Sharp Bounds on the Approximation Rates, Metric Entropy, and n-Widths of Shallow Neural Networks

DOI10.1007/S10208-022-09595-3MaRDI QIDQ6489780

Publication date: 22 April 2024

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Approximation by arbitrary nonlinear expressions; widths and entropy (41A46) Neural nets and related approaches to inference from stochastic processes (62M45)

Related Items (2)

Two-layer networks with the $\text{ReLU}^k$ activation function: Barron spaces and derivative approximation ⋮ An iterative method for the solution of Laplace-like equations in high and very high space dimensions

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Eigenvalues, embeddings and generalised trigonometric functions
Inequalities of Bernstein-Jackson-type and the degree of compactness of operators in Banach spaces
Universal Donsker classes and metric entropy
Gelfand numbers of operators with values in a Hilbert space
Entropy numbers, s-numbers, and eigenvalue problems
A simple lemma on greedy approximation in Hilbert space and convergence rates for projection pursuit regression and neural network training
Uniform approximation by neural networks
Improved upper bounds for approximation by zonotopes
Information-theoretic determination of minimax rates of convergence
Optimal nonlinear approximation
Tight upper bounds for the discrepancy of half-spaces
Random approximants and neural networks
Gelfand numbers and widths
Approximation rates for neural networks with general activation functions
High-order approximation rates for shallow neural networks with cosine and $\mathrm{ReLU}^k$ activation functions
Gelfand numbers and metric entropy of convex hulls in Hilbert spaces
Approximation and learning by greedy algorithms
Entropy numbers of convex hulls in Banach spaces and applications
The sizes of compact subsets of Hilbert space and continuity of Gaussian processes
General Lagrange and Hermite interpolation in $R^n$ with applications to finite element methods
The best constants in the Khintchine inequality
s-Numbers of operators in Banach spaces
On Lattices Admitting Unique Lagrange Interpolations
Universal approximation bounds for superpositions of a sigmoidal function
Efficient agnostic learning of neural networks with bounded fan-in
Metric Entropy of Convex Hulls in Hilbert Spaces
Metric Entropy of Convex Hulls in Banach Spaces
Bounds on rates of variable-basis and neural-network approximation
Comparison of worst case errors in linear and neural network approximation
Approximation by Combinations of ReLU and Squared ReLU Ridge Functions With <inline-formula> <tex-math notation="LaTeX">$\ell^1$ </tex-math> </inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\ell^0$ </tex-math> </inline-formula> Controls
On a Class of Finite Elements Generated by Lagrange Interpolation
Finite Neuron Method and Convergence Analysis
History of Banach Spaces and Linear Operators
Breaking the Curse of Dimensionality with Convex Neural Networks
Convex Analysis
Estimation of Linear Functionals on Sobolev Spaces with Application to Fourier Transforms and Spline Interpolation
Compressed sensing
Geometric discrepancy. An illustrated guide

This page was built for publication: Sharp Bounds on the Approximation Rates, Metric Entropy, and n-Widths of Shallow Neural Networks