# VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning

arXiv: https://arxiv.org/abs/2105.04906 · HTML: https://mlsanity.com/paper/2105.04906/

## Key facts

- Cited by 1,057 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 66 references that are in the map.
- First posted on arXiv 11 May 2021.

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

- [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)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [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)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [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)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [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)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [Big Self-Supervised Models are Strong Semi-Supervised Learners](https://mlsanity.com/paper/2006.10029/) (2020)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Unsupervised Visual Representation Learning by Context Prediction](https://mlsanity.com/paper/1505.05192/) (2015)
- [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)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [Learning Representations by Maximizing Mutual Information Across Views](https://mlsanity.com/paper/1906.00910/) (2019)
- [Data-Efficient Image Recognition with Contrastive Predictive Coding](https://mlsanity.com/paper/1905.09272/) (2019)

## Built on by (most cited first, 30 of 1057)

- [Self-Supervised Learning from Images with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2301.08243/) (2023)
- [Understanding Dimensional Collapse in Contrastive Self-supervised Learning](https://mlsanity.com/paper/2110.09348/) (2021)
- [Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Loss](https://mlsanity.com/paper/2106.04156/) (2021)
- [Behavior Transformers: Cloning k modes with one stone](https://mlsanity.com/paper/2206.11251/) (2022)
- [The Stable Signature: Rooting Watermarks in Latent Diffusion Models](https://mlsanity.com/paper/2303.15435/) (2023)
- [Masked Siamese Networks for Label-Efficient Learning](https://mlsanity.com/paper/2204.07141/) (2022)
- [Context Autoencoder for Self-Supervised Representation Learning](https://mlsanity.com/paper/2202.03026/) (2022)
- [LeWorldModel: Stable End-to-End Joint-Embedding Predictive Architecture from Pixels](https://mlsanity.com/paper/2603.19312/) (2026)
- [LeJEPA: Provable and Scalable Self-Supervised Learning Without the Heuristics](https://mlsanity.com/paper/2511.08544/) (2025)
- [A Cookbook of Self-Supervised Learning](https://mlsanity.com/paper/2304.12210/) (2023)
- [Multimodal Foundation Models: From Specialists to General-Purpose Assistants](https://mlsanity.com/paper/2309.10020/) (2023)
- [A Survey on Self-supervised Learning: Algorithms, Applications, and Future Trends](https://mlsanity.com/paper/2301.05712/) (2023)
- [CROMA: Remote Sensing Representations with Contrastive Radar-Optical Masked Autoencoders](https://mlsanity.com/paper/2311.00566/) (2023)
- [Virchow2: Scaling Self-Supervised Mixed Magnification Models in Pathology](https://mlsanity.com/paper/2408.00738/) (2024)
- [Reconstructing the Mind's Eye: fMRI-to-Image with Contrastive Learning and Diffusion Priors](https://mlsanity.com/paper/2305.18274/) (2023)
- [The Surprising Effectiveness of Representation Learning for Visual Imitation](https://mlsanity.com/paper/2112.01511/) (2021)
- [RankMe: Assessing the downstream performance of pretrained self-supervised representations by their rank](https://mlsanity.com/paper/2210.02885/) (2022)
- [Self-Supervised Models are Continual Learners](https://mlsanity.com/paper/2112.04215/) (2021)
- [Contrastive and Non-Contrastive Self-Supervised Learning Recover Global and Local Spectral Embedding Methods](https://mlsanity.com/paper/2205.11508/) (2022)
- [Decoupled Contrastive Learning](https://mlsanity.com/paper/2110.06848/) (2021)
- [Self-supervised Learning in Remote Sensing: A Review](https://mlsanity.com/paper/2206.13188/) (2022)
- [Contrastive Masked Autoencoders are Stronger Vision Learners](https://mlsanity.com/paper/2207.13532/) (2022)
- [CyCLIP: Cyclic Contrastive Language-Image Pretraining](https://mlsanity.com/paper/2205.14459/) (2022)
- [VICRegL: Self-Supervised Learning of Local Visual Features](https://mlsanity.com/paper/2210.01571/) (2022)
- [Are Large-scale Datasets Necessary for Self-Supervised Pre-training?](https://mlsanity.com/paper/2112.10740/) (2021)
- [V-JEPA 2.1: Unlocking Dense Features in Video Self-Supervised Learning](https://mlsanity.com/paper/2603.14482/) (2026)
- [Solo-learn: A Library of Self-supervised Methods for Visual Representation Learning](https://mlsanity.com/paper/2108.01775/) (2021)
- [Can contrastive learning avoid shortcut solutions?](https://mlsanity.com/paper/2106.11230/) (2021)
- [An Empirical Study of Graph Contrastive Learning](https://mlsanity.com/paper/2109.01116/) (2021)
- [Efficient Training of Visual Transformers with Small Datasets](https://mlsanity.com/paper/2106.03746/) (2021)

## Abstract (arXiv)

Recent self-supervised methods for image representation learning are based on maximizing the agreement between embedding vectors from different views of the same image. A trivial solution is obtained when the encoder outputs constant vectors. This collapse problem is often avoided through implicit biases in the learning architecture, that often lack a clear justification or interpretation. In this paper, we introduce VICReg (Variance-Invariance-Covariance Regularization), a method that explicitly avoids the collapse problem with a simple regularization term on the variance of the embeddings along each dimension individually. VICReg combines the variance term with a decorrelation mechanism based on redundancy reduction and covariance regularization, and achieves results on par with the state of the art on several downstream tasks. In addition, we show that incorporating our new variance term into other methods helps stabilize the training and leads to performance improvements.