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Multi-Grade Deep Learning
Inspired by the human education process which arranges learning in grades, we propose a multi-grade learning model: We successively solve a number of optimization problems of small sizes, which are organized in grades, to learn a shallow neural network for each grade.
Sparse Deep Neural Network for Nonlinear Partial Differential Equations
Noting that DNNs have an intrinsic multi-scale structure which is favorable for adaptive representation of functions, by employing a penalty with multiple parameters, we develop DNNs with a multi-scale sparse regularization (SDNN) for effectively representing functions having certain singularities.
Convergence of Deep Neural Networks with General Activation Functions and Pooling
In this current work, we study the convergence of deep neural networks as the depth tends to infinity for two other important activation functions: the leaky ReLU and the sigmoid function.
Convergence of Deep Convolutional Neural Networks
Based on the conditions, we present sufficient conditions for piecewise convergence of general deep ReLU networks with increasing widths, and as well as pointwise convergence of deep ReLU convolutional neural networks.
Convergence of Deep ReLU Networks
We explore convergence of deep neural networks with the popular ReLU activation function, as the depth of the networks tends to infinity.
Dynamic PET cardiac and parametric image reconstruction: a fixed-point proximity gradient approach using patch-based DCT and tensor SVD regularization
For the cardiac/lung phantom, an additional cardiac gated 2D-OSEM set was reconstructed.
