# A Probabilistic Model Behind Self-Supervised Learning

arXiv: https://arxiv.org/abs/2402.01399 · HTML: https://mlsanity.com/paper/2402.01399/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 64 of its 79 references that are in the map.
- First posted on arXiv 2 Feb 2024.

## Builds on (most cited first, 30 of 64)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [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)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [wav2vec 2.0: A Framework for Self-Supervised Learning of Speech Representations](https://mlsanity.com/paper/2006.11477/) (2020)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [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)
- [Unsupervised Representation Learning by Predicting Image Rotations](https://mlsanity.com/paper/1803.07728/) (2018)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [SimMIM: A Simple Framework for Masked Image Modeling](https://mlsanity.com/paper/2111.09886/) (2021)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [Deep Clustering for Unsupervised Learning of Visual Features](https://mlsanity.com/paper/1807.05520/) (2018)
- [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)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [A Theoretical Analysis of Contrastive Unsupervised Representation Learning](https://mlsanity.com/paper/1902.09229/) (2019)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [On Mutual Information Maximization for Representation Learning](https://mlsanity.com/paper/1907.13625/) (2019)

## Built on by (most cited first, 5 of 5)

- [Clustering Properties of Self-Supervised Learning](https://mlsanity.com/paper/2501.18452/) (2025)
- [Understanding Self-Supervised Learning via Gaussian Mixture Models](https://mlsanity.com/paper/2411.03517/) (2024)
- [Understanding Self-Supervised Learning via Latent Distribution Matching](https://mlsanity.com/paper/2605.03517/) (2026)
- [Self-Supervised Learning from Structural Invariance](https://mlsanity.com/paper/2602.02381/) (2026)
- [Predictive Self-Supervised Learning Provably Identifies Stochastic Signals under Nuisance](https://mlsanity.com/paper/2609.37789/) (2026)

## Abstract (arXiv)

In self-supervised learning (SSL), representations are learned via an auxiliary task without annotated labels. A common task is to classify augmentations or different modalities of the data, which share semantic content (e.g. an object in an image) but differ in style (e.g. the object's location). Many approaches to self-supervised learning have been proposed, e.g. SimCLR, CLIP, and DINO, which have recently gained much attention for their representations achieving downstream performance comparable to supervised learning. However, a theoretical understanding of self-supervised methods eludes. Addressing this, we present a generative latent variable model for self-supervised learning and show that several families of discriminative SSL, including contrastive methods, induce a comparable distribution over representations, providing a unifying theoretical framework for these methods. The proposed model also justifies connections drawn to mutual information and the use of a ''projection head''. Learning representations by fitting the model generatively (termed SimVAE) improves performance over discriminative and other VAE-based methods on simple image benchmarks and significantly narrows the gap between generative and discriminative representation learning in more complex settings. Importantly, as our analysis predicts, SimVAE outperforms self-supervised learning where style information is required, taking an important step toward understanding self-supervised methods and achieving task-agnostic representations.