# Hyperbolic vs Euclidean Embeddings in Few-Shot Learning: Two Sides of the Same Coin

arXiv: https://arxiv.org/abs/2309.10013 · HTML: https://mlsanity.com/paper/2309.10013/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 30 references that are in the map.
- First posted on arXiv 18 Sep 2023.

## Builds on (most cited first, 19 of 19)

- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoders](https://mlsanity.com/paper/1901.06033/) (2019)
- [Fully Hyperbolic Neural Networks](https://mlsanity.com/paper/2105.14686/) (2021)
- [Hyperbolic Image Segmentation](https://mlsanity.com/paper/2203.05898/) (2022)
- [Mixed-curvature Variational Autoencoders](https://mlsanity.com/paper/1911.08411/) (2019)
- [From Trees to Continuous Embeddings and Back: Hyperbolic Hierarchical Clustering](https://mlsanity.com/paper/2010.00402/) (2020)
- [Hyperbolic Contrastive Learning for Visual Representations beyond Objects](https://mlsanity.com/paper/2212.00653/) (2022)
- [Neural Embeddings of Graphs in Hyperbolic Space](https://mlsanity.com/paper/1705.10359/) (2017)
- [Clipped Hyperbolic Classifiers Are Super-Hyperbolic Classifiers](https://mlsanity.com/paper/2107.11472/) (2021)
- [Hyperbolic Busemann Learning with Ideal Prototypes](https://mlsanity.com/paper/2106.14472/) (2021)
- [Contrastive Multi-view Hyperbolic Hierarchical Clustering](https://mlsanity.com/paper/2205.02618/) (2022)

## Built on by (most cited first, 6 of 6)

- [Non-Euclidean Mixture Model for Social Network Embedding](https://mlsanity.com/paper/2411.04876/) (2024)
- [Fast and Geometrically Grounded Lorentz Neural Networks](https://mlsanity.com/paper/2601.21529/) (2026)
- [Similarity Gates Approve Reversals: A Validity Audit of Embedding-Cosine Thresholds in Agent Systems](https://mlsanity.com/paper/2608.10216/) (2026)
- [Siamese networks for Poincar'e embeddings and the reconstruction of evolutionary trees](https://mlsanity.com/paper/2410.07387/) (2024)
- [Hyperbolic Multimodal Continual Learning: A Closest-Admissible Solution](https://mlsanity.com/paper/2609.29329/) (2026)
- [Curvature Under Attack in hZACH-ViT: Gauge Symmetry, Boundary Saturation, and Adversarial Failure](https://mlsanity.com/paper/2610.00680/) (2026)

## Abstract (arXiv)

Recent research in representation learning has shown that hierarchical data lends itself to low-dimensional and highly informative representations in hyperbolic space. However, even if hyperbolic embeddings have gathered attention in image recognition, their optimization is prone to numerical hurdles. Further, it remains unclear which applications stand to benefit the most from the implicit bias imposed by hyperbolicity, when compared to traditional Euclidean features. In this paper, we focus on prototypical hyperbolic neural networks. In particular, the tendency of hyperbolic embeddings to converge to the boundary of the Poincar'e ball in high dimensions and the effect this has on few-shot classification. We show that the best few-shot results are attained for hyperbolic embeddings at a common hyperbolic radius. In contrast to prior benchmark results, we demonstrate that better performance can be achieved by a fixed-radius encoder equipped with the Euclidean metric, regardless of the embedding dimension.