Natural language often exhibits inherent hierarchical structure ingrained with complex syntax and semantics. However, most state-of-the-art deep generative models learn embeddings only in Euclidean vector space, without accounting for this structural
property of language. In this paper, we investigate text generation in a hyperbolic latent space to learn continuous hierarchical representations. An Adversarial Poincare Variational Autoencoder (APo-VAE) is presented, where both the prior and variational posterior of latent variables are defined over a Poincare ball via wrapped normal distributions. By adopting the primal-dual formulation of Kullback-Leibler divergence, an adversarial learning procedure is introduced to empower robust model training. Extensive experiments in language modeling, unaligned style transfer, and dialog-response generation demonstrate the effectiveness of the proposed APo-VAE model over VAEs in Euclidean latent space, thanks to its superb capabilities in capturing latent language hierarchies in hyperbolic space.
