Analysis of Information Flow in Hidden Layers of the Trained Neural Network by Canonical Correlation Analysis

Convolutional neural network (CNN) have been extensively applied for a variety of tasks. However, the internal processes of hidden units in solving problems are mostly unknown. In this study, we presented the use of canonical correlation analysis (CCA) to understand the information flow of the hidden layers in CNN. The proposed method analyzed and compared the information flow by measuring the correlations between a given feature vector and the activation pattern at each layer of the CNN. We quantified and analyzed specific information flows using the CCA to examine how the architecture works in the two experiments. In the first experiment, we analyzed the information flow of the U-net and auto-encoder architectures to remove the distorted light source information, and showed that the U-net works more efficiently for this task. In the second experiment, we analyzed the information flow of the architecture used for multitask learning, in which the classification of shifted characters in images and the estimation of the shift amount are performed simultaneously, and showed that it performed properly according to the task.