  In this paper, we tackle interactive debugging of "gray-box" concept-based
models (CBMs). These models learn task-relevant concepts appearing in the
inputs and then compute a prediction by aggregating the concept activations.
Our work stems from the observation that in CBMs both the concepts and the
aggregation function can be affected by different kinds of bugs, and that
fixing these bugs requires different kinds of corrective supervision. To this
end, we introduce a simple schema for human supervisors to identify and
prioritize bugs in both components, and discuss solution strategies and open
problems. We also introduce a novel loss function for debugging the aggregation
step that generalizes existing strategies for aligning black-box models to CBMs
by making them robust to how the concepts change during training.
