# FroSSL: Frobenius Norm Minimization for Efficient Multiview Self-Supervised Learning

arXiv: https://arxiv.org/abs/2310.02903 · HTML: https://mlsanity.com/paper/2310.02903/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 41 references that are in the map.
- First posted on arXiv 4 Oct 2023.

## Builds on (most cited first, 30 of 31)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [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)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [Large Batch Training of Convolutional Networks](https://mlsanity.com/paper/1708.03888/) (2017)
- [Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Loss](https://mlsanity.com/paper/2106.04156/) (2021)
- [Whitening for Self-Supervised Representation Learning](https://mlsanity.com/paper/2007.06346/) (2020)
- [RankMe: Assessing the downstream performance of pretrained self-supervised representations by their rank](https://mlsanity.com/paper/2210.02885/) (2022)
- [Solo-learn: A Library of Self-supervised Methods for Visual Representation Learning](https://mlsanity.com/paper/2108.01775/) (2021)
- [On the duality between contrastive and non-contrastive self-supervised learning](https://mlsanity.com/paper/2206.02574/) (2022)
- [Self-Supervised Learning with Kernel Dependence Maximization](https://mlsanity.com/paper/2106.08320/) (2021)
- [Exploring the Equivalence of Siamese Self-Supervised Learning via A Unified Gradient Framework](https://mlsanity.com/paper/2112.05141/) (2021)
- [Self-Supervised Learning with an Information Maximization Criterion](https://mlsanity.com/paper/2209.07999/) (2022)
- [On the Stepwise Nature of Self-Supervised Learning](https://mlsanity.com/paper/2303.15438/) (2023)
- [Learning Efficient Coding of Natural Images with Maximum Manifold Capacity Representations](https://mlsanity.com/paper/2303.03307/) (2023)
- [A Note on Connecting Barlow Twins with Negative-Sample-Free Contrastive Learning](https://mlsanity.com/paper/2104.13712/) (2021)
- [DiME: Maximizing Mutual Information by a Difference of Matrix-Based Entropies](https://mlsanity.com/paper/2301.08164/) (2023)
- [Matrix Information Theory for Self-Supervised Learning](https://mlsanity.com/paper/2305.17326/) (2023)
- [EMP-SSL: Towards Self-Supervised Learning in One Training Epoch](https://mlsanity.com/paper/2304.03977/) (2023)
- [VNE: An Effective Method for Improving Deep Representation by Manipulating Eigenvalue Distribution](https://mlsanity.com/paper/2304.01434/) (2023)
- [Implicit variance regularization in non-contrastive SSL](https://mlsanity.com/paper/2212.04858/) (2022)
- [Eigendecomposition-free Training of Deep Networks with Zero Eigenvalue-based Losses](https://mlsanity.com/paper/1803.08071/) (2018)
- [TiCo: Transformation Invariance and Covariance Contrast for Self-Supervised Visual Representation Learning](https://mlsanity.com/paper/2206.10698/) (2022)
- [Bag of Image Patch Embedding Behind the Success of Self-Supervised Learning](https://mlsanity.com/paper/2206.08954/) (2022)

## Built on by (most cited first, 2 of 2)

- [NeSyPr: Neurosymbolic Proceduralization For Efficient Embodied Reasoning](https://mlsanity.com/paper/2510.19429/) (2025)
- [T-REGS: Minimum Spanning Tree Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2510.23484/) (2025)

## Abstract (arXiv)

Self-supervised learning (SSL) is a popular paradigm for representation learning. Recent multiview methods can be classified as sample-contrastive, dimension-contrastive, or asymmetric network-based, with each family having its own approach to avoiding informational collapse. While these families converge to solutions of similar quality, it can be empirically shown that some methods are epoch-inefficient and require longer training to reach a target performance. Two main approaches to improving efficiency are covariance eigenvalue regularization and using more views. However, these two approaches are difficult to combine due to the computational complexity of computing eigenvalues. We present the objective function FroSSL which reconciles both approaches while avoiding eigendecomposition entirely. FroSSL works by minimizing covariance Frobenius norms to avoid collapse and minimizing mean-squared error to achieve augmentation invariance. We show that FroSSL reaches competitive accuracies more quickly than any other SSL method and provide theoretical and empirical support that this faster convergence is due to how FroSSL affects the eigenvalues of the embedding covariance matrices. We also show that FroSSL learns competitive representations on linear probe evaluation when used to train a ResNet-18 on several datasets, including STL-10, Tiny ImageNet, and ImageNet-100.