Representation of functions by superpositions of a step or sigmoid function and their applications to neural network theory

Original Contribution: Approximation of continuous functions on Rd by linear combinations of shifted rotations of a sigmoid function with and without scaling

Neural Networks

A Weak Condition on Linear Independence of Unscaled Shifts of a Function and Finite Mappings by Neural Networks

ICANN '02 Proceedings of the International Conference on Artificial Neural Networks

On the partitioning capabilities of feedforward neural networks with sigmoid nodes

Neural Computation

Activation functions defined on higher-dimensional spaces for approximation on compact sets with and without scaling

Neural Computation

A Sobolev-type upper bound for rates of approximation by linear combinations of Heaviside plane waves

Journal of Approximation Theory

Computational Properties of Networks of Synchronous Groups of Spiking Neurons

Neural Computation

Minimization of error functionals over perceptron networks

Neural Computation

Approximation capability of layered neural networks with sigmoid units on two layers

Neural Computation

Combining exploratory projection pursuit and projection pursuit regression with application to neural networks

Neural Computation

Estimates of Network Complexity and Integral Representations

ICANN '08 Proceedings of the 18th international conference on Artificial Neural Networks, Part I

Simultaneous approximations of polynomials and derivatives and their applications to neural networks

Neural Computation

An integral upper bound for neural network approximation

Neural Computation

An approximation by neural networkswith a fixed weight

Computers & Mathematics with Applications

Model Complexity of Neural Networks and Integral Transforms

ICANN '09 Proceedings of the 19th International Conference on Artificial Neural Networks: Part I

Establishing criteria to ensure successful feedforward artificial neural network modelling of mechanical systems

Mathematical and Computer Modelling: An International Journal

Approximation properties of local bases assembled from neural network transfer functions

Mathematical and Computer Modelling: An International Journal

Complexity estimates based on integral transforms induced by computational units

Neural Networks