in processing hierarchical information of data. While a variety of hyperbolic neural network structures have been proposed, they mainly focus on discriminative tasks, and generative models in the hyperbolic space have scarcely been studied. In this work, we propose a hyperbolic generative adversarial network (GAN) within the Lorentz model for generating hyperbolic data. In addition to existing hyperbolic operations, we design novel hyperbolic layers to guarantee stable training. We first use synthetic data to show that our network is able to learn simple distribution in the hyperbolic space. Moreover, by virtue of an autoencoder, we construct a neural network model, named HAEGAN, for generating more complex data in the hyperbolic space. HAEGAN contains three parts: first, a hyperbolic autoencoder; second, a hyperbolic GAN for generating the latent embedding of the autoencoder; third, a generator that inherits the decoder from autoencoder and the generator from the GAN. Experiments show that HAEGAN is able to generate complex data with state-of-the-art structure-related performance.