Efficient Loss Function by Minimizing the Detrimental Effect of Floating-Point Errors on Gradient-Based Attacks
Authors: Yunrui Yu, Cheng-Zhong Xu

Attackers can deceive neural networks by adding human imperceptive perturbations to their input data; this reveals the vulnerability and weak robustness of current deep-learning networks. Many attack techniques have been proposed to evaluate the model's robustness. Gradient-based attacks suffer from severely overestimating the robustness. This paper identifies that the relative error in calculated gradients caused by floating-point errors, including floating-point underflow and rounding errors, is a fundamental reason why gradient-based attacks fail to accurately assess the model's robustness. Although it is hard to eliminate the relative error in the gradients, we can control its effect on the gradient-based attacks. Correspondingly, we propose an efficient loss function by minimizing the detrimental impact of the floating-point errors on the attacks. Experimental results show that it is more efficient and reliable than other loss functions when examined across a wide range of defence mechanisms.