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 KL divergence, an
adversarial learning procedure is introduced to empower robust model training.
Extensive experiments in language modeling and dialog-response generation tasks
demonstrate the winning 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.

本文探讨了一种超几何潜空间的文本生成方法，通过引入 Adversarial Poincare Variational Autoencoder 的模型，在超平面球中以包裹的正态分布方式定义潜变量的先验和变分后验。本文通过在语言建模和对话响应生成任务中的实验表明了该方法在捕获超几何空间中的潜在语言层次结构方面的优越性。