# Scale-Invariant Adversarial Attack for Evaluating and Enhancing Adversarial Defenses

arXiv: https://arxiv.org/abs/2201.12527 · HTML: https://mlsanity.com/paper/2201.12527/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 34 references that are in the map.
- First posted on arXiv 29 Jan 2022.

## Builds on (most cited first, 28 of 28)

- [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)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [CosFace: Large Margin Cosine Loss for Deep Face Recognition](https://mlsanity.com/paper/1801.09414/) (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)
- [Fast is better than free: Revisiting adversarial training](https://mlsanity.com/paper/2001.03994/) (2020)
- [Square Attack: a query-efficient black-box adversarial attack via random search](https://mlsanity.com/paper/1912.00049/) (2019)
- [Adversarial Training for Free!](https://mlsanity.com/paper/1904.12843/) (2019)
- [Countering Adversarial Images using Input Transformations](https://mlsanity.com/paper/1711.00117/) (2017)
- [Unlabeled Data Improves Adversarial Robustness](https://mlsanity.com/paper/1905.13736/) (2019)
- [Mitigating Adversarial Effects Through Randomization](https://mlsanity.com/paper/1711.01991/) (2017)
- [Using Pre-Training Can Improve Model Robustness and Uncertainty](https://mlsanity.com/paper/1901.09960/) (2019)
- [Minimally distorted Adversarial Examples with a Fast Adaptive Boundary Attack](https://mlsanity.com/paper/1907.02044/) (2019)
- [Uncovering the Limits of Adversarial Training against Norm-Bounded Adversarial Examples](https://mlsanity.com/paper/2010.03593/) (2020)
- [NormFace: L2 Hypersphere Embedding for Face Verification](https://mlsanity.com/paper/1704.06369/) (2017)
- [Adversarial Logit Pairing](https://mlsanity.com/paper/1803.06373/) (2018)
- [Adversarial Risk and the Dangers of Evaluating Against Weak Attacks](https://mlsanity.com/paper/1802.05666/) (2018)
- [Understanding and Improving Fast Adversarial Training](https://mlsanity.com/paper/2007.02617/) (2020)
- [Bag of Tricks for Adversarial Training](https://mlsanity.com/paper/2010.00467/) (2020)
- [Boosting Adversarial Training with Hypersphere Embedding](https://mlsanity.com/paper/2002.08619/) (2020)
- [RayS: A Ray Searching Method for Hard-label Adversarial Attack](https://mlsanity.com/paper/2006.12792/) (2020)
- [Controlling Neural Level Sets](https://mlsanity.com/paper/1905.11911/) (2019)
- [Guided Adversarial Attack for Evaluating and Enhancing Adversarial Defenses](https://mlsanity.com/paper/2011.14969/) (2020)

## Built on by (most cited first, 2 of 2)

- [Beyond Vulnerabilities: A Survey of Adversarial Attacks as Both Threats and Defenses in Computer Vision Systems](https://mlsanity.com/paper/2508.01845/) (2025)
- [Towards the Transferable Audio Adversarial Attack via Ensemble Methods](https://mlsanity.com/paper/2304.08811/) (2023)

## Abstract (arXiv)

Efficient and effective attacks are crucial for reliable evaluation of defenses, and also for developing robust models. Projected Gradient Descent (PGD) attack has been demonstrated to be one of the most successful adversarial attacks. However, the effect of the standard PGD attack can be easily weakened by rescaling the logits, while the original decision of every input will not be changed. To mitigate this issue, in this paper, we propose Scale-Invariant Adversarial Attack (SI-PGD), which utilizes the angle between the features in the penultimate layer and the weights in the softmax layer to guide the generation of adversaries. The cosine angle matrix is used to learn angularly discriminative representation and will not be changed with the rescaling of logits, thus making SI-PGD attack to be stable and effective. We evaluate our attack against multiple defenses and show improved performance when compared with existing attacks. Further, we propose Scale-Invariant (SI) adversarial defense mechanism based on the cosine angle matrix, which can be embedded into the popular adversarial defenses. The experimental results show the defense method with our SI mechanism achieves state-of-the-art performance among multi-step and single-step defenses.