Multilayer feedforward networks are universal approximators
Neural Networks
Approximation by superposition of sigmoidal and radial basis functions
Advances in Applied Mathematics
Feedforward nets for interpolation and classification
Journal of Computer and System Sciences
Neural networks for localized approximation
Mathematics of Computation
Single-Iteration Training Algorithm for Multi-Layer Feed-Forward Neural Networks
Neural Processing Letters
Learning in Neural Networks: Theoretical Foundations
Learning in Neural Networks: Theoretical Foundations
Interpolation by ridge polynomials and its application in neural networks
Journal of Computational and Applied Mathematics - Selected papers of the international symposium on applied mathematics, August 2000, Dalian, China
Capabilities of a four-layered feedforward neural network: four layers versus three
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
A simple method to derive bounds on the size and to train multilayer neural networks
IEEE Transactions on Neural Networks
Quasi-interpolation for data fitting by the radial basis functions
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Constructive approximation to multivariate function by decay RBF neural network
IEEE Transactions on Neural Networks
Approximation capability of interpolation neural networks
Neurocomputing
The multidimensional function approximation based on constructive wavelet RBF neural network
Applied Soft Computing
Quasi-interpolation for surface reconstruction from scattered data with radial basis function
Computer Aided Geometric Design
The errors of approximation for feedforward neural networks in the Lp metric
Mathematical and Computer Modelling: An International Journal
Constructive approximate interpolation by neural networks in the metric space
Mathematical and Computer Modelling: An International Journal
Multi-level hermite variational interpolation and quasi-interpolation
The Visual Computer: International Journal of Computer Graphics
Computers and Industrial Engineering
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We present a type of single-hidden layer feedforward neural networks with sigmoidal nondecreasing activation function. We call them ai-nets. They can approximately interpolate, with arbitrary precision, any set of distinct data in one or several dimensions. They can uniformly approximate any continuous function of one variable and can be used for constructing uniform approximants of continuous functions of several variables. All these capabilities are based on a closed expression of the networks.