Approximation Analysis of Deep Learning and Related Topics
DescriptionDeep learning has been very successful in speech recognition, image classification and many other fields, but its theoretical foundation concerning structured deep neural networks for approximation and generalization has not been well developed yet. It is desirable to have good theoretical understanding of network structures and architectures matching practical applications. In this project we propose to conduct approximation analysis for some deep learning schemes and study some related approximation theory problems and applications. We first plan to carry out generalization analysis for classification with some deep learning schemes including an algorithm with deep convolutional layers of neurons followed by a fully-connected layer. We then plan to study deep learning with functional data to establish generalization error bounds for the produced regression and classification problems. Some problems on function approximation by deep neural networks with structures for deep learning will be studied by approaches from learning theory and wavelet analysis. We also plan to apply deep learning algorithms to some practical applications including readability classification of Chinese text documents.
|Effective start/end date||1/01/21 → …|