The transferability of adversarial examples can be exploited to launch black-box attacks. However, adversarial examples often present poor transferability. To alleviate this issue, by observing that the diversity of inputs can boost transferability, input regularization based methods are proposed, which craft adversarial examples by combining several transformed inputs. We reveal that input regularization based methods make resultant adversarial examples biased towards flat extreme regions. Inspired by this, we propose an attack called flatness-aware adversarial attack (FAA) which explicitly adds a flatness-aware regularization term in the optimization target to promote the resultant adversarial examples towards flat extreme regions. The flatness-aware regularization term involves gradients of samples around the resultant adversarial examples but optimizing gradients requires the evaluation of Hessian matrix in high-dimension spaces which generally is intractable. To address the problem, we derive an approximate solution to circumvent the construction of Hessian matrix, thereby making FAA practical and cheap. Extensive experiments show the transferability of adversarial examples crafted by FAA can be considerably boosted compared with state-of-the-art baselines.
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