6 papers
Qualitative neural network approximation over R and C: Elementary proofs for analytic and polynomial activation
Josiah Park, Stephan Wojtowytsch
In this article, we prove approximation theorems in classes of deep and shallow neural networks with analytic activation functions by elementary arguments. We prove for both real a…
Neural Network Approximation of Refinable Functions
Ingrid Daubechies, Ronald DeVore, Nadav Dym +6
In the desire to quantify the success of neural networks in deep learning and other applications, there is a great interest in understanding which functions are efficiently approxi…
Energy on spheres and discreteness of minimizing measures
Dmitriy Bilyk, Alexey Glazyrin, Ryan Matzke +2
In the present paper we study the minimization of energy integrals on the sphere with a focus on an interesting clustering phenomenon: for certain types of potentials, optimal meas…
Frame Potentials and Orthogonal Vectors
Josiah Park
An extension is given of a recent result of Glazyrin, showing that an orthonormal basis joined with the vectors , where min…
Lattices from tight frames and vertex transitive graphs
Lenny Fukshansky, Deanna Needell, Josiah Park +1
We show that real tight frames that generate lattices must be rational, and use this observation to describe a construction of lattices from vertex transitive graphs. In the case o…
Balian-Low Theorems in Several Variables
Michael Northington, Josiah Park
Recently, Nitzan and Olsen showed that Balian-Low theorems (BLTs) hold for discrete Gabor systems defined on . Here we extend these results to a multivariable setting…