# Probabilistic Contrastive Learning with Explicit Concentration on the Hypersphere

arXiv: https://arxiv.org/abs/2405.16460 · HTML: https://mlsanity.com/paper/2405.16460/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 43 of its 56 references that are in the map.
- First posted on arXiv 26 May 2024.

## Builds on (most cited first, 30 of 43)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [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)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Understanding the Behaviour of Contrastive Loss](https://mlsanity.com/paper/2012.09740/) (2020)
- [Snapshot Ensembles: Train 1, get M for free](https://mlsanity.com/paper/1704.00109/) (2017)
- [Big Self-Supervised Models Advance Medical Image Classification](https://mlsanity.com/paper/2101.05224/) (2021)
- [NormFace: L2 Hypersphere Embedding for Face Verification](https://mlsanity.com/paper/1704.06369/) (2017)
- [OpenOOD v1.5: Enhanced Benchmark for Out-of-Distribution Detection](https://mlsanity.com/paper/2306.09301/) (2023)
- [Probabilistic Face Embeddings](https://mlsanity.com/paper/1904.09658/) (2019)
- [How to Exploit Hyperspherical Embeddings for Out-of-Distribution Detection?](https://mlsanity.com/paper/2203.04450/) (2022)
- [Stochastic Segmentation Networks: Modelling Spatially Correlated Aleatoric Uncertainty](https://mlsanity.com/paper/2006.06015/) (2020)
- [MonoRUn: Monocular 3D Object Detection by Reconstruction and Uncertainty Propagation](https://mlsanity.com/paper/2103.12605/) (2021)
- [Best of Both Worlds: Multimodal Contrastive Learning with Tabular and Imaging Data](https://mlsanity.com/paper/2303.14080/) (2023)

## Abstract (arXiv)

Self-supervised contrastive learning has predominantly adopted deterministic methods, which are not suited for environments characterized by uncertainty and noise. This paper introduces a new perspective on incorporating uncertainty into contrastive learning by embedding representations within a spherical space, inspired by the von Mises-Fisher distribution (vMF). We introduce an unnormalized form of vMF and leverage the concentration parameter, kappa, as a direct, interpretable measure to quantify uncertainty explicitly. This approach not only provides a probabilistic interpretation of the embedding space but also offers a method to calibrate model confidence against varying levels of data corruption and characteristics. Our empirical results demonstrate that the estimated concentration parameter correlates strongly with the degree of unforeseen data corruption encountered at test time, enables failure analysis, and enhances existing out-of-distribution detection methods.