Relationship Between Weight Correlation of the Convolution Kernels and the Optimal Architecture of CNN

Currently, deep learning has been one of the most popular research topics, and it has already been successfully applied in many fields such as image recognition, recommendation systems and so on. Convolutional neural network (CNN), as an important application in the field of deep learning classification, has attracted a lot of research interests. The performance of CNN is greatly affected by the number of convolution kernels. However, how to determine the optimal number of convolution kernels automatically in each convolution layer is still an unsolved problem. In this work, a simple CNN composed of a single convolution layer followed by a pool layer is studied. It is found that the correlation between the weights of the convolution kernels is related with the optimal number of kernels in the CNN. Usually, with the increasing of the kernel size, a lower weight correlation threshold will correspond to the optimal number of kernels. Furthermore, it is found that the weight correlation threshold is only affected by the kernel size, but is not affected by different kinds of datasets. These results imply that the weight correlation of the convolution kernels is an important indicator for determining the optimal architecture of CNN.