Approximation by ridge functions and neural networks with one hidden layer
Journal of Approximation Theory
Universal approximation bounds for superpositions of a sigmoidal function
IEEE Transactions on Information Theory
Function Approximation by Neural Networks
ISNN '08 Proceedings of the 5th international symposium on Neural Networks: Advances in Neural Networks
Multivariate sigmoidal neural network approximation
Neural Networks
Double approximate identity neural networks universal approximation in real lebesgue spaces
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part I
The universal approximation capabilities of mellin approximate identity neural networks
ISNN'13 Proceedings of the 10th international conference on Advances in Neural Networks - Volume Part I
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Neural networks are widely used in many applications including astronomical physics,image processing, recognition, robotics, and automated target tracking, etc. Their ability to approximate arbitrary functions is the main reason for this popularity. In this paper, we discuss the constructive approximation on the whole real line by a neural networks with a sigmoidal activation function and a fixed weight. Using the convolution method, we show neural network approximation with a fixed weight to a continuous function on a compact interval. Also, we demonstrate a computational work that shows good agreement with theory.