# Denoising Cosine Similarity: A Theory-Driven Approach for Efficient Representation Learning

arXiv: https://arxiv.org/abs/2304.09552 · HTML: https://mlsanity.com/paper/2304.09552/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 47 of its 77 references that are in the map.
- First posted on arXiv 19 Apr 2023.

## Builds on (most cited first, 30 of 47)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [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)
- [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)
- [Improved Baselines with Momentum Contrastive Learning](https://mlsanity.com/paper/2003.04297/) (2020)
- [SimCSE: Simple Contrastive Learning of Sentence Embeddings](https://mlsanity.com/paper/2104.08821/) (2021)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (2016)
- [Data-Efficient Image Recognition with Contrastive Predictive Coding](https://mlsanity.com/paper/1905.09272/) (2019)
- [AST: Audio Spectrogram Transformer](https://mlsanity.com/paper/2104.01778/) (2021)
- [Contrastive Learning with Hard Negative Samples](https://mlsanity.com/paper/2010.04592/) (2020)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [A Theoretical Analysis of Contrastive Unsupervised Representation Learning](https://mlsanity.com/paper/1902.09229/) (2019)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [Debiased Contrastive Learning](https://mlsanity.com/paper/2007.00224/) (2020)
- [With a Little Help from My Friends: Nearest-Neighbor Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2104.14548/) (2021)

## Abstract (arXiv)

Representation learning has been increasing its impact on the research and practice of machine learning, since it enables to learn representations that can apply to various downstream tasks efficiently. However, recent works pay little attention to the fact that real-world datasets used during the stage of representation learning are commonly contaminated by noise, which can degrade the quality of learned representations. This paper tackles the problem to learn robust representations against noise in a raw dataset. To this end, inspired by recent works on denoising and the success of the cosine-similarity-based objective functions in representation learning, we propose the denoising Cosine-Similarity (dCS) loss. The dCS loss is a modified cosine-similarity loss and incorporates a denoising property, which is supported by both our theoretical and empirical findings. To make the dCS loss implementable, we also construct the estimators of the dCS loss with statistical guarantees. Finally, we empirically show the efficiency of the dCS loss over the baseline objective functions in vision and speech domains.