The robustness of deep learning models against adversarial attacks has received increasing attention in recent years. However, both deep learning and adversarial training rely on the availability of a large amount of labeled data and usually do not generalize well to new, unseen classes when only a few training samples are accessible. To address this problem, we explicitly introduce a new challenging problem -- how to learn a robust deep model with limited training samples per class, called defensive few-shot learning in this paper. Simply employing the existing adversarial training techniques in the literature cannot solve this problem. This is because few-shot learning needs to learn transferable knowledge from disjoint auxiliary data, and thus it is invalid to assume the sample-level distribution consistency between the training and test sets as commonly assumed in existing adversarial training techniques. In this paper, instead of assuming such a distribution consistency, we propose to make this assumption at a task-level in the episodic training paradigm in order to better transfer the defense knowledge. Furthermore, inside each task, we design a task-conditioned distribution constraint to narrow the distribution gap between clean and adversarial examples at a sample-level. These give rise to a novel mechanism called multi-level distribution based adversarial training (MDAT) for learning transferable adversarial defense. In addition, a unified $mathcal{F}_{beta}$ score is introduced to evaluate different defense methods under the same principle. Extensive experiments demonstrate that MDAT achieves higher effectiveness and robustness over existing alternatives in the few-shot case.
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