On the density of translation networks defined on the unit ball
From MaRDI portal
Publication:6633210
DOI10.3934/MFC.2023017zbMATH Open1548.41025MaRDI QIDQ6633210
Lin Liu, Bao-Huai Sheng, Xiaojun Sun, Xiaoling Pan
Publication date: 5 November 2024
Published in: Mathematical Foundations of Computing (Search for Journal in Brave)
densityFourier-Laplace seriesJacobi orthogonal polynomialsconvolutional structure on the unit ballzonal translations
Rate of convergence, degree of approximation (41A25) Approximation by arbitrary linear expressions (41A45)
Cites Work
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Approximation by neural networks with sigmoidal functions
- The errors of simultaneous approximation of multivariate functions by neural networks
- The essential order of approximation for neural networks
- Analysis on the unit ball and on the simplex
- A way of construction spherical zonal translation network operators with linear bounded operators
- Best approximation of functions on the ball on the weighted Sobolev space equipped with a Gaussian measure
- The approximation operators with sigmoidal functions
- Widths of weighted Sobolev classes on the ball
- Approximation by Ridge functions and neural networks with one hidden layer
- Approximation by superposition of sigmoidal and radial basis functions
- Best approximation and \(K\)-functionals
- Weighted approximation of functions on the unit sphere
- Generalized translation operator and approximation in several variables
- Approximation of smooth functions on compact two-point homogeneous spaces
- Degree of approximation by neural and translation networks with a single hidden layer
- Essential rate for approximation by spherical neural networks
- Approximation properties of zonal function networks using scattered data on the sphere
- Theory of deep convolutional neural networks. II: Spherical analysis
- Theory of deep convolutional neural networks: downsampling
- Universality of deep convolutional neural networks
- Localized polynomial frames on the ball
- On approximation by reproducing kernel spaces in weighted \(L^p\) spaces
- Multivariate polynomial inequalities with respect to doubling weights and \(A_{\infty}\) weights
- Best Polynomial Approximation on the Unit Sphere and the Unit Ball
- An application of Bernstein-Durrmeyer operators
- Summability of Fourier orthogonal series for Jacobi weight on a ball in ℝ^{𝕕}
- Best Weighted Polynomial Approximation via Jacobi Expansions
- Deep distributed convolutional neural networks: Universality
- Approximation Theory and Harmonic Analysis on Spheres and Balls
- A Convolution Structure for Jacobi Series
- Mean convergence of orthogonal series and Lagrange interpolation
- Approximation by superpositions of a sigmoidal function
- Theory of deep convolutional neural networks. III: Approximating radial functions
- Convergence of deep convolutional neural networks
Related Items (3)
Moduli of smoothness, \(K\)-functionals and Jackson-type inequalities associated with Kernel function approximation in learning theory ⋮ Reproducing property of bounded linear operators and kernel regularized least square regressions ⋮ Approximation by convolution translation networks on conic domains
This page was built for publication: On the density of translation networks defined on the unit ball
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6633210)