# The Euclidean Space is Evil: Hyperbolic Attribute Editing for Few-shot Image Generation

arXiv: https://arxiv.org/abs/2211.12347 · HTML: https://mlsanity.com/paper/2211.12347/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 61 references that are in the map.
- First posted on arXiv 22 Nov 2022.

## Builds on (most cited first, 30 of 44)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [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)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Learning to Compare: Relation Network for Few-Shot Learning](https://mlsanity.com/paper/1711.06025/) (2017)
- [Encoding in Style: a StyleGAN Encoder for Image-to-Image Translation](https://mlsanity.com/paper/2008.00951/) (2020)
- [Interpreting the Latent Space of GANs for Semantic Face Editing](https://mlsanity.com/paper/1907.10786/) (2019)
- [GANSpace: Discovering Interpretable GAN Controls](https://mlsanity.com/paper/2004.02546/) (2020)
- [Closed-Form Factorization of Latent Semantics in GANs](https://mlsanity.com/paper/2007.06600/) (2020)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Generative Visual Manipulation on the Natural Image Manifold](https://mlsanity.com/paper/1609.03552/) (2016)
- [Unsupervised Discovery of Interpretable Directions in the GAN Latent Space](https://mlsanity.com/paper/2002.03754/) (2020)
- [Data Augmentation Generative Adversarial Networks](https://mlsanity.com/paper/1711.04340/) (2017)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [On the "steerability" of generative adversarial networks](https://mlsanity.com/paper/1907.07171/) (2019)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [GANalyze: Toward Visual Definitions of Cognitive Image Properties](https://mlsanity.com/paper/1906.10112/) (2019)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)
- [Embedding Text in Hyperbolic Spaces](https://mlsanity.com/paper/1806.04313/) (2018)
- [Image Counterfactual Sensitivity Analysis for Detecting Unintended Bias](https://mlsanity.com/paper/1906.06439/) (2019)
- [FIGR: Few-shot Image Generation with Reptile](https://mlsanity.com/paper/1901.02199/) (2019)
- [Navigating the GAN Parameter Space for Semantic Image Editing](https://mlsanity.com/paper/2011.13786/) (2020)

## Built on by (most cited first, 22 of 22)

- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [Hyperbolic Deep Learning for Foundation Models: A Survey](https://mlsanity.com/paper/2507.17787/) (2025)
- [A Survey on Generative Modeling with Limited Data, Few Shots, and Zero Shot](https://mlsanity.com/paper/2307.14397/) (2023)
- [Emergent Visual-Semantic Hierarchies in Image-Text Representations](https://mlsanity.com/paper/2407.08521/) (2024)
- [Learning Structured Representations with Hyperbolic Embeddings](https://mlsanity.com/paper/2412.01023/) (2024)
- [Image Synthesis under Limited Data: A Survey and Taxonomy](https://mlsanity.com/paper/2307.16879/) (2023)
- [HyperSDFusion: Bridging Hierarchical Structures in Language and Geometry for Enhanced 3D Text2Shape Generation](https://mlsanity.com/paper/2403.00372/) (2024)
- [radarODE: An ODE-Embedded Deep Learning Model for Contactless ECG Reconstruction from Millimeter-Wave Radar](https://mlsanity.com/paper/2408.01672/) (2024)
- [A Fashion Item Recommendation Model in Hyperbolic Space](https://mlsanity.com/paper/2409.02599/) (2024)
- [Stable Attribute Group Editing for Reliable Few-shot Image Generation](https://mlsanity.com/paper/2302.00179/) (2023)
- [BIFR"OST: 3D-Aware Image compositing with Language Instructions](https://mlsanity.com/paper/2410.19079/) (2024)
- [HypDAE: Hyperbolic Diffusion Autoencoders for Hierarchical Few-shot Image Generation](https://mlsanity.com/paper/2411.17784/) (2024)
- [Curvature Learning for Generalization of Hyperbolic Neural Networks](https://mlsanity.com/paper/2508.17232/) (2025)
- [Path-Decoupled Hyperbolic Flow Matching for Few-Shot Adaptation](https://mlsanity.com/paper/2602.20479/) (2026)
- [ComFusion: Personalized Subject Generation in Multiple Specific Scenes From Single Image](https://mlsanity.com/paper/2402.11849/) (2024)
- [Universal Few-Shot Spatial Control for Diffusion Models](https://mlsanity.com/paper/2509.07530/) (2025)
- [Balanced Hyperbolic Embeddings Are Natural Out-of-Distribution Detectors](https://mlsanity.com/paper/2506.10146/) (2025)
- [HypeVPR: Exploring Hyperbolic Space for Perspective to Equirectangular Visual Place Recognition](https://mlsanity.com/paper/2506.04764/) (2025)
- [Multi-Scale Representation of Follicular Lymphoma Pathology Images in a Single Hyperbolic Space](https://mlsanity.com/paper/2506.18523/) (2025)
- [FusionGen: Feature Fusion-Based Few-Shot EEG Data Generation](https://mlsanity.com/paper/2510.10604/) (2025)
- [HCFSLN: Adaptive Hyperbolic Few-Shot Learning for Multimodal Anxiety Detection](https://mlsanity.com/paper/2511.06988/) (2025)
- [IG-GAN: A Generative Adversarial Network for Aerodynamic Data Generation Based on Intrinsic Geometry](https://mlsanity.com/paper/2607.11497/) (2026)

## Abstract (arXiv)

Few-shot image generation is a challenging task since it aims to generate diverse new images for an unseen category with only a few images. Existing methods suffer from the trade-off between the quality and diversity of generated images. To tackle this problem, we propose Hyperbolic Attribute Editing~(HAE), a simple yet effective method. Unlike other methods that work in Euclidean space, HAE captures the hierarchy among images using data from seen categories in hyperbolic space. Given a well-trained HAE, images of unseen categories can be generated by moving the latent code of a given image toward any meaningful directions in the Poincar'e disk with a fixing radius. Most importantly, the hyperbolic space allows us to control the semantic diversity of the generated images by setting different radii in the disk. Extensive experiments and visualizations demonstrate that HAE is capable of not only generating images with promising quality and diversity using limited data but achieving a highly controllable and interpretable editing process.