  Despite the exceptional performance of deep neural networks (DNNs) across
different domains, they are vulnerable to adversarial samples, in particular
for tasks related to computer vision. Such vulnerability is further influenced
by the digital container formats used in computers, where the discrete
numerical values are commonly used for storing the pixel values. This paper
examines how information loss in file formats impacts the effectiveness of
adversarial attacks. Notably, we observe a pronounced hindrance to the
adversarial attack performance due to the information loss of the non-integer
pixel values. To address this issue, we explore to leverage the gradient
information of the attack samples within the model to mitigate the information
loss. We introduce the Do More Steps (DMS) algorithm, which hinges on two core
techniques: gradient ascent-based \textit{adversarial integerization} (DMS-AI)
and integrated gradients-based \textit{attribution selection} (DMS-AS). Our
goal is to alleviate such lossy process to retain the attack performance when
storing these adversarial samples digitally. In particular, DMS-AI integerizes
the non-integer pixel values according to the gradient direction, and DMS-AS
selects the non-integer pixels by comparing attribution results. We conduct
thorough experiments to assess the effectiveness of our approach, including the
implementations of the DMS-AI and DMS-AS on two large-scale datasets with
various latest gradient-based attack methods. Our empirical findings
conclusively demonstrate the superiority of our proposed DMS-AI and DMS-AS
pixel integerization methods over the standardised methods, such as rounding,
truncating and upper approaches, in maintaining attack integrity.
