Abstract
— A spectral approximation of a Boolean function is proposed for approximating the decision boundary of an ensemble of Deep Neural Networks (DNNs) solving two-class pattern recognition problems. The Walsh combination of relatively weak DNN classifiers is shown experimentally to be capable of detecting adversarial attacks. By observing the difference in Walsh coefficient approximation between clean and adversarial images, it appears that transferability of attack may be used for detection. Approximating the decision boundary may also 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. Index Terms—Adversarial robustness, Boolean functions, ensemble, deep neural networks, machine learning, pattern analysis, spectral analysis.