# Hyperbolic Vision Transformers: Combining Improvements in Metric Learning

arXiv: https://arxiv.org/abs/2203.10833 · HTML: https://mlsanity.com/paper/2203.10833/

## Key facts

- Cited by 111 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 69 references that are in the map.
- First posted on arXiv 21 Mar 2022.

## Builds on (most cited first, 30 of 45)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Learning to Compare: Relation Network for Few-Shot Learning](https://mlsanity.com/paper/1711.06025/) (2017)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Perceiver IO: A General Architecture for Structured Inputs & Outputs](https://mlsanity.com/paper/2107.14795/) (2021)
- [How to train your ViT? Data, Augmentation, and Regularization in Vision Transformers](https://mlsanity.com/paper/2106.10270/) (2021)
- [Deep Metric Learning via Lifted Structured Feature Embedding](https://mlsanity.com/paper/1511.06452/) (2015)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Multi-Similarity Loss with General Pair Weighting for Deep Metric Learning](https://mlsanity.com/paper/1904.06627/) (2019)
- [A Metric Learning Reality Check](https://mlsanity.com/paper/2003.08505/) (2020)
- [Sampling Matters in Deep Embedding Learning](https://mlsanity.com/paper/1706.07567/) (2017)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [No Fuss Distance Metric Learning using Proxies](https://mlsanity.com/paper/1703.07464/) (2017)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Proxy Anchor Loss for Deep Metric Learning](https://mlsanity.com/paper/2003.13911/) (2020)

## Built on by (most cited first, 30 of 111)

- [Hyperbolic Image-Text Representations](https://mlsanity.com/paper/2304.09172/) (2023)
- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [E^2VPT: An Effective and Efficient Approach for Visual Prompt Tuning](https://mlsanity.com/paper/2307.13770/) (2023)
- [Fully Hyperbolic Convolutional Neural Networks for Computer Vision](https://mlsanity.com/paper/2303.15919/) (2023)
- [HYperbolic Self-Paced Learning for Self-Supervised Skeleton-based Action Representations](https://mlsanity.com/paper/2303.06242/) (2023)
- [Hypformer: Exploring Efficient Transformer Fully in Hyperbolic Space](https://mlsanity.com/paper/2407.01290/) (2024)
- [Unicom: Universal and Compact Representation Learning for Image Retrieval](https://mlsanity.com/paper/2304.05884/) (2023)
- [HIER: Metric Learning Beyond Class Labels via Hierarchical Regularization](https://mlsanity.com/paper/2212.14258/) (2022)
- [Poincar'e ResNet](https://mlsanity.com/paper/2303.14027/) (2023)
- [HypLiLoc: Towards Effective LiDAR Pose Regression with Hyperbolic Fusion](https://mlsanity.com/paper/2304.00932/) (2023)
- [Hyperbolic Category Discovery](https://mlsanity.com/paper/2504.06120/) (2025)
- [Hyperbolic Deep Learning for Foundation Models: A Survey](https://mlsanity.com/paper/2507.17787/) (2025)
- [Emergent Visual-Semantic Hierarchies in Image-Text Representations](https://mlsanity.com/paper/2407.08521/) (2024)
- [Rethinking the compositionality of point clouds through regularization in the hyperbolic space](https://mlsanity.com/paper/2209.10318/) (2022)
- [Hyperbolic Active Learning for Semantic Segmentation under Domain Shift](https://mlsanity.com/paper/2306.11180/) (2023)
- [HYPE: Hyperbolic Entailment Filtering for Underspecified Images and Texts](https://mlsanity.com/paper/2404.17507/) (2024)
- [Lorentzian Residual Neural Networks](https://mlsanity.com/paper/2412.14695/) (2024)
- [Hyperbolic Safety-Aware Vision-Language Models](https://mlsanity.com/paper/2503.12127/) (2025)
- [DA-VPT: Semantic-Guided Visual Prompt Tuning for Vision Transformers](https://mlsanity.com/paper/2505.23694/) (2025)
- [HLFormer: Enhancing Partially Relevant Video Retrieval with Hyperbolic Learning](https://mlsanity.com/paper/2507.17402/) (2025)
- [Learning Structured Representations with Hyperbolic Embeddings](https://mlsanity.com/paper/2412.01023/) (2024)
- [Hyperbolic Contrastive Learning](https://mlsanity.com/paper/2302.01409/) (2023)
- [Hyp-OW: Exploiting Hierarchical Structure Learning with Hyperbolic Distance Enhances Open World Object Detection](https://mlsanity.com/paper/2306.14291/) (2023)
- [HyperCore: The Core Framework for Building Hyperbolic Foundation Models with Comprehensive Modules](https://mlsanity.com/paper/2504.08912/) (2025)
- [Improving Visual Recognition with Hyperbolical Visual Hierarchy Mapping](https://mlsanity.com/paper/2404.00974/) (2024)
- [Understanding Hyperbolic Metric Learning through Hard Negative Sampling](https://mlsanity.com/paper/2404.15523/) (2024)
- [Hyperbolic Learning with Multimodal Large Language Models](https://mlsanity.com/paper/2408.05097/) (2024)
- [Hyperbolic Hierarchical Contrastive Hashing](https://mlsanity.com/paper/2212.08904/) (2022)
- [Towards Improved Proxy-based Deep Metric Learning via Data-Augmented Domain Adaptation](https://mlsanity.com/paper/2401.00617/) (2024)
- [Flattening the Parent Bias: Hierarchical Semantic Segmentation in the Poincar'e Ball](https://mlsanity.com/paper/2404.03778/) (2024)

## Abstract (arXiv)

Metric learning aims to learn a highly discriminative model encouraging the embeddings of similar classes to be close in the chosen metrics and pushed apart for dissimilar ones. The common recipe is to use an encoder to extract embeddings and a distance-based loss function to match the representations -- usually, the Euclidean distance is utilized. An emerging interest in learning hyperbolic data embeddings suggests that hyperbolic geometry can be beneficial for natural data. Following this line of work, we propose a new hyperbolic-based model for metric learning. At the core of our method is a vision transformer with output embeddings mapped to hyperbolic space. These embeddings are directly optimized using modified pairwise cross-entropy loss. We evaluate the proposed model with six different formulations on four datasets achieving the new state-of-the-art performance. The source code is available at https://github.com/htdt/hyp_metric.