On the rate of convergence of image classifiers based on convolutional neural networks

Deep neural networks are nowadays among the most successful and most widely used methods in machine learning, see, e.g., Schmidhuber (2015), Rawat and Wang (2017), and the literature cited therein. In many applications the most successful networks are deep convolutional networks, see, e.g., Krizhevsky, Sutskever and Hinton (2012) and Kim (2014) concerning applications in image classification or language recognition, resp. These networks can be considered as a special case of deep feedforward neural networks, where symmetry constraints are imposed on the weights of the networks. For general deep feedforward neural networks it was recently shown that under suitable compository assumptions on the structure of the regression function these networks are able to achieve dimension reduction in estimation of high-dimensional regression functions (cf., Kohler