# Hyperbolic Generative Adversarial Network

arXiv: https://arxiv.org/abs/2102.05567 · HTML: https://mlsanity.com/paper/2102.05567/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 41 references that are in the map.
- First posted on arXiv 10 Feb 2021.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Arbitrary Style Transfer in Real-time with Adaptive Instance Normalization](https://mlsanity.com/paper/1703.06868/) (2017)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)
- [Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoders](https://mlsanity.com/paper/1901.06033/) (2019)
- [Embedding Text in Hyperbolic Spaces](https://mlsanity.com/paper/1806.04313/) (2018)
- [ALICE: Towards Understanding Adversarial Learning for Joint Distribution Matching](https://mlsanity.com/paper/1709.01215/) (2017)
- [APo-VAE: Text Generation in Hyperbolic Space](https://mlsanity.com/paper/2005.00054/) (2020)

## Built on by (most cited first, 5 of 5)

- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [Poincar'e ResNet](https://mlsanity.com/paper/2303.14027/) (2023)
- [The Euclidean Space is Evil: Hyperbolic Attribute Editing for Few-shot Image Generation](https://mlsanity.com/paper/2211.12347/) (2022)
- [Autoencoding Hyperbolic Representation for Adversarial Generation](https://mlsanity.com/paper/2201.12825/) (2022)
- [Why are hyperbolic neural networks effective? A study on hierarchical representation capability](https://mlsanity.com/paper/2402.02478/) (2024)

## Abstract (arXiv)

Recently, Hyperbolic Spaces in the context of Non-Euclidean Deep Learning have gained popularity because of their ability to represent hierarchical data. We propose that it is possible to take advantage of the hierarchical characteristic present in the images by using hyperbolic neural networks in a GAN architecture. In this study, different configurations using fully connected hyperbolic layers in the GAN, CGAN, and WGAN are tested, in what we call the HGAN, HCGAN, and HWGAN, respectively. The results are measured using the Inception Score (IS) and the Fr'echet Inception Distance (FID) on the MNIST dataset. Depending on the configuration and space curvature, better results are achieved for each proposed hyperbolic versions than their euclidean counterpart.