Can Domain Knowledge Alleviate Adversarial Attacks in Multi-Label Classifiers?

Adversarial attacks on machine learning-based classifiers, along with defense mechanisms, have been widely studied in the context of single-label classification problems. In this paper, we shift the attention to multi-label classification, where the availability of domain knowledge on the relationships among the considered classes may offer a natural way to spot incoherent predictions, i.e., predictions associated to adversarial examples lying outside of the training data distribution. We explore this intuition in a framework in which first-order logic knowledge is converted into constraints and injected into a semi-supervised learning problem. Within this setting, the constrained classifier learns to fulfill the domain knowledge over the marginal distribution, and can naturally reject samples with incoherent predictions. Even though our method does not exploit any knowledge of attacks during training, our experimental analysis surprisingly unveils that domain-knowledge constraints can help detect adversarial examples effectively, especially if such constraints are not known to the attacker. While we also show that an adaptive attack exploiting knowledge of the constraints may still deceive our classifier, it remains an open issue to understand how hard for an attacker would be to infer such constraints in practical cases. For this reason, we believe that our approach may provide a significant step towards designing robust multi-label classifiers.