Understanding the Feedforward Artificial Neural Network Model From the Perspective of Network Flow

In recent years, deep learning based on artificial neural network (ANN) has achieved great success in pattern recognition. However, there is no clear understanding of such neural computational models [1], for instance, for a trained ANN-classifier, we have no idea of why some classes are easy to be predicted correctly, but some are difficult to be predicted correctly. In this paper, we try to unravel ''black-box" structure of classifiers and explain the mechanism of classification decisions made by classifiers from network flow. Specifically, we consider the feed forward artificial neural network as a network flow model, which consists of many directional class-pathways. Each class-pathway encodes one class. The class-pathway of a class is obtained by connecting the activated neural nodes in each layer from input to output, where activation value of neural node (node-value) is defined by the weights of each layer in a trained ANN-classifier. From the perspective of the class-pathway, training an ANN-classifier can be regarded as the formulation process of class-pathways of different classes. By analyzing the the distances of each two class-pathways in a trained ANN-classifiers, we try to answer the questions, why the classifier performs so? The smaller the distance of the class-pathways between two classes is, the higher the probability of the predicted error each other for these two classes will be. Furthermore, we can use the analysis as a new way to measure the performance of classifier and compare them despite their high prediction accuracy reporting on the small test sets. At last, from the neural encodes view, we define the importance of each neural node through the class-pathways, which is helpful to optimize the structure of a classifier. Experiments for two types of ANN model including multi-layer perceptron (MLP) and convolutional neural network (CNN) verify that the network flow based on class-pathway is a reasonable explanation for ANN models.