Sets of multivariable functions that can be approximated with" dimension-independent" rates
either by linear approximators or by neural networks having various types of computational …

We develop some mathematical tools for comparison of rates of fixed versus variable basis
function approximation. Using these tools, we describe sets of multivariable functions, for …

The author considers the problem of approximating arbitrary differentiable functions defined
on compact sets of R/sup d/, as well as their derivatives, by finite sums of the form a/sub 0/+ …

Feedforward neural networks can uniformly approximate continuous functions. It is shown
that a simple geometric proof of this theorem, proposed originally for networks of Heaviside …

The choice of activation functions may strongly influence complexity and performance of
neural networks. However a limited number of activation functions have been used in …

Deals with the approximation of continuous functions by feedforward neural networks. After
presenting one of the main results of Ito, the paper tries to get a universal approximator …

Artificial neural networks (ANNs) were first proposed, by Hecht-Nieisen (1987), as
multivariate function approximators based on Kolmogorov's theorem. Since then, several …

Function approximation problems for ordinary neural networks may be rather difficult, if the
function becomes complicated, due to the necessity of big network size and the possibilities …

The problem of constructing universal networks capable of approximating all functions
having bounded derivatives is discussed. It is demonstrated that, using standard ideas from …

In this article, we develop a framework for showing that neural networks can overcome the
curse of dimensionality in different high-dimensional approximation problems. Our approach …