# Mitigating Black-Box Adversarial Attacks via Output Noise Perturbation

arXiv: https://arxiv.org/abs/2109.15160 · HTML: https://mlsanity.com/paper/2109.15160/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 40 references that are in the map.
- First posted on arXiv 30 Sep 2021.

## Builds on (most cited first, 30 of 33)

- [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)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [Practical Black-Box Attacks against Machine Learning](https://mlsanity.com/paper/1602.02697/) (2016)
- [Ensemble Adversarial Training: Attacks and Defenses](https://mlsanity.com/paper/1705.07204/) (2017)
- [Distillation as a Defense to Adversarial Perturbations against Deep Neural Networks](https://mlsanity.com/paper/1511.04508/) (2015)
- [ZOO: Zeroth Order Optimization based Black-box Attacks to Deep Neural Networks without Training Substitute Models](https://mlsanity.com/paper/1708.03999/) (2017)
- [On Adaptive Attacks to Adversarial Example Defenses](https://mlsanity.com/paper/2002.08347/) (2020)
- [Adversarial Examples Are Not Easily Detected: Bypassing Ten Detection Methods](https://mlsanity.com/paper/1705.07263/) (2017)
- [Delving into Transferable Adversarial Examples and Black-box Attacks](https://mlsanity.com/paper/1611.02770/) (2016)
- [Countering Adversarial Images using Input Transformations](https://mlsanity.com/paper/1711.00117/) (2017)
- [Black-box Adversarial Attacks with Limited Queries and Information](https://mlsanity.com/paper/1804.08598/) (2018)
- [Decision-Based Adversarial Attacks: Reliable Attacks Against Black-Box Machine Learning Models](https://mlsanity.com/paper/1712.04248/) (2017)
- [Mitigating Adversarial Effects Through Randomization](https://mlsanity.com/paper/1711.01991/) (2017)
- [Defense-GAN: Protecting Classifiers Against Adversarial Attacks Using Generative Models](https://mlsanity.com/paper/1805.06605/) (2018)
- [HopSkipJumpAttack: A Query-Efficient Decision-Based Attack](https://mlsanity.com/paper/1904.02144/) (2019)
- [Simple Black-box Adversarial Attacks](https://mlsanity.com/paper/1905.07121/) (2019)
- [Certified Adversarial Robustness with Additive Noise](https://mlsanity.com/paper/1809.03113/) (2018)
- [Towards Robust Neural Networks via Random Self-ensemble](https://mlsanity.com/paper/1712.00673/) (2017)
- [AutoZOOM: Autoencoder-based Zeroth Order Optimization Method for Attacking Black-box Neural Networks](https://mlsanity.com/paper/1805.11770/) (2018)
- [Parametric Noise Injection: Trainable Randomness to Improve Deep Neural Network Robustness against Adversarial Attack](https://mlsanity.com/paper/1811.09310/) (2018)
- [Improving Black-box Adversarial Attacks with a Transfer-based Prior](https://mlsanity.com/paper/1906.06919/) (2019)
- [Sign-OPT: A Query-Efficient Hard-label Adversarial Attack](https://mlsanity.com/paper/1909.10773/) (2019)
- [NATTACK: Learning the Distributions of Adversarial Examples for an Improved Black-Box Attack on Deep Neural Networks](https://mlsanity.com/paper/1905.00441/) (2019)
- [GenAttack: Practical Black-box Attacks with Gradient-Free Optimization](https://mlsanity.com/paper/1805.11090/) (2018)
- [SafetyNet: Detecting and Rejecting Adversarial Examples Robustly](https://mlsanity.com/paper/1704.00103/) (2017)
- [Simple Black-Box Adversarial Perturbations for Deep Networks](https://mlsanity.com/paper/1612.06299/) (2016)
- [On the Robustness of the CVPR 2018 White-Box Adversarial Example Defenses](https://mlsanity.com/paper/1804.03286/) (2018)

## Built on by (most cited first, 3 of 3)

- [Preprocessors Matter! Realistic Decision-Based Attacks on Machine Learning Systems](https://mlsanity.com/paper/2210.03297/) (2022)
- [Federated and Transfer Learning: A Survey on Adversaries and Defense Mechanisms](https://mlsanity.com/paper/2207.02337/) (2022)
- [Robustness of Practical Perceptual Hashing Algorithms to Hash-Evasion and Hash-Inversion Attacks](https://mlsanity.com/paper/2406.00918/) (2024)

## Abstract (arXiv)

In black-box adversarial attacks, adversaries query the deep neural network (DNN), use the output to reconstruct gradients, and then optimize the adversarial inputs iteratively. In this paper, we study the method of adding white noise to the DNN output to mitigate such attacks, with a unique focus on the trade-off analysis of noise level and query cost. The attacker's query count (QC) is derived mathematically as a function of noise standard deviation. With this result, the defender can conveniently find the noise level needed to mitigate attacks for the desired security level specified by QC and limited DNN performance loss. Our analysis shows that the added noise is drastically magnified by the small variation of DNN outputs, which makes the reconstructed gradient have an extremely low signal-to-noise ratio (SNR). Adding slight white noise with a standard deviation less than 0.01 is enough to increase QC by many orders of magnitude without introducing any noticeable classification accuracy reduction. Our experiments demonstrate that this method can effectively mitigate both soft-label and hard-label black-box attacks under realistic QC constraints. We also show that this method outperforms many other defense methods and is robust to the attacker's countermeasures.