Analysis of the rate of convergence of an over-parametrized convolutional neural network image classifier learned by gradient descent

In deep learning, the task is to estimate the functional relationship between input and output using deep neural networks. For the particular application area of image classification, the input data consists of observed images and the output data represents classes of the corresponding images that describe what kind of objects are present in the images. The most successful methods, especially in the area of image classification can be attributed to deep learning approaches (see, e.g., Krizhevsky, Sutskever and Hinton (2012), LeCun, Bengio and Hinton (2015), and Rawat and Wang (2017)) and, in particular, to convolutional neural networks (CNNs).