# Understanding Hyperbolic Metric Learning through Hard Negative Sampling

arXiv: https://arxiv.org/abs/2404.15523 · HTML: https://mlsanity.com/paper/2404.15523/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 93 of its 130 references that are in the map.
- First posted on arXiv 23 Apr 2024.

## Builds on (most cited first, 30 of 93)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [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)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Improved Baselines with Momentum Contrastive Learning](https://mlsanity.com/paper/2003.04297/) (2020)
- [Unsupervised Feature Learning via Non-Parametric Instance-level Discrimination](https://mlsanity.com/paper/1805.01978/) (2018)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Big Self-Supervised Models are Strong Semi-Supervised Learners](https://mlsanity.com/paper/2006.10029/) (2020)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Learning to Compare: Relation Network for Few-Shot Learning](https://mlsanity.com/paper/1711.06025/) (2017)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [What Makes for Good Views for Contrastive Learning?](https://mlsanity.com/paper/2005.10243/) (2020)
- [Self-Supervised Learning of Pretext-Invariant Representations](https://mlsanity.com/paper/1912.01991/) (2019)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [CURL: Contrastive Unsupervised Representations for Reinforcement Learning](https://mlsanity.com/paper/2004.04136/) (2020)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [Learning Representations by Maximizing Mutual Information Across Views](https://mlsanity.com/paper/1906.00910/) (2019)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)

## Built on by (most cited first, 10 of 10)

- [A Fashion Item Recommendation Model in Hyperbolic Space](https://mlsanity.com/paper/2409.02599/) (2024)
- [Hyperbolic Dual Feature Augmentation for Open-Environment](https://mlsanity.com/paper/2506.08906/) (2025)
- [HIDISC: A Hyperbolic Framework for Domain Generalization with Generalized Category Discovery](https://mlsanity.com/paper/2510.17188/) (2025)
- [AdaptFuse: Training-Free Sequential Preference Inference via Externalized Bayesian Computation](https://mlsanity.com/paper/2604.03925/) (2026)
- [A Strong View-Free Baseline Approach for Single-View Image Guided Point Cloud Completion](https://mlsanity.com/paper/2506.15747/) (2025)
- [H3Former: Hypergraph-based Semantic-Aware Aggregation via Hyperbolic Hierarchical Contrastive Loss for Fine-Grained Visual Classification](https://mlsanity.com/paper/2511.10260/) (2025)
- [NexusFlow: Unifying Disparate Tasks under Partial Supervision via Invertible Flow Networks](https://mlsanity.com/paper/2512.06251/) (2025)
- [Intrinsic Concept Extraction Based on Compositional Interpretability](https://mlsanity.com/paper/2603.11795/) (2026)
- [Semi-Supervised Hyperbolic Hierarchical Clustering with Set-Level Structural Priors](https://mlsanity.com/paper/2606.01525/) (2026)
- [What Drives Hierarchy-Aware Image Retrieval? Taxonomy Alignment, Objective Choice, and Geometry](https://mlsanity.com/paper/2609.25638/) (2026)

## Abstract (arXiv)

In recent years, there has been a growing trend of incorporating hyperbolic geometry methods into computer vision. While these methods have achieved state-of-the-art performance on various metric learning tasks using hyperbolic distance measurements, the underlying theoretical analysis supporting this superior performance remains under-exploited. In this study, we investigate the effects of integrating hyperbolic space into metric learning, particularly when training with contrastive loss. We identify a need for a comprehensive comparison between Euclidean and hyperbolic spaces regarding the temperature effect in the contrastive loss within the existing literature. To address this gap, we conduct an extensive investigation to benchmark the results of Vision Transformers (ViTs) using a hybrid objective function that combines loss from Euclidean and hyperbolic spaces. Additionally, we provide a theoretical analysis of the observed performance improvement. We also reveal that hyperbolic metric learning is highly related to hard negative sampling, providing insights for future work. This work will provide valuable data points and experience in understanding hyperbolic image embeddings. To shed more light on problem-solving and encourage further investigation into our approach, our code is available online (https://github.com/YunYunY/HypMix).