  Back propagation based visualizations have been proposed to interpret deep
neural networks (DNNs), some of which produce interpretations with good visual
quality. However, there exist doubts about whether these intuitive
visualizations are related to the network decisions. Recent studies have
confirmed this suspicion by verifying that almost all these modified
back-propagation visualizations are not faithful to the model's decision-making
process. Besides, these visualizations produce vague "relative importance
scores", among which low values can't guarantee to be independent of the final
prediction. Hence, it's highly desirable to develop a novel back-propagation
framework that guarantees theoretical faithfulness and produces a quantitative
attribution score with a clear understanding. To achieve the goal, we resort to
mutual information theory to generate the interpretations, studying how much
information of output is encoded in each input neuron. The basic idea is to
learn a source signal by back-propagation such that the mutual information
between input and output should be as much as possible preserved in the mutual
information between input and the source signal. In addition, we propose a
Mutual Information Preserving Inverse Network, termed MIP-IN, in which the
parameters of each layer are recursively trained to learn how to invert. During
the inversion, forward Relu operation is adopted to adapt the general
interpretations to the specific input. We then empirically demonstrate that the
inverted source signal satisfies completeness and minimality property, which
are crucial for a faithful interpretation. Furthermore, the empirical study
validates the effectiveness of interpretations generated by MIP-IN.
