# APo-VAE: Text Generation in Hyperbolic Space

arXiv: https://arxiv.org/abs/2005.00054 · HTML: https://mlsanity.com/paper/2005.00054/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2020.

## Built on by (most cited first, 14 of 14)

- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [Hyperbolic Learning with Synthetic Captions for Open-World Detection](https://mlsanity.com/paper/2404.05016/) (2024)
- [AdaVAE: Exploring Adaptive GPT-2s in Variational Auto-Encoders for Language Modeling](https://mlsanity.com/paper/2205.05862/) (2022)
- [Autoencoding Hyperbolic Representation for Adversarial Generation](https://mlsanity.com/paper/2201.12825/) (2022)
- [Hyperbolic Relevance Matching for Neural Keyphrase Extraction](https://mlsanity.com/paper/2205.02047/) (2022)
- [Improving Semantic Control in Discrete Latent Spaces with Transformer Quantized Variational Autoencoders](https://mlsanity.com/paper/2402.00723/) (2024)
- [Hyperbolic Generative Adversarial Network](https://mlsanity.com/paper/2102.05567/) (2021)
- [Continual Hyperbolic Learning of Instances and Classes](https://mlsanity.com/paper/2506.10710/) (2025)
- [Prototype Based Classification from Hierarchy to Fairness](https://mlsanity.com/paper/2205.13997/) (2022)
- [Unit Ball Model for Embedding Hierarchical Structures in the Complex Hyperbolic Space](https://mlsanity.com/paper/2105.03966/) (2021)
- [HyHTM: Hyperbolic Geometry based Hierarchical Topic Models](https://mlsanity.com/paper/2305.09258/) (2023)
- [Neural Conversation Models and How to Rein Them in: A Survey of Failures and Fixes](https://mlsanity.com/paper/2308.06095/) (2023)
- [Geometry-Aware Hyperbolic Residual-Quantized Variational Autoencoders](https://mlsanity.com/paper/2609.26342/) (2026)

## Abstract (arXiv)

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.