# Deep Metric Learning with Spherical Embedding

arXiv: https://arxiv.org/abs/2011.02785 · HTML: https://mlsanity.com/paper/2011.02785/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Nov 2020.

## Built on by (most cited first, 25 of 25)

- [PromptStyler: Prompt-driven Style Generation for Source-free Domain Generalization](https://mlsanity.com/paper/2307.15199/) (2023)
- [Non-isotropy Regularization for Proxy-based Deep Metric Learning](https://mlsanity.com/paper/2203.08547/) (2022)
- [Variational Graph Normalized Auto-Encoders](https://mlsanity.com/paper/2108.08046/) (2021)
- [Robust and Decomposable Average Precision for Image Retrieval](https://mlsanity.com/paper/2110.01445/) (2021)
- [Optimization of Rank Losses for Image Retrieval](https://mlsanity.com/paper/2309.08250/) (2023)
- [Informative and Representative Triplet Selection for Multilabel Remote Sensing Image Retrieval](https://mlsanity.com/paper/2105.03647/) (2021)
- [On the Importance of Embedding Norms in Self-Supervised Learning](https://mlsanity.com/paper/2502.09252/) (2025)
- [Introspective Deep Metric Learning](https://mlsanity.com/paper/2309.09982/) (2023)
- [The Hidden Pitfalls of the Cosine Similarity Loss](https://mlsanity.com/paper/2406.16468/) (2024)
- [DAS: Densely-Anchored Sampling for Deep Metric Learning](https://mlsanity.com/paper/2208.00119/) (2022)
- [Hyperspherical Embedding for Point Cloud Completion](https://mlsanity.com/paper/2307.05634/) (2023)
- [Neural Bregman Divergences for Distance Learning](https://mlsanity.com/paper/2206.04763/) (2022)
- [Deep Metric Learning with Chance Constraints](https://mlsanity.com/paper/2209.09060/) (2022)
- [Understanding Open-Set Recognition by Jacobian Norm and Inter-Class Separation](https://mlsanity.com/paper/2209.11436/) (2022)
- [T-REGS: Minimum Spanning Tree Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2510.23484/) (2025)
- [Directional Textual Inversion for Personalized Text-to-Image Generation](https://mlsanity.com/paper/2512.13672/) (2025)
- [Weight Rescaling: Effective and Robust Regularization for Deep Neural Networks with Batch Normalization](https://mlsanity.com/paper/2102.03497/) (2021)
- [Generalized Sum Pooling for Metric Learning](https://mlsanity.com/paper/2308.09228/) (2023)
- [Towards Non-Euclidean Foundation Models: Advancing AI Beyond Euclidean Frameworks](https://mlsanity.com/paper/2505.14417/) (2025)
- [Dynamic Graph Structure Learning via Resistance Curvature Flow](https://mlsanity.com/paper/2601.08149/) (2026)
- [Metric Learning as a Service with Covariance Embedding](https://mlsanity.com/paper/2211.15197/) (2022)
- [Angular triangle distance for ordinal metric learning](https://mlsanity.com/paper/2211.15200/) (2022)
- [Contrastive Metric Learning for Point Cloud Segmentation in Highly Granular Detectors](https://mlsanity.com/paper/2603.23356/) (2026)
- [Optimization Dynamics Imprint Semantic Specificity in Contrastive Embedding Norms](https://mlsanity.com/paper/2606.30625/) (2026)
- [When Features Become Instances: Inverted Contrastive Learning for Unsupervised Feature Selection](https://mlsanity.com/paper/2609.00782/) (2026)

## Abstract (arXiv)

Deep metric learning has attracted much attention in recent years, due to seamlessly combining the distance metric learning and deep neural network. Many endeavors are devoted to design different pair-based angular loss functions, which decouple the magnitude and direction information for embedding vectors and ensure the training and testing measure consistency. However, these traditional angular losses cannot guarantee that all the sample embeddings are on the surface of the same hypersphere during the training stage, which would result in unstable gradient in batch optimization and may influence the quick convergence of the embedding learning. In this paper, we first investigate the effect of the embedding norm for deep metric learning with angular distance, and then propose a spherical embedding constraint (SEC) to regularize the distribution of the norms. SEC adaptively adjusts the embeddings to fall on the same hypersphere and performs more balanced direction update. Extensive experiments on deep metric learning, face recognition, and contrastive self-supervised learning show that the SEC-based angular space learning strategy significantly improves the performance of the state-of-the-art.