36 citations · 98 across the 26 of their papers we have counts for
8 papers · 1 filter
Uniform Convergence of Deep Neural Networks with Lipschitz Continuous Activation Functions and Variable Widths
Yuesheng Xu, Haizhang Zhang
We consider deep neural networks with a Lipschitz continuous activation function and with weight matrices of variable widths. We establish a uniform convergence analysis framework…
Successive Affine Learning for Deep Neural Networks
Yuesheng Xu
This paper introduces a successive affine learning (SAL) model for constructing deep neural networks (DNNs). Traditionally, a DNN is built by solving a non-convex optimization prob…
Multi-Grade Deep Learning
Yuesheng Xu
The current deep learning model is of a single-grade, that is, it learns a deep neural network by solving a single nonconvex optimization problem. When the layer number of the neur…
Convergence of Deep Neural Networks with General Activation Functions and Pooling
Wentao Huang, Yuesheng Xu, Haizhang Zhang
Deep neural networks, as a powerful system to represent high dimensional complex functions, play a key role in deep learning. Convergence of deep neural networks is a fundamental i…
Convergence of Deep Convolutional Neural Networks
Yuesheng Xu, Haizhang Zhang
Convergence of deep neural networks as the depth of the networks tends to infinity is fundamental in building the mathematical foundation for deep learning. In a previous study, we…
Convergence of Deep ReLU Networks
Yuesheng Xu, Haizhang Zhang
We explore convergence of deep neural networks with the popular ReLU activation function, as the depth of the networks tends to infinity. To this end, we introduce the notion of ac…
Efficient First Order Methods for Linear Composite Regularizers
Andreas Argyriou, Charles A. Micchelli, Massimiliano Pontil +2
A wide class of regularization problems in machine learning and statistics employ a regularization term which is obtained by composing a simple convex function ωwith a linear trans…
Refinement of Operator-valued Reproducing Kernels
Yuesheng Xu, Haizhang Zhang, Qinghui Zhang
This paper studies the construction of a refinement kernel for a given operator-valued reproducing kernel such that the vector-valued reproducing kernel Hilbert space of the refine…