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
Constructive Approximation of Discontinuous Functions by Neural Networks
Neural Processing Letters
Approximate interpolation by neural networks with the inverse multiquadric functions
ISICA'07 Proceedings of the 2nd international conference on Advances in computation and intelligence
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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.