# The Role of Entropy and Reconstruction in Multi-View Self-Supervised Learning

arXiv: https://arxiv.org/abs/2307.10907 · HTML: https://mlsanity.com/paper/2307.10907/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 53 references that are in the map.
- First posted on arXiv 20 Jul 2023.

## Builds on (most cited first, 30 of 38)

- [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)
- [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)
- [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)
- [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)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Deep Clustering for Unsupervised Learning of Visual Features](https://mlsanity.com/paper/1807.05520/) (2018)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [What Makes for Good Views for Contrastive Learning?](https://mlsanity.com/paper/2005.10243/) (2020)
- [Learning Representations by Maximizing Mutual Information Across Views](https://mlsanity.com/paper/1906.00910/) (2019)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Large Batch Training of Convolutional Networks](https://mlsanity.com/paper/1708.03888/) (2017)
- [Self-labelling via simultaneous clustering and representation learning](https://mlsanity.com/paper/1911.05371/) (2019)
- [On Mutual Information Maximization for Representation Learning](https://mlsanity.com/paper/1907.13625/) (2019)
- [Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Loss](https://mlsanity.com/paper/2106.04156/) (2021)
- [Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style](https://mlsanity.com/paper/2106.04619/) (2021)
- [Contrastive Learning Inverts the Data Generating Process](https://mlsanity.com/paper/2102.08850/) (2021)

## Built on by (most cited first, 13 of 13)

- [Information-Guided Diffusion Sampling for Dataset Distillation](https://mlsanity.com/paper/2507.04619/) (2025)
- [Poly-View Contrastive Learning](https://mlsanity.com/paper/2403.05490/) (2024)
- [Towards an Improved Understanding and Utilization of Maximum Manifold Capacity Representations](https://mlsanity.com/paper/2406.09366/) (2024)
- [Separating common from salient patterns with Contrastive Representation Learning](https://mlsanity.com/paper/2402.11928/) (2024)
- [Understanding Self-Supervised Learning via Latent Distribution Matching](https://mlsanity.com/paper/2605.03517/) (2026)
- [Generalized Category Discovery via Token Manifold Capacity Learning](https://mlsanity.com/paper/2505.14044/) (2025)
- [A Coding-Theoretic Analysis of Hyperspherical Prototypical Learning Geometry](https://mlsanity.com/paper/2407.07664/) (2024)
- [Maximally Useful and Minimally Redundant: The Key to Self Supervised Learning for Imbalanced Data](https://mlsanity.com/paper/2509.08469/) (2025)
- [Multimodal Datasets with Controllable Mutual Information](https://mlsanity.com/paper/2510.21686/) (2025)
- [MAPLE: Self-Supervised Learning-Enhanced Nonlinear Dimensionality Reduction for Visual Analysis](https://mlsanity.com/paper/2601.20173/) (2026)
- [Maximum Manifold Capacity Representations in State Representation Learning](https://mlsanity.com/paper/2405.13848/) (2024)
- [Provable Subspace Identification of Nonlinear Multi-view CCA](https://mlsanity.com/paper/2602.23785/) (2026)
- [Predictive Self-Supervised Learning Provably Identifies Stochastic Signals under Nuisance](https://mlsanity.com/paper/2609.37789/) (2026)

## Abstract (arXiv)

The mechanisms behind the success of multi-view self-supervised learning (MVSSL) are not yet fully understood. Contrastive MVSSL methods have been studied through the lens of InfoNCE, a lower bound of the Mutual Information (MI). However, the relation between other MVSSL methods and MI remains unclear. We consider a different lower bound on the MI consisting of an entropy and a reconstruction term (ER), and analyze the main MVSSL families through its lens. Through this ER bound, we show that clustering-based methods such as DeepCluster and SwAV maximize the MI. We also re-interpret the mechanisms of distillation-based approaches such as BYOL and DINO, showing that they explicitly maximize the reconstruction term and implicitly encourage a stable entropy, and we confirm this empirically. We show that replacing the objectives of common MVSSL methods with this ER bound achieves competitive performance, while making them stable when training with smaller batch sizes or smaller exponential moving average (EMA) coefficients. Github repo: https://github.com/apple/ml-entropy-reconstruction.