  A new 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 complexity of the
ensemble decision boundary. 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. By observing
the difference in Walsh coefficient approximation between clean and adversarial
images, it is shown experimentally that transferability of attack may be used
for detection. Furthermore, approximating the decision boundary 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. Code for approximating Boolean functions using Walsh coefficients:
https://doi.org/10.24433/CO.3695905.v1
