  Deep neural networks (DNNs) are vulnerable to adversarial examples obtained
by adding small perturbations to original examples. The added perturbations in
existing attacks are mainly determined by the gradient of the loss function
with respect to the inputs. In this paper, the close relationship between
gradient-based attacks and the numerical methods for solving ordinary
differential equation (ODE) is studied for the first time. Inspired by the
numerical solution of ODE, a new prediction-correction (PC) based adversarial
attack is proposed. In our proposed PC-based attack, some existing attack can
be selected to produce a predicted example first, and then the predicted
example and the current example are combined together to determine the added
perturbations. The proposed method possesses good extensibility and can be
applied to all available gradient-based attacks easily. Extensive experiments
demonstrate that compared with the state-of-the-art gradient-based adversarial
attacks, our proposed PC-based attacks have higher attack success rates, and
exhibit better transferability.
