Learning with Explanation Constraints

As larger deep learning models are hard to interpret, there has been a recent focus on generating explanations of these black-box models. In contrast, we may have apriori explanations of how models should behave. In this paper, we formalize this notion as learning from explanation constraints and provide a learning theoretic framework to analyze how such explanations can improve the learning of our models. One may naturally ask, "When would these explanations be helpful?"Our We provide a characterization of the benefits of these models (in terms of the reduction of their Rademacher complexities) for a canonical class of explanations given by gradient information in the settings of both linear models and two layer neural networks.