# Towards Interpretable Adversarial Examples via Sparse Adversarial Attack

arXiv: https://arxiv.org/abs/2506.17250 · HTML: https://mlsanity.com/paper/2506.17250/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 57 references that are in the map.
- First posted on arXiv 8 Jun 2025.

## Builds on (most cited first, 30 of 41)

- [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)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [DeepFool: a simple and accurate method to fool deep neural networks](https://mlsanity.com/paper/1511.04599/) (2015)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [Ensemble Adversarial Training: Attacks and Defenses](https://mlsanity.com/paper/1705.07204/) (2017)
- [The Limitations of Deep Learning in Adversarial Settings](https://mlsanity.com/paper/1511.07528/) (2015)
- [Fast is better than free: Revisiting adversarial training](https://mlsanity.com/paper/2001.03994/) (2020)
- [Improving Transferability of Adversarial Examples with Input Diversity](https://mlsanity.com/paper/1803.06978/) (2018)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [One pixel attack for fooling deep neural networks](https://mlsanity.com/paper/1710.08864/) (2017)
- [Delving into Transferable Adversarial Examples and Black-box Attacks](https://mlsanity.com/paper/1611.02770/) (2016)
- [Evading Defenses to Transferable Adversarial Examples by Translation-Invariant Attacks](https://mlsanity.com/paper/1904.02884/) (2019)
- [HopSkipJumpAttack: A Query-Efficient Decision-Based Attack](https://mlsanity.com/paper/1904.02144/) (2019)
- [Fooling automated surveillance cameras: adversarial patches to attack person detection](https://mlsanity.com/paper/1904.08653/) (2019)
- [Sparse and Imperceivable Adversarial Attacks](https://mlsanity.com/paper/1909.05040/) (2019)
- [SparseFool: a few pixels make a big difference](https://mlsanity.com/paper/1811.02248/) (2018)
- [PhysGAN: Generating Physical-World-Resilient Adversarial Examples for Autonomous Driving](https://mlsanity.com/paper/1907.04449/) (2019)
- [Sparse-RS: a versatile framework for query-efficient sparse black-box adversarial attacks](https://mlsanity.com/paper/2006.12834/) (2020)
- [Structured Adversarial Attack: Towards General Implementation and Better Interpretability](https://mlsanity.com/paper/1808.01664/) (2018)

## Built on by (most cited first, 1 of 1)

- [Exploring Sparsity and Smoothness of Arbitrary Lp Norms in Adversarial Attacks](https://mlsanity.com/paper/2602.06578/) (2026)

## Abstract (arXiv)

Sparse attacks are to optimize the magnitude of adversarial perturbations for fooling deep neural networks (DNNs) involving only a few perturbed pixels (i.e., under the l0 constraint), suitable for interpreting the vulnerability of DNNs. However, existing solutions fail to yield interpretable adversarial examples due to their poor sparsity. Worse still, they often struggle with heavy computational overhead, poor transferability, and weak attack strength. In this paper, we aim to develop a sparse attack for understanding the vulnerability of CNNs by minimizing the magnitude of initial perturbations under the l0 constraint, to overcome the existing drawbacks while achieving a fast, transferable, and strong attack to DNNs. In particular, a novel and theoretical sound parameterization technique is introduced to approximate the NP-hard l0 optimization problem, making directly optimizing sparse perturbations computationally feasible. Besides, a novel loss function is designed to augment initial perturbations by maximizing the adversary property and minimizing the number of perturbed pixels simultaneously. Extensive experiments are conducted to demonstrate that our approach, with theoretical performance guarantees, outperforms state-of-the-art sparse attacks in terms of computational overhead, transferability, and attack strength, expecting to serve as a benchmark for evaluating the robustness of DNNs. In addition, theoretical and empirical results validate that our approach yields sparser adversarial examples, empowering us to discover two categories of noises, i.e., "obscuring noise" and "leading noise", which will help interpret how adversarial perturbation misleads the classifiers into incorrect predictions. Our code is available at https://github.com/fudong03/SparseAttack.