  This paper presents a method to explain how the information of each input
variable is gradually discarded during the forward propagation in a deep neural
network (DNN), which provides new perspectives to explain DNNs. We define two
types of entropy-based metrics, i.e. (1) the discarding of pixel-wise
information used in the forward propagation, and (2) the uncertainty of the
input reconstruction, to measure input information contained by a specific
layer from two perspectives. Unlike previous attribution metrics, the proposed
metrics ensure the fairness of comparisons between different layers of
different DNNs. We can use these metrics to analyze the efficiency of
information processing in DNNs, which exhibits strong connections to the
performance of DNNs. We analyze information discarding in a pixel-wise manner,
which is different from the information bottleneck theory measuring feature
information w.r.t. the sample distribution. Experiments have shown the
effectiveness of our metrics in analyzing classic DNNs and explaining existing
deep-learning techniques.
