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

Technical Note: Defining and Quantifying AND-OR Interactions for Faithful and Concise Explanation of DNNs