Analysis of Deep CNNs Induced by 2-D Convolutions and Related Approximation Theory Problems
DescriptionDeep learning has been a powerful tool in many practical applications. In computer vision, deep learning based on deep convolutional neural networks (CNNs) of matrices by 2-D convolutions is very efficient in capturing features of natural images, but itsmathematical theory, especially its approximation ability, is not well understood.The goal of this project is to study the approximation ability of deep CNNs induced by 2-D convolutions and parallel channels, and to investigate related approximation theoretical problems. First we propose a new distributed scheme of deep CNNs induced by 2-D convolutions and channels without zero-padding which can be applied in mobile devices and is related to depth wise separable CNNs. We plan to establish an approximation theory for these CNN schemes in terms of the number of channels. Then we consider some approximation theoretical problems arising from deep learning, including localization of deep neural networks, approximation by ReLU deep neural networks of functions from Sobolev spaces of mixed smoothness, and approximation and learning of functions of tensor structured matrices by 2-D multichannel distributed deep CNNs in terms of sparse tensor structures of matrices and the induced functions. Interactions among deep learning, approximation theory, and wavelets are crucial in the project.
|Effective start/end date||1/01/21 → …|