# Unlabeled Data Help: Minimax Analysis and Adversarial Robustness

arXiv: https://arxiv.org/abs/2202.06996 · HTML: https://mlsanity.com/paper/2202.06996/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 67 references that are in the map.
- First posted on arXiv 14 Feb 2022.

## Builds on (most cited first, 30 of 51)

- [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)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Unsupervised Representation Learning by Predicting Image Rotations](https://mlsanity.com/paper/1803.07728/) (2018)
- [Context Encoders: Feature Learning by Inpainting](https://mlsanity.com/paper/1604.07379/) (2016)
- [Unsupervised Learning of Visual Representations by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1603.09246/) (2016)
- [Colorful Image Colorization](https://mlsanity.com/paper/1603.08511/) (2016)
- [Unsupervised Visual Representation Learning by Context Prediction](https://mlsanity.com/paper/1505.05192/) (2015)
- [Practical Black-Box Attacks against Machine Learning](https://mlsanity.com/paper/1602.02697/) (2016)
- [What Makes for Good Views for Contrastive Learning?](https://mlsanity.com/paper/2005.10243/) (2020)
- [Prototypical Contrastive Learning of Unsupervised Representations](https://mlsanity.com/paper/2005.04966/) (2020)
- [A Theoretical Analysis of Contrastive Unsupervised Representation Learning](https://mlsanity.com/paper/1902.09229/) (2019)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Unlabeled Data Improves Adversarial Robustness](https://mlsanity.com/paper/1905.13736/) (2019)
- [Using Pre-Training Can Improve Model Robustness and Uncertainty](https://mlsanity.com/paper/1901.09960/) (2019)
- [Debiased Contrastive Learning](https://mlsanity.com/paper/2007.00224/) (2020)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Adversarially Robust Generalization Requires More Data](https://mlsanity.com/paper/1804.11285/) (2018)
- [Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Loss](https://mlsanity.com/paper/2106.04156/) (2021)
- [What Should Not Be Contrastive in Contrastive Learning](https://mlsanity.com/paper/2008.05659/) (2020)
- [Are Labels Required for Improving Adversarial Robustness?](https://mlsanity.com/paper/1905.13725/) (2019)
- [Adversarial Robustness: From Self-Supervised Pre-Training to Fine-Tuning](https://mlsanity.com/paper/2003.12862/) (2020)
- [Predicting What You Already Know Helps: Provable Self-Supervised Learning](https://mlsanity.com/paper/2008.01064/) (2020)
- [Contrastive learning, multi-view redundancy, and linear models](https://mlsanity.com/paper/2008.10150/) (2020)
- [Adversarial Self-Supervised Contrastive Learning](https://mlsanity.com/paper/2006.07589/) (2020)
- [Rademacher Complexity for Adversarially Robust Generalization](https://mlsanity.com/paper/1810.11914/) (2018)
- [Adversarial Training Can Hurt Generalization](https://mlsanity.com/paper/1906.06032/) (2019)
- [Feature Purification: How Adversarial Training Performs Robust Deep Learning](https://mlsanity.com/paper/2005.10190/) (2020)
- [Deep Neural Network Approximation Theory](https://mlsanity.com/paper/1901.02220/) (2019)

## Built on by (most cited first, 4 of 4)

- [A Survey on Statistical Theory of Deep Learning: Approximation, Training Dynamics, and Generative Models](https://mlsanity.com/paper/2401.07187/) (2024)
- [Adversarial Rademacher Complexity of Deep Neural Networks](https://mlsanity.com/paper/2211.14966/) (2022)
- [Interpolation for Robust Learning: Data Augmentation on Wasserstein Geodesics](https://mlsanity.com/paper/2302.02092/) (2023)
- [Distributionally and Adversarially Robust Logistic Regression via Intersecting Wasserstein Balls](https://mlsanity.com/paper/2407.13625/) (2024)

## Abstract (arXiv)

The recent proposed self-supervised learning (SSL) approaches successfully demonstrate the great potential of supplementing learning algorithms with additional unlabeled data. However, it is still unclear whether the existing SSL algorithms can fully utilize the information of both labelled and unlabeled data. This paper gives an affirmative answer for the reconstruction-based SSL algorithm citeplee2020predicting under several statistical models. While existing literature only focuses on establishing the upper bound of the convergence rate, we provide a rigorous minimax analysis, and successfully justify the rate-optimality of the reconstruction-based SSL algorithm under different data generation models. Furthermore, we incorporate the reconstruction-based SSL into the existing adversarial training algorithms and show that learning from unlabeled data helps improve the robustness.