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Data-agnostic quasi-imperceptible perturbations on inputs are known todegrade recognition accuracy of deep convolutional networks severely. Thisphenomenon is considered to be a potential security issue. Moreover, someresults on statistical generalization guarantees indicate that the phenomenoncan be a key to improve the networks' generalization. However, thecharacteristics of the shared directions of such harmful perturbations remainunknown. Our primal finding is that convolutional networks are sensitive to thedirections of Fourier basis functions. We derived the property by specializinga hypothesis of the cause of the sensitivity, known as the linearity of neuralnetworks, to convolutional networks and empirically validated it. As aby-product of the analysis, we propose an algorithm to create shift-invariantuniversal adversarial perturbations available in black-box settings.

On the Structural Sensitivity of Deep Convolutional Networks to the Directions of Fourier Basis Functions