# Constrained Gradient Descent: A Powerful and Principled Evasion Attack Against Neural Networks

arXiv: https://arxiv.org/abs/2112.14232 · HTML: https://mlsanity.com/paper/2112.14232/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 69 references that are in the map.
- First posted on arXiv 28 Dec 2021.

## Builds on (most cited first, 30 of 52)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [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)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [DeepFool: a simple and accurate method to fool deep neural networks](https://mlsanity.com/paper/1511.04599/) (2015)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [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)
- [Evasion Attacks against Machine Learning at Test Time](https://mlsanity.com/paper/1708.06131/) (2017)
- [Square Attack: a query-efficient black-box adversarial attack via random search](https://mlsanity.com/paper/1912.00049/) (2019)
- [ZOO: Zeroth Order Optimization based Black-box Attacks to Deep Neural Networks without Training Substitute Models](https://mlsanity.com/paper/1708.03999/) (2017)
- [RobustBench: a standardized adversarial robustness benchmark](https://mlsanity.com/paper/2010.09670/) (2020)
- [Adversarial Training for Free!](https://mlsanity.com/paper/1904.12843/) (2019)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [Adversarial Examples Are Not Easily Detected: Bypassing Ten Detection Methods](https://mlsanity.com/paper/1705.07263/) (2017)
- [Countering Adversarial Images using Input Transformations](https://mlsanity.com/paper/1711.00117/) (2017)
- [Feature Squeezing: Detecting Adversarial Examples in Deep Neural Networks](https://mlsanity.com/paper/1704.01155/) (2017)
- [Certified Robustness to Adversarial Examples with Differential Privacy](https://mlsanity.com/paper/1802.03471/) (2018)
- [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)
- [Defense-GAN: Protecting Classifiers Against Adversarial Attacks Using Generative Models](https://mlsanity.com/paper/1805.06605/) (2018)
- [Minimally distorted Adversarial Examples with a Fast Adaptive Boundary Attack](https://mlsanity.com/paper/1907.02044/) (2019)
- [Defense against Adversarial Attacks Using High-Level Representation Guided Denoiser](https://mlsanity.com/paper/1712.02976/) (2017)
- [Do Adversarially Robust ImageNet Models Transfer Better?](https://mlsanity.com/paper/2007.08489/) (2020)

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

- [LLM Whisperer: An Inconspicuous Attack to Bias LLM Responses](https://mlsanity.com/paper/2406.04755/) (2024)
- [Group-based Robustness: A General Framework for Customized Robustness in the Real World](https://mlsanity.com/paper/2306.16614/) (2023)
- [Enhancing Output Diversity Improves Conjugate Gradient-based Adversarial Attacks](https://mlsanity.com/paper/2408.03972/) (2024)
- [Differentiable Adversarial Attacks for Marked Temporal Point Processes](https://mlsanity.com/paper/2501.10606/) (2025)

## Abstract (arXiv)

We propose new, more efficient targeted white-box attacks against deep neural networks. Our attacks better align with the attacker's goal: (1) tricking a model to assign higher probability to the target class than to any other class, while (2) staying within an ε-distance of the attacked input. First, we demonstrate a loss function that explicitly encodes (1) and show that Auto-PGD finds more attacks with it. Second, we propose a new attack method, Constrained Gradient Descent (CGD), using a refinement of our loss function that captures both (1) and (2). CGD seeks to satisfy both attacker objectives -- misclassification and bounded ℓp-norm -- in a principled manner, as part of the optimization, instead of via ad hoc post-processing techniques (e.g., projection or clipping). We show that CGD is more successful on CIFAR10 (0.9--4.2%) and ImageNet (8.6--13.6%) than state-of-the-art attacks while consuming less time (11.4--18.8%). Statistical tests confirm that our attack outperforms others against leading defenses on different datasets and values of ε.