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Found 13 papers, 0 papers with code
Incorporating Domain Differential Equations into Graph Convolutional Networks to Lower Generalization Discrepancy
We theoretically derive conditions where GCNs incorporating such domain differential equations are robust to mismatched training and testing data compared to baseline domain agnostic models.
Hypothesis Spaces for Deep Learning
The representer theorems unfold that solutions of these learning models can be expressed as linear combination of a finite number of kernel sessions determined by given data and the reproducing kernel.
Deep Neural Network Solutions for Oscillatory Fredholm Integral Equations
We first developed a numerical method for solving the equation with DNNs as an approximate solution by designing a numerical quadrature that tailors to computing oscillatory integrals involving DNNs.
Multi-Grade Deep Learning for Partial Differential Equations with Applications to the Burgers Equation
We develop in this paper a multi-grade deep learning method for solving nonlinear partial differential equations (PDEs).
Uniform Convergence of Deep Neural Networks with Lipschitz Continuous Activation Functions and Variable Widths
We consider deep neural networks with a Lipschitz continuous activation function and with weight matrices of variable widths.
Sparse Representer Theorems for Learning in Reproducing Kernel Banach Spaces
Sparsity of a learning solution is a desirable feature in machine learning.
Successive Affine Learning for Deep Neural Networks
The MGDL model learns a DNN in several grades, in each of which one constructs a shallow DNN consisting of a relatively small number of layers.
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.
