What can linguistics and deep learning contribute to each other?

Joe Pater's target article calls for greater interaction between neural network research and linguistics. I expand on this call and show how such interaction can benefit both fields. Linguists can contribute to research on neural networks for language technologies by clearly delineating the linguistic capabilities that can be expected of such systems, and by constructing controlled experimental paradigms that can determine whether those desiderata have been met. In the other direction, neural networks can benefit the scientific study of language by providing infrastructure for modeling human sentence processing and for evaluating the necessity of particular innate constraints on language acquisition.