随着数据的大量积累以及计算能力的不断提升，深度学习近年来在多项应用中取得成功。但深度学习的基础理论，即为何深层神经网络具有优异泛化能力的研究，目前尚无突破进展。本项目研究深度学习的泛化能力，旨在建立较为完整的深层神经网络margin理论，分析网络深度与margin的联系，刻画网络的margin复杂度。为透彻理解深度学习提供理论基础。研究并设计全新深度学习算法，以优化margin为目标，进一步增强泛化能力。研究给定边数条件下，泛化意义下最优网络结构。将深度学习算法、最优网络结构等成果用于解决计算机视觉、自然语言理解等领域的实际问题。

Deep learning has demonstrated great empirical success with increasing data and computation power. However, there is a lack of theoretical foundation of deep learning. Specifically, there is no learning theory that explains why deep neural networks generalize well. In this project we plan to study the generalization theory of deep learning; and establish a margin theory for deep neural networks. We plan to characterize the margin complexity of deep neural networks, analyze how the empirical margin distribution depends on the depth of the network. The goal of this project is to provide theoretical understanding of deep learning. We also aim to develop new deep learning algorithms, which directly optimize the empirical margins, and therefore guarantee the generalization ability. We next plan to study the optimal structure of networks with a given number of edges (free parameters). We will apply the new algorithms to computer vision and natural language processing problems as well.