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Found 7 papers, 0 papers with code
Kernel based analysis of massive data
In this paper, we develop a very general theory of approximation by networks, which we have called eignets, to achieve local, stratified approximation.
Theory inspired deep network for instantaneous-frequency extraction and signal components recovery from discrete blind-source data
This paper is concerned with the inverse problem of recovering the unknown signal components, along with extraction of their instantaneous frequencies (IFs), governed by the adaptive harmonic model (AHM), from discrete (and possibly non-uniform) samples of the blind-source composite signal.
Dimension independent bounds for general shallow networks
In the context of manifold learning, our bounds provide estimates on the degree of approximation for an out-of-sample extension of the target function to the ambient space.
Deep Algorithms: designs for networks
A new design methodology for neural networks that is guided by traditional algorithm design is presented.
Function approximation with zonal function networks with activation functions analogous to the rectified linear unit functions
A zonal function (ZF) network on the $q$ dimensional sphere $\mathbb{S}^q$ is a network of the form $\mathbf{x}\mapsto \sum_{k=1}^n a_k\phi(\mathbf{x}\cdot\mathbf{x}_k)$ where $\phi :[-1, 1]\to\mathbf{R}$ is the activation function, $\mathbf{x}_k\in\mathbb{S}^q$ are the centers, and $a_k\in\mathbb{R}$.
A Fourier-invariant method for locating point-masses and computing their attributes
Motivated by the interest of observing the growth of cancer cells among normal living cells and exploring how galaxies and stars are truly formed, the objective of this paper is to introduce a rigorous and effective method for counting point-masses, determining their spatial locations, and computing their attributes.
A unified method for super-resolution recovery and real exponential-sum separation
In this paper, motivated by diffraction of traveling light waves, a simple mathematical model is proposed, both for the multivariate super-resolution problem and the problem of blind-source separation of real-valued exponential sums.
