# Learning Decorrelated Representations Efficiently Using Fast Fourier Transform

arXiv: https://arxiv.org/abs/2301.01569 · HTML: https://mlsanity.com/paper/2301.01569/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 35 references that are in the map.
- First posted on arXiv 4 Jan 2023.

## Builds on (most cited first, 22 of 22)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [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)
- [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)
- [An Empirical Study of Training Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.02057/) (2021)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Big Self-Supervised Models are Strong Semi-Supervised Learners](https://mlsanity.com/paper/2006.10029/) (2020)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [Large Batch Training of Convolutional Networks](https://mlsanity.com/paper/1708.03888/) (2017)
- [With a Little Help from My Friends: Nearest-Neighbor Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2104.14548/) (2021)
- [Whitening for Self-Supervised Representation Learning](https://mlsanity.com/paper/2007.06346/) (2020)
- [Holographic Embeddings of Knowledge Graphs](https://mlsanity.com/paper/1510.04935/) (2015)
- [On Feature Decorrelation in Self-Supervised Learning](https://mlsanity.com/paper/2105.00470/) (2021)
- [Solo-learn: A Library of Self-supervised Methods for Visual Representation Learning](https://mlsanity.com/paper/2108.01775/) (2021)
- [On the Equivalence of Holographic and Complex Embeddings for Link Prediction](https://mlsanity.com/paper/1702.05563/) (2017)

## Abstract (arXiv)

Barlow Twins and VICReg are self-supervised representation learning models that use regularizers to decorrelate features. Although these models are as effective as conventional representation learning models, their training can be computationally demanding if the dimension d of the projected embeddings is high. As the regularizers are defined in terms of individual elements of a cross-correlation or covariance matrix, computing the loss for n samples takes O(n d^2) time. In this paper, we propose a relaxed decorrelating regularizer that can be computed in O(n d log d) time by Fast Fourier Transform. We also propose an inexpensive technique to mitigate undesirable local minima that develop with the relaxation. The proposed regularizer exhibits accuracy comparable to that of existing regularizers in downstream tasks, whereas their training requires less memory and is faster for large d. The source code is available.