  Identifying the roles of individual units is critical for understanding the
mechanism of convolutional neural networks (CNNs). However, it is challenging
to give the fully automatic and quantitative measures for effectiveness
assessment of individual units in CNN. To this end, we propose a novel method
for quantitatively clarifying the status and usefulness of single unit of CNN
in image classification tasks. The technical substance of our method is ranking
the importance of unit for each class in classification based on calculation of
specifically defined entropy using algebraic topological tools. It could be
implemented totally by machine without any human intervention. Some interesting
phenomena including certain kind of phase transition are observed via the
evolution of accuracy and loss of network in the successive ablation process of
units. All of the network units are divided into four categories according to
their performance on training and testing data. The role categorization is
excellent startpoint for network construction and simplification. The diverse
utility and contribution to the network generalization of units in
classification tasks are thoroughly illustrated by extensive experiments on
network (VGG) and dataset (ImageNet) with considerable scale. It is easy for
our method to have extensional applications on other network models and tasks
without essential difficulties.
