Understanding the class separation process of convolutional neural networks

Abstract

Extensive research shows that deep neural networks (DNNs) capture better feature representations than the previous handcrafted feature engineering, which leads to a significant performance improvement. However, it raises the question of how does the neural network spontaneously learn the intermediate representation, during the training process, to correctly separate the test data set into different categories? In this paper, based on the existing research work, we continue to take a small step towards understanding the dynamics of convolutional neural networks (CNN). Specifically, we model the test data set as a relationship graph, and each intermediate layer representation learned by CNN will transform the relationship graph correspondingly. Through these continuous transformations, we investigate the class separation process of CNN from two perspectives: 1) show the evolution of the degree of correlation between samples through the histogram of similarity between vertices; 2) by visualizing and quantifying the degree of separation (i.e., modularity) of the important relationship subgraph, we can show the contribution of each convolution layer of CNN to class separation. In the preliminary experiment, it can be found that: 1) each convolution layer of CNN gradually reduced the similarity of most edges between the samples to a very low level, that is, the dense relationship graph gradually evolved into a sparse graph; 2) the remaining important relationship subgraph consist of edges with high similarity shows evident modularity; 3) both visualization and quantification results show that the modularity of intra-class subgraph increases when the layers go deeper. Moreover, the degradation and plateau in the modularity curve reveal the existence of redundant layers. In this paper, we reveal some more in-depth dynamics of CNN, and introduced another modularity, which is widely used as the theoretical guidance tool of layer pruning. It can save more model parameters without losing the accuracy of classification.