Although deep learning models perform remarkably well across a range of tasks such as language translation and object recognition, it remains unclear what high-level logic, if any, they follow. Understanding this logic may lead to more transparency, better model design, and faster experimentation. Recent machine learning research has leveraged statistical methods to identify hidden units that behave (e.g., activate) similarly to human understandable logic, but those analyses require considerable manual effort. Our insight is that many of those studies follow a common analysis pattern, and therefore there is opportunity to provide a declarative abstraction to easily express, execute and optimize them. This paper describes DeepBase, a system to inspect neural network behaviors through a unified interface. We model logic with user-provided hypothesis functions that annotate the data with high-level labels (e.g., part-of-speech tags, image captions). DeepBase lets users quickly identify individual or groups of units that have strong statistical dependencies with desired hypotheses. We discuss how DeepBase can express existing analyses, propose a set of simple and effective optimizations to speed up a standard Python implementation by up to 72x, and reproduce recent studies from the NLP literature.