# Equivariant Contrastive Learning

arXiv: https://arxiv.org/abs/2111.00899 · HTML: https://mlsanity.com/paper/2111.00899/

## Key facts

- Cited by 66 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 53 references that are in the map.
- First posted on arXiv 28 Oct 2021.

## Builds on (most cited first, 30 of 33)

- [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)
- [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)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Unsupervised Representation Learning by Predicting Image Rotations](https://mlsanity.com/paper/1803.07728/) (2018)
- [Unsupervised Learning of Visual Representations by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1603.09246/) (2016)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Colorful Image Colorization](https://mlsanity.com/paper/1603.08511/) (2016)
- [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)
- [Understanding image representations by measuring their equivariance and equivalence](https://mlsanity.com/paper/1411.5908/) (2014)
- [What Should Not Be Contrastive in Contrastive Learning](https://mlsanity.com/paper/2008.05659/) (2020)
- [Unsupervised Representation Learning by Sorting Sequences](https://mlsanity.com/paper/1708.01246/) (2017)
- [Boosting Few-Shot Visual Learning with Self-Supervision](https://mlsanity.com/paper/1906.05186/) (2019)
- [Interactive Supercomputing on 40,000 Cores for Machine Learning and Data Analysis](https://mlsanity.com/paper/1807.07814/) (2018)
- [Learning to See by Moving](https://mlsanity.com/paper/1505.01596/) (2015)
- [Contrastive Learning with Stronger Augmentations](https://mlsanity.com/paper/2104.07713/) (2021)
- [AET vs. AED: Unsupervised Representation Learning by Auto-Encoding Transformations rather than Data](https://mlsanity.com/paper/1901.04596/) (2019)
- [Towards Domain-Agnostic Contrastive Learning](https://mlsanity.com/paper/2011.04419/) (2020)
- [Viewmaker Networks: Learning Views for Unsupervised Representation Learning](https://mlsanity.com/paper/2010.07432/) (2020)
- [Learning image representations tied to ego-motion](https://mlsanity.com/paper/1505.02206/) (2015)
- [Improvements to context based self-supervised learning](https://mlsanity.com/paper/1711.06379/) (2017)
- [Generic 3D Representation via Pose Estimation and Matching](https://mlsanity.com/paper/1710.08247/) (2017)

## Built on by (most cited first, 30 of 66)

- [A Cookbook of Self-Supervised Learning](https://mlsanity.com/paper/2304.12210/) (2023)
- [DiffCSE: Difference-based Contrastive Learning for Sentence Embeddings](https://mlsanity.com/paper/2204.10298/) (2022)
- [Learning and Leveraging World Models in Visual Representation Learning](https://mlsanity.com/paper/2403.00504/) (2024)
- [Let Invariant Rationale Discovery Inspire Graph Contrastive Learning](https://mlsanity.com/paper/2206.07869/) (2022)
- [Equivariant Similarity for Vision-Language Foundation Models](https://mlsanity.com/paper/2303.14465/) (2023)
- [Understanding Masked Image Modeling via Learning Occlusion Invariant Feature](https://mlsanity.com/paper/2208.04164/) (2022)
- [Self-supervised learning of Split Invariant Equivariant representations](https://mlsanity.com/paper/2302.10283/) (2023)
- [InfoNCE: Identifying the Gap Between Theory and Practice](https://mlsanity.com/paper/2407.00143/) (2024)
- [Mine yOur owN Anatomy: Revisiting Medical Image Segmentation with Extremely Limited Labels](https://mlsanity.com/paper/2209.13476/) (2022)
- [Latent Space Symmetry Discovery](https://mlsanity.com/paper/2310.00105/) (2023)
- [Structuring Representation Geometry with Rotationally Equivariant Contrastive Learning](https://mlsanity.com/paper/2306.13924/) (2023)
- [Position Prediction as an Effective Pretraining Strategy](https://mlsanity.com/paper/2207.07611/) (2022)
- [Facial Video-based Remote Physiological Measurement via Self-supervised Learning](https://mlsanity.com/paper/2210.15401/) (2022)
- [EquiMod: An Equivariance Module to Improve Self-Supervised Learning](https://mlsanity.com/paper/2211.01244/) (2022)
- [CheXWorld: Exploring Image World Modeling for Radiograph Representation Learning](https://mlsanity.com/paper/2504.13820/) (2025)
- [Learning Equivariant Segmentation with Instance-Unique Querying](https://mlsanity.com/paper/2210.00911/) (2022)
- [SimCSE++: Improving Contrastive Learning for Sentence Embeddings from Two Perspectives](https://mlsanity.com/paper/2305.13192/) (2023)
- [OneVision-Encoder: Codec-Aligned Sparsity as a Foundational Principle for Multimodal Intelligence](https://mlsanity.com/paper/2602.08683/) (2026)
- [Improving Fine-tuning of Self-supervised Models with Contrastive Initialization](https://mlsanity.com/paper/2208.00238/) (2022)
- [Self-supervised visual learning from interactions with objects](https://mlsanity.com/paper/2407.06704/) (2024)
- [Equivariant Self-Supervision for Musical Tempo Estimation](https://mlsanity.com/paper/2209.01478/) (2022)
- [Differentiable Data Augmentation for Contrastive Sentence Representation Learning](https://mlsanity.com/paper/2210.16536/) (2022)
- [Self-Supervised Representation Learning for Geospatial Objects: A Survey](https://mlsanity.com/paper/2408.12133/) (2024)
- [Pose-Aware Self-Supervised Learning with Viewpoint Trajectory Regularization](https://mlsanity.com/paper/2403.14973/) (2024)
- [Collapse-Proof Non-Contrastive Self-Supervised Learning](https://mlsanity.com/paper/2410.04959/) (2024)
- [Towards a Unified Representation Evaluation Framework Beyond Downstream Tasks](https://mlsanity.com/paper/2505.06224/) (2025)
- [Towards Self-Supervised Gaze Estimation](https://mlsanity.com/paper/2203.10974/) (2022)
- [In-Context Symmetries: Self-Supervised Learning through Contextual World Models](https://mlsanity.com/paper/2405.18193/) (2024)
- [Distortion-Disentangled Contrastive Learning](https://mlsanity.com/paper/2303.05066/) (2023)
- [Learning Better Contrastive View from Radiologist's Gaze](https://mlsanity.com/paper/2305.08826/) (2023)

## Abstract (arXiv)

In state-of-the-art self-supervised learning (SSL) pre-training produces semantically good representations by encouraging them to be invariant under meaningful transformations prescribed from human knowledge. In fact, the property of invariance is a trivial instance of a broader class called equivariance, which can be intuitively understood as the property that representations transform according to the way the inputs transform. Here, we show that rather than using only invariance, pre-training that encourages non-trivial equivariance to some transformations, while maintaining invariance to other transformations, can be used to improve the semantic quality of representations. Specifically, we extend popular SSL methods to a more general framework which we name Equivariant Self-Supervised Learning (E-SSL). In E-SSL, a simple additional pre-training objective encourages equivariance by predicting the transformations applied to the input. We demonstrate E-SSL's effectiveness empirically on several popular computer vision benchmarks, e.g. improving SimCLR to 72.5% linear probe accuracy on ImageNet. Furthermore, we demonstrate usefulness of E-SSL for applications beyond computer vision; in particular, we show its utility on regression problems in photonics science. Our code, datasets and pre-trained models are available at https://github.com/rdangovs/essl to aid further research in E-SSL.