Approximation by Superpositions of a Sigmoidal Function

By Grzegorz Lewicki, Giuseppe Marino. 2003

915 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e5903c482d81df7f2be306006ef9ecfbe7fc7a39

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The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Computational Theory and Mathematics

In Statistical and Nonlinear Physics

Citations in the corpus

Pairs trading and outranking: The multi-step-ahead forecasting case (2010, background): “It is influenced by theoretical works showing that a single hidden layer is sufficient for ANN’s to approximate any complex non-linear function (Cybenko, 1989; Hornik et al., 1989).”
Granular neural web agents for stock prediction (2002, background): “Second, it has been shown that a neural network is an universal approximator, capable of approximating any continuous function [1].”
Visualizations of Deep Neural Networks in Computer Vision: A Survey (2017, background): “Despite being theoretically able to approximate any function [8], their popularity decreased in the 1970’s because their computationally expensive training was not feasible with available computing resources [49].”
Financial time series prediction using polynomial pipelined neural networks (2008, background): “This means that neural networks can approximate any continuous function to any desire accuracy (Cybenko, 1989; Funahashi, 1989; Hornik, 1991; Hornik, Stinchcombe, & White, 1989; Irie & Miyake, 1988).”
Polynomial Convergence of Gradient Descent for Training One-Hidden-Layer Neural Networks (2018, background): “Fundamental results [16, 7, 4] show that a neural network with a single hidden layer provides a universal representation up to arbitrary approximation, with the number of hidden units depending on the function being approximated and the desired accuracy.”
Training Shallow and Thin Networks for Acceleration via Knowledge Distillation with Conditional Adversarial Networks (2017, background): “Do DNNs really need to be deep and wide? Early theoretical studies suggest that shallow networks are powerful and can approximate arbitrary functions [8, 13].”
On stock return prediction with LSTM networks (2017, background): “One of the interesting discoveries was the universal approximation theorem proven by (e.g.) Cybenko (1989).”
Artificial neural network modeling studies to predict the yield of enzymatic synthesis of betulinic acid ester (2010, background): “It was reported in the literature that one hidden layer is normally adequate to provide an accurate prediction and can be the first choice for any practical feed-forward network design (Irie and Miyake, 1988; Cybenko, 1989; Hush and Horne, 1993; Shankar and Bandyopadhyay, 2007).”
Precision Learning: Towards Use of Known Operators in Neural Networks (2017, positive): “In this paper, we wish to explore the general bounds on such approaches and make comparisons to the universal approximation theorem [12].”
Shallow Learning For Deep Networks (2018, background): “1, a variety of theoretical results exist (e.g. (Cybenko, 1989; Barron, 1994)).”
Robust Adaptive Control of Feedback Linearizable MIMO Nonlinear Systems With Prescribed Performance (2008, neutral): “The regressor terms may contain high order connections of sigmoid functions [36], radial basis functions (RBFs) with fixed centers and widths [37]–[39], shifted sigmoids [40], [41], thus forming high order neural networks (HONNs), RBFs and Shifted Sigmoidal Neural Networks, respectively.”
Prescribed performance adaptive control of SISO feedback linearizable systems with disturbances (2008, background): “The regressor terms may contain high order connections of sigmoid functions [17], radial basis functions (RBFs) with fixed centers and widths [18]–[20], shifted sigmoids [21], [22], thus forming high order neural networks (HONNs), RBFs and Shifted Sigmoidal Neural Networks, respectively.”