# Adversarial Noise Attacks of Deep Learning Architectures -- Stability Analysis via Sparse Modeled Signals

arXiv: https://arxiv.org/abs/1805.11596 · HTML: https://mlsanity.com/paper/1805.11596/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2018.

## Built on by (most cited first, 9 of 9)

- [Revisiting Sparse Convolutional Model for Visual Recognition](https://mlsanity.com/paper/2210.12945/) (2022)
- [Adversarial robustness of sparse local Lipschitz predictors](https://mlsanity.com/paper/2202.13216/) (2022)
- [Reframing Neural Networks: Deep Structure in Overcomplete Representations](https://mlsanity.com/paper/2103.05804/) (2021)
- [Pivotal Auto-Encoder via Self-Normalizing ReLU](https://mlsanity.com/paper/2406.16052/) (2024)
- [Adversarial Attacks in Weight-Space Classifiers](https://mlsanity.com/paper/2502.20314/) (2025)
- [Rethinking the Role of Spatial Mixing](https://mlsanity.com/paper/2503.16760/) (2025)
- [Structural Extensions of Basis Pursuit: Guarantees on Adversarial Robustness](https://mlsanity.com/paper/2205.08955/) (2022)
- [A Tensor-based Convolutional Neural Network for Small Dataset Classification](https://mlsanity.com/paper/2303.17061/) (2023)
- [On The Relationship Between Universal Adversarial Attacks And Sparse Representations](https://mlsanity.com/paper/2311.08265/) (2023)

## Abstract (arXiv)

Despite their impressive performance, deep convolutional neural networks (CNNs) have been shown to be sensitive to small adversarial perturbations. These nuisances, which one can barely notice, are powerful enough to fool sophisticated and well performing classifiers, leading to ridiculous misclassification results. In this paper we analyze the stability of state-of-the-art deep-learning classification machines to adversarial perturbations, where we assume that the signals belong to the (possibly multi-layer) sparse representation model. We start with convolutional sparsity and then proceed to its multi-layered version, which is tightly connected to CNNs. Our analysis links between the stability of the classification to noise and the underlying structure of the signal, quantified by the sparsity of its representation under a fixed dictionary. In addition, we offer similar stability theorems for two practical pursuit algorithms, which are posed as two different deep-learning architectures - the layered Thresholding and the layered Basis Pursuit. Our analysis establishes the better robustness of the later to adversarial attacks. We corroborate these theoretical results by numerical experiments on three datasets: MNIST, CIFAR-10 and CIFAR-100.