# Sparsity-based Defense against Adversarial Attacks on Linear Classifiers

arXiv: https://arxiv.org/abs/1801.04695 · HTML: https://mlsanity.com/paper/1801.04695/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2018.

## Built on by (most cited first, 8 of 8)

- [Robust Classification Under ℓ0 Attack for the Gaussian Mixture Model](https://mlsanity.com/paper/2104.02189/) (2021)
- [Minimax rates of convergence for nonparametric regression under adversarial attacks](https://mlsanity.com/paper/2410.09402/) (2024)
- [Efficient and Robust Classification for Sparse Attacks](https://mlsanity.com/paper/2201.09369/) (2022)
- [Robust width: A lightweight and certifiable adversarial defense](https://mlsanity.com/paper/2405.15971/) (2024)
- [Group-Structured Adversarial Training](https://mlsanity.com/paper/2106.10324/) (2021)
- [Generalized Likelihood Ratio Test for Adversarially Robust Hypothesis Testing](https://mlsanity.com/paper/2112.02209/) (2021)
- [Binary Classification Under ℓ0 Attacks for General Noise Distribution](https://mlsanity.com/paper/2203.04855/) (2022)
- [Adversarial Robustness in Zero-Shot Learning:An Empirical Study on Class and Concept-Level Vulnerabilities](https://mlsanity.com/paper/2512.18651/) (2025)

## Abstract (arXiv)

Deep neural networks represent the state of the art in machine learning in a growing number of fields, including vision, speech and natural language processing. However, recent work raises important questions about the robustness of such architectures, by showing that it is possible to induce classification errors through tiny, almost imperceptible, perturbations. Vulnerability to such "adversarial attacks", or "adversarial examples", has been conjectured to be due to the excessive linearity of deep networks. In this paper, we study this phenomenon in the setting of a linear classifier, and show that it is possible to exploit sparsity in natural data to combat ℓ∞-bounded adversarial perturbations. Specifically, we demonstrate the efficacy of a sparsifying front end via an ensemble averaged analysis, and experimental results for the MNIST handwritten digit database. To the best of our knowledge, this is the first work to show that sparsity provides a theoretically rigorous framework for defense against adversarial attacks.