# How to Exploit Hyperspherical Embeddings for Out-of-Distribution Detection?

arXiv: https://arxiv.org/abs/2203.04450 · HTML: https://mlsanity.com/paper/2203.04450/

## Key facts

- Cited by 128 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 63 references that are in the map.
- First posted on arXiv 8 Mar 2022.

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

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [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)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Improved Baselines with Momentum Contrastive Learning](https://mlsanity.com/paper/2003.04297/) (2020)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [CosFace: Large Margin Cosine Loss for Deep Face Recognition](https://mlsanity.com/paper/1801.09414/) (2018)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [Prototypical Contrastive Learning of Unsupervised Representations](https://mlsanity.com/paper/2005.04966/) (2020)
- [Contrastive Learning with Hard Negative Samples](https://mlsanity.com/paper/2010.04592/) (2020)
- [Towards Open Set Deep Networks](https://mlsanity.com/paper/1511.06233/) (2015)
- [ReAct: Out-of-distribution Detection With Rectified Activations](https://mlsanity.com/paper/2111.12797/) (2021)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [Deep Metric Learning via Lifted Structured Feature Embedding](https://mlsanity.com/paper/1511.06452/) (2015)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instances](https://mlsanity.com/paper/2007.08176/) (2020)
- [Generalized ODIN: Detecting Out-of-distribution Image without Learning from Out-of-distribution Data](https://mlsanity.com/paper/2002.11297/) (2020)
- [Understanding the Behaviour of Contrastive Loss](https://mlsanity.com/paper/2012.09740/) (2020)
- [On the Importance of Gradients for Detecting Distributional Shifts in the Wild](https://mlsanity.com/paper/2110.00218/) (2021)
- [SSD: A Unified Framework for Self-Supervised Outlier Detection](https://mlsanity.com/paper/2103.12051/) (2021)
- [Learning Confidence for Out-of-Distribution Detection in Neural Networks](https://mlsanity.com/paper/1802.04865/) (2018)
- [MOS: Towards Scaling Out-of-distribution Detection for Large Semantic Space](https://mlsanity.com/paper/2105.01879/) (2021)
- [No Fuss Distance Metric Learning using Proxies](https://mlsanity.com/paper/1703.07464/) (2017)

## Built on by (most cited first, 30 of 128)

- [OpenOOD v1.5: Enhanced Benchmark for Out-of-Distribution Detection](https://mlsanity.com/paper/2306.09301/) (2023)
- [Non-Parametric Outlier Synthesis](https://mlsanity.com/paper/2303.02966/) (2023)
- [ARGS: Alignment as Reward-Guided Search](https://mlsanity.com/paper/2402.01694/) (2024)
- [Process Reward Model with Q-Value Rankings](https://mlsanity.com/paper/2410.11287/) (2024)
- [Dream the Impossible: Outlier Imagination with Diffusion Models](https://mlsanity.com/paper/2309.13415/) (2023)
- [Scaling for Training Time and Post-hoc Out-of-distribution Detection Enhancement](https://mlsanity.com/paper/2310.00227/) (2023)
- [Nearest Neighbor Guidance for Out-of-Distribution Detection](https://mlsanity.com/paper/2309.14888/) (2023)
- [Fast Decision Boundary based Out-of-Distribution Detector](https://mlsanity.com/paper/2312.11536/) (2023)
- [NECO: NEural Collapse Based Out-of-distribution detection](https://mlsanity.com/paper/2310.06823/) (2023)
- [Learning to Augment Distributions for Out-of-Distribution Detection](https://mlsanity.com/paper/2311.01796/) (2023)
- [How Does Unlabeled Data Provably Help Out-of-Distribution Detection?](https://mlsanity.com/paper/2402.03502/) (2024)
- [Is Fine-tuning Needed? Pre-trained Language Models Are Near Perfect for Out-of-Domain Detection](https://mlsanity.com/paper/2305.13282/) (2023)
- [Neuron Activation Coverage: Rethinking Out-of-distribution Detection and Generalization](https://mlsanity.com/paper/2306.02879/) (2023)
- [Understanding the Feature Norm for Out-of-Distribution Detection](https://mlsanity.com/paper/2310.05316/) (2023)
- [Out-of-Distribution Detection: A Task-Oriented Survey of Recent Advances](https://mlsanity.com/paper/2409.11884/) (2024)
- [DIVERSIFY: A General Framework for Time Series Out-of-distribution Detection and Generalization](https://mlsanity.com/paper/2308.02282/) (2023)
- [ConjNorm: Tractable Density Estimation for Out-of-Distribution Detection](https://mlsanity.com/paper/2402.17888/) (2024)
- [When and How Does Known Class Help Discover Unknown Ones? Provable Understanding Through Spectral Analysis](https://mlsanity.com/paper/2308.05017/) (2023)
- [LAPT: Label-driven Automated Prompt Tuning for OOD Detection with Vision-Language Models](https://mlsanity.com/paper/2407.08966/) (2024)
- [Your Data Is Not Perfect: Towards Cross-Domain Out-of-Distribution Detection in Class-Imbalanced Data](https://mlsanity.com/paper/2412.06284/) (2024)
- [Adapting Multi-modal Large Language Model to Concept Drift From Pre-training Onwards](https://mlsanity.com/paper/2405.13459/) (2024)
- [From Global to Local: Multi-scale Out-of-distribution Detection](https://mlsanity.com/paper/2308.10239/) (2023)
- [Scaling Riemannian Diffusion Models](https://mlsanity.com/paper/2310.20030/) (2023)
- [AdaNeg: Adaptive Negative Proxy Guided OOD Detection with Vision-Language Models](https://mlsanity.com/paper/2410.20149/) (2024)
- [Learning Structured Representations with Hyperbolic Embeddings](https://mlsanity.com/paper/2412.01023/) (2024)
- [Fewer Tokens, Greater Scaling: Self-Adaptive Visual Bases for Efficient and Expansive Representation Learning](https://mlsanity.com/paper/2511.19515/) (2025)
- [On the Importance of Feature Separability in Predicting Out-Of-Distribution Error](https://mlsanity.com/paper/2303.15488/) (2023)
- [AUTO: Adaptive Outlier Optimization for Test-Time OOD Detection](https://mlsanity.com/paper/2303.12267/) (2023)
- [HYPO: Hyperspherical Out-of-Distribution Generalization](https://mlsanity.com/paper/2402.07785/) (2024)
- [Conjugated Semantic Pool Improves OOD Detection with Pre-trained Vision-Language Models](https://mlsanity.com/paper/2410.08611/) (2024)

## Abstract (arXiv)

Out-of-distribution (OOD) detection is a critical task for reliable machine learning. Recent advances in representation learning give rise to distance-based OOD detection, where testing samples are detected as OOD if they are relatively far away from the centroids or prototypes of in-distribution (ID) classes. However, prior methods directly take off-the-shelf contrastive losses that suffice for classifying ID samples, but are not optimally designed when test inputs contain OOD samples. In this work, we propose CIDER, a novel representation learning framework that exploits hyperspherical embeddings for OOD detection. CIDER jointly optimizes two losses to promote strong ID-OOD separability: a dispersion loss that promotes large angular distances among different class prototypes, and a compactness loss that encourages samples to be close to their class prototypes. We analyze and establish the unexplored relationship between OOD detection performance and the embedding properties in the hyperspherical space, and demonstrate the importance of dispersion and compactness. CIDER establishes superior performance, outperforming the latest rival by 19.36% in FPR95. Code is available at https://github.com/deeplearning-wisc/cider.