Title: AttackDist: Characterizing Zero-day Adversarial Samples by Counter Attack. Abstract: Deep Neural Networks (DNNs) have been shown vulnerable to adversarial attacks, which could produce adversarial samples that easily fool the state-of-the-art DNNs. The harmfulness of adversarial attacks calls for the defense mechanisms under fire. However, the relationship between adversarial attacks and defenses is like spear and shield. Whenever a defense method is proposed, a new attack would be followed to bypass the defense immediately. Devising a definitive defense against new attacks~(zero-day attacks) is proven to be challenging. We tackle this challenge by characterizing the intrinsic properties of adversarial samples, via measuring the norm of the perturbation after a counterattack. Our method is based on the idea that, from an optimization perspective, adversarial samples would be closer to the decision boundary; thus the perturbation to counterattack adversarial samples would be significantly smaller than normal cases. Motivated by this, we propose AttackDist, an attack-agnostic property to characterize adversarial samples. We first theoretically clarify under which condition AttackDist can provide a certified detecting performance, then show that a potential application of AttackDist is distinguishing zero-day adversarial examples without knowing the mechanisms of new attacks. As a proof-of-concept, we evaluate AttackDist on two widely used benchmarks. The evaluation results show that AttackDist can outperform the state-of-the-art detection measures by large margins in detecting zero-day adversarial attacks.