Generating Adversarial Images in Quantized Domains

Benoît Bonnet, Teddy Furon, Patrick Bas

Abstract: Many adversarial attacks produce floating-point tensors which are no longer adversarial when converted to raster or JPEG images due to rounding. This paper proposes a method dedicated to quantize adversarial perturbations. This “smart” quantization is conveniently implemented as versatile post-processing. It can be used on top of any white-box attack targeting any model. Its principle is tantamount to a constrained optimization problem aiming to minimize the quantization error while keeping the image adversarial after quantization. A Lagrangian formulation is proposed and an appropriate search of the Lagrangian multiplier enables to increase the success rate. We also add a control mechanism of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _\infty $ </tex-math></inline-formula> -distortion. Our method operates in both spatial and JPEG domains with little complexity. This study shows that forging adversarial <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">images</i> is not a hard constraint: our quantization does not introduce any extra distortion. Moreover, adversarial images quantized as JPEG also challenge defenses relying on the robustness of neural networks against JPEG compression.