# Information theoretic underpinning of self-supervised learning by clustering

arXiv: https://arxiv.org/abs/2605.11870 · HTML: https://mlsanity.com/paper/2605.11870/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 49 references that are in the map.
- First posted on arXiv 12 May 2026.

## Builds on (most cited first, 30 of 37)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [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)
- [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)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (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)
- [Unsupervised Representation Learning by Predicting Image Rotations](https://mlsanity.com/paper/1803.07728/) (2018)
- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [Unsupervised Learning of Visual Representations by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1603.09246/) (2016)
- [SimMIM: A Simple Framework for Masked Image Modeling](https://mlsanity.com/paper/2111.09886/) (2021)
- [Colorful Image Colorization](https://mlsanity.com/paper/1603.08511/) (2016)
- [Unsupervised Visual Representation Learning by Context Prediction](https://mlsanity.com/paper/1505.05192/) (2015)
- [Deep Clustering for Unsupervised Learning of Visual Features](https://mlsanity.com/paper/1807.05520/) (2018)
- [iBOT: Image BERT Pre-Training with Online Tokenizer](https://mlsanity.com/paper/2111.07832/) (2021)
- [A Theoretical Analysis of Contrastive Unsupervised Representation Learning](https://mlsanity.com/paper/1902.09229/) (2019)
- [Self-labelling via simultaneous clustering and representation learning](https://mlsanity.com/paper/1911.05371/) (2019)
- [Learning Representations for Automatic Colorization](https://mlsanity.com/paper/1603.06668/) (2016)
- [Split-Brain Autoencoders: Unsupervised Learning by Cross-Channel Prediction](https://mlsanity.com/paper/1611.09842/) (2016)
- [Colorization as a Proxy Task for Visual Understanding](https://mlsanity.com/paper/1703.04044/) (2017)
- [Efficient Visual Pretraining with Contrastive Detection](https://mlsanity.com/paper/2103.10957/) (2021)
- [VICRegL: Self-Supervised Learning of Local Visual Features](https://mlsanity.com/paper/2210.01571/) (2022)
- [SiT: Self-supervised vIsion Transformer](https://mlsanity.com/paper/2104.03602/) (2021)
- [Unsupervised Learning by Predicting Noise](https://mlsanity.com/paper/1704.05310/) (2017)
- [Unsupervised Object-Level Representation Learning from Scene Images](https://mlsanity.com/paper/2106.11952/) (2021)
- [Learning Image Representations by Completing Damaged Jigsaw Puzzles](https://mlsanity.com/paper/1802.01880/) (2018)

## Abstract (arXiv)

Self-supervised learning (SSL) is recognized as an essential tool for building foundation models for Artificial Intelligence applications. The advances in SSL have been made thanks to vigorous arguments about the principles of SSL and through extensive empirical research. The aim of this paper is to contribute to the development of the underpinning theory of SSL, focusing on the deep clustering approach. By analogy to supervised learning, we formulate SSL as K-L divergence optimization. The mode collapse is prevented by imposing an optimisation constraint on the teacher distribution. This leads to normalization using inverse cluster priors. We show that using Jensen inequality this normalization simplifies to the popular batch centering procedure. Distillation and centering are common {heuristics-based} practices in SSL, {but our work underpins them theoretically.} The theoretical model developed not only supports specific existing successful SSL methods, but also suggests directions for future investigations.