Toward Few-step Adversarial Training from a Frequency Perspective

Abstract

We investigate adversarial-sample generation methods from a frequency domain perspective and extend standard $l_{\infty }$ Projected Gradient Descent (PGD) to the frequency domain. The resulting method, which we call Spectral Projected Gradient Descent (SPGD), has better success rate compared to PGD during early steps of the method. Adversarially training models using SPGD achieves greater adversarial accuracy compared to PGD when holding the number of attack steps constant. The use of SPGD can, therefore, reduce the overhead of adversarial training when utilizing adversarial generation with a smaller number of steps. However, we also prove that SPGD is equivalent to a variant of the PGD ordinarily used for the $l_{\infty }$ threat model. This PGD variant omits the sign function which is ordinarily applied to the gradient. SPGD can, therefore, be performed without explicitly transforming into the frequency domain. Finally, we visualize the perturbations SPGD generates and find they use both high and low-frequency components, which suggests that removing either high-frequency components or low-frequency components is not an effective defense.

arXiv comment9 pages, 9 figures, SPAI'20, ACM ASIACCS 2020

References in corpus (8)

• Explaining and Harnessing Adversarial Examples
• Intriguing properties of neural networks
• Wild Patterns: Ten Years After the Rise of Adversarial Machine Learning
• An Alternative Surrogate Loss for PGD-based Adversarial Testing
• Jpeg Image Compression Using Discrete Cosine Transform - A Survey
• Gradient Masking Causes CLEVER to Overestimate Adversarial Perturbation Size
• Adversarial Defense by Suppressing High-frequency Components
• Bandlimiting Neural Networks Against Adversarial Attacks

Cited by in corpus (1)

• A Frequency Perspective of Adversarial Robustness