%0 Conference Proceedings %T APo-VAE: Text Generation in Hyperbolic Space %A Dai, Shuyang %A Gan, Zhe %A Cheng, Yu %A Tao, Chenyang %A Carin, Lawrence %A Liu, Jingjing %Y Toutanova, Kristina %Y Rumshisky, Anna %Y Zettlemoyer, Luke %Y Hakkani-Tur, Dilek %Y Beltagy, Iz %Y Bethard, Steven %Y Cotterell, Ryan %Y Chakraborty, Tanmoy %Y Zhou, Yichao %S Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies %D 2021 %8 June %I Association for Computational Linguistics %C Online %F dai-etal-2021-apo %X 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. %R 10.18653/v1/2021.naacl-main.36 %U https://aclanthology.org/2021.naacl-main.36 %U https://doi.org/10.18653/v1/2021.naacl-main.36 %P 416-431