  Various attribution methods have been developed to explain deep neural
networks (DNNs) by inferring the attribution/importance/contribution score of
each input variable to the final output. However, existing attribution methods
are often built upon different heuristics. There remains a lack of a unified
theoretical understanding of why these methods are effective and how they are
related. To this end, for the first time, we formulate core mechanisms of
fourteen attribution methods, which were designed on different heuristics, into
the same mathematical system, i.e., the system of Taylor interactions.
Specifically, we prove that attribution scores estimated by fourteen
attribution methods can all be reformulated as the weighted sum of two types of
effects, i.e., independent effects of each individual input variable and
interaction effects between input variables. The essential difference among the
fourteen attribution methods mainly lies in the weights of allocating different
effects. Based on the above findings, we propose three principles for a fair
allocation of effects to evaluate the faithfulness of the fourteen attribution
methods.
