Degree of Approximation Results for Feedforward Networks Approximating Unknown Mappings and Their Derivatives

Hornik, Kurt; Stinchcombe, Maxwell B.; White, Halbert; Auer, Péter

doi:10.1162/neco.1994.6.6.1262

Cited by 143 publications

(105 citation statements)

References 7 publications

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“…The latter, therefore, shares all the advantages of the former, including the very good convergence rate [11] and its application in Sobolev space [17].…”

Section: Approximation With Logistic Differential Equationsmentioning

confidence: 89%

Parameter Estimation of Sigmoid Superpositions: Dynamical System Approach

2003

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“…The latter, therefore, shares all the advantages of the former, including the very good convergence rate [11] and its application in Sobolev space [17].…”

Section: Approximation With Logistic Differential Equationsmentioning

confidence: 89%

Parameter Estimation of Sigmoid Superpositions: Dynamical System Approach

2003

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“…Also the hidden layer has 6 nodes, in each node; weighted inputs are processed by a transfer function as shown in Fig. 4 (Hornik et al 1994).…”

Section: Model Descriptionmentioning

confidence: 99%

An Artificial Neural Networks Model for Predicting Permeability Properties of Nano Silica–Rice Husk Ash Ternary Blended Concrete

Najigivi

Khaloo

zad

et al. 2013

Int J Concr Struct Mater

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In this study, a two-layer feed-forward neural network was constructed and applied to determine a mapping associating mix design and testing factors of cement-nano silica (NS)-rice husk ash ternary blended concrete samples with their performance in conductance to the water absorption properties. To generate data for the neural network model (NNM), a total of 174 field cores from 58 different mixes at three ages were tested in the laboratory for each of percentage, velocity and coefficient of water absorption and mix volumetric properties. The significant factors (six items) that affect the permeability properties of ternary blended concrete were identified by experimental studies which were: (1) percentage of cement; (2) content of rice husk ash; (3) percentage of 15 nm of SiO 2 particles; (4) content of NS particles with average size of 80 nm; (5) effect of curing medium and (6) curing time. The mentioned significant factors were then used to define the domain of a neural network which was trained based on the Levenberg-Marquardt back propagation algorithm using Matlab software. Excellent agreement was observed between simulation and laboratory data. It is believed that the novel developed NNM with three outputs will be a useful tool in the study of the permeability properties of ternary blended concrete and its maintenance.

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“…they require a smaller number of adjustable parameters than approximators which are linear with respect to the parameters (such as polynomials for instance, or radial basis function with fixed centers and variances) (Hornik et al 1994). Specifically, the number of parameters required increases linearly with the number of input variables, whereas it grows exponentially for approximators which are linear with respect to the parameters.…”

Section: Some Feedforward Neural Network Are Parsimonious Universal mentioning

confidence: 99%

Reducing the Complexity of Neural Nets for Industrial Applications and Biological Models

Dreyfus¹

1999

Neuronal Information Processing

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The fundamental property of feedforward neural networks -parsimonious approximationmakes them excellent candidates for modeling static nonlinear processes from measured data. Similarly, feedback (or recurrent) neural networks have very attractive properties for the dynamic nonlinear modeling of artificial or natural processes; however, the design of such networks is more complex than that of feedforward neural nets, because the designer has additional degrees of freedom. In the present paper, we show that this complexity may be greatly reduced by (i) incorporating into the very structure of the network all the available mathematical knowledge about the process to be modeled, and by (ii) transforming the resulting network into a "universal" form, termed canonical form, which further reduces the complexity of analyzing and training dynamic neural models.

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Degree of Approximation Results for Feedforward Networks Approximating Unknown Mappings and Their Derivatives

Cited by 143 publications

References 7 publications

Parameter Estimation of Sigmoid Superpositions: Dynamical System Approach

Parameter Estimation of Sigmoid Superpositions: Dynamical System Approach

An Artificial Neural Networks Model for Predicting Permeability Properties of Nano Silica–Rice Husk Ash Ternary Blended Concrete

Reducing the Complexity of Neural Nets for Industrial Applications and Biological Models

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