  In this technical note, we aim to explain a deep neural network (DNN) by
quantifying the encoded interactions between input variables, which reflects
the DNN's inference logic. Specifically, we first rethink the definition of
interactions, and then formally define faithfulness and conciseness for
interaction-based explanation. To this end, we propose two kinds of
interactions, i.e., the AND interaction and the OR interaction. For
faithfulness, we prove the uniqueness of the AND (OR) interaction in
quantifying the effect of the AND (OR) relationship between input variables.
Besides, based on AND-OR interactions, we design techniques to boost the
conciseness of the explanation, while not hurting the faithfulness. In this
way, the inference logic of a DNN can be faithfully and concisely explained by
a set of symbolic concepts.
