Title: Adversarial Attack across Datasets. Abstract: It has been observed that Deep Neural Networks (DNNs) are vulnerable to transfer attacks in the query-free black-box setting. However, all the previous studies on transfer attack assume that the white-box surrogate models possessed by the attacker and the black-box victim models are trained on the same dataset, which means the attacker implicitly knows the label set and the input size of the victim model. However, this assumption is usually unrealistic as the attacker may not know the dataset used by the victim model, and further, the attacker needs to attack any randomly encountered images that may not come from the same dataset. Therefore, in this paper, we define a new Generalized Transferable Attack (GTA) problem where we assume the attacker has a set of surrogate models trained on different datasets (with different label sets and image sizes), and none of them is equal to the dataset used by the victim model.  We then propose a novel method called Image Classification Eraser (ICE) to erase classification information for any encountered images from arbitrary datasets. Extensive experiments on Cifar-10, Cifar-100, and TieredImageNet demonstrate the effectiveness of the proposed ICE on the GTA problem. Further, we show that existing transfer attack methods can be modified to tackle the GTA problem, but with significantly worse performance compared with ICE. 