# Adversarial Detection by Approximation of Ensemble Boundary

arXiv: https://arxiv.org/abs/2211.10227 · HTML: https://mlsanity.com/paper/2211.10227/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 62 references that are in the map.
- First posted on arXiv 18 Nov 2022.

## Builds on (most cited first, 24 of 24)

- [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)
- [DeepFool: a simple and accurate method to fool deep neural networks](https://mlsanity.com/paper/1511.04599/) (2015)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Universal adversarial perturbations](https://mlsanity.com/paper/1610.08401/) (2016)
- [Evasion Attacks against Machine Learning at Test Time](https://mlsanity.com/paper/1708.06131/) (2017)
- [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)
- [HopSkipJumpAttack: A Query-Efficient Decision-Based Attack](https://mlsanity.com/paper/1904.02144/) (2019)
- [Adversarially Robust Generalization Requires More Data](https://mlsanity.com/paper/1804.11285/) (2018)
- [Improving Adversarial Robustness via Promoting Ensemble Diversity](https://mlsanity.com/paper/1901.08846/) (2019)
- [EAD: Elastic-Net Attacks to Deep Neural Networks via Adversarial Examples](https://mlsanity.com/paper/1709.04114/) (2017)
- [Are adversarial examples inevitable?](https://mlsanity.com/paper/1809.02104/) (2018)
- [Robustness of classifiers: from adversarial to random noise](https://mlsanity.com/paper/1608.08967/) (2016)
- [A Survey On Universal Adversarial Attack](https://mlsanity.com/paper/2103.01498/) (2021)
- [Adversarial Example Detection for DNN Models: A Review and Experimental Comparison](https://mlsanity.com/paper/2105.00203/) (2021)
- [Adversarial Example Defenses: Ensembles of Weak Defenses are not Strong](https://mlsanity.com/paper/1706.04701/) (2017)
- [Optimism in the Face of Adversity: Understanding and Improving Deep Learning through Adversarial Robustness](https://mlsanity.com/paper/2010.09624/) (2020)
- [Adversarial Examples on Object Recognition: A Comprehensive Survey](https://mlsanity.com/paper/2008.04094/) (2020)
- [FADER: Fast Adversarial Example Rejection](https://mlsanity.com/paper/2010.09119/) (2020)
- [Unity is strength: Improving the Detection of Adversarial Examples with Ensemble Approaches](https://mlsanity.com/paper/2111.12631/) (2021)

## Abstract (arXiv)

Despite being effective in many application areas, Deep Neural Networks (DNNs) are vulnerable to being attacked. In object recognition, the attack takes the form of a small perturbation added to an image, that causes the DNN to misclassify, but to a human appears no different. Adversarial attacks lead to defences that are themselves subject to attack, and the attack/ defence strategies provide important information about the properties of DNNs. In this paper, a novel method of detecting adversarial attacks is proposed for an ensemble of Deep Neural Networks (DNNs) solving two-class pattern recognition problems. The ensemble is combined using Walsh coefficients which are capable of approximating Boolean functions and thereby controlling the decision boundary complexity. The hypothesis in this paper is that decision boundaries with high curvature allow adversarial perturbations to be found, but change the curvature of the decision boundary, which is then approximated in a different way by Walsh coefficients compared to the clean images. Besides controlling boundary complexity, the coefficients also measure the correlation with class labels, which may aid in understanding the learning and transferability properties of DNNs. While the experiments here use images, the proposed approach of modelling two-class ensemble decision boundaries could in principle be applied to any application area.