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Keywords = abstract quasi-interpolation operator

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16 pages, 321 KB  
Article
Abstract Univariate Neural Network Approximation Using a q-Deformed and λ-Parametrized Hyperbolic Tangent Activation Function
by George A. Anastassiou
Fractal Fract. 2023, 7(3), 208; https://doi.org/10.3390/fractalfract7030208 - 21 Feb 2023
Cited by 1 | Viewed by 1973
Abstract
In this work, we perform univariate approximation with rates, basic and fractional, of continuous functions that take values into an arbitrary Banach space with domain on a closed interval or all reals, by quasi-interpolation neural network operators. These approximations are achieved by deriving [...] Read more.
In this work, we perform univariate approximation with rates, basic and fractional, of continuous functions that take values into an arbitrary Banach space with domain on a closed interval or all reals, by quasi-interpolation neural network operators. These approximations are achieved by deriving Jackson-type inequalities via the first modulus of continuity of the on hand function or its abstract integer derivative or Caputo fractional derivatives. Our operators are expressed via a density function based on a q-deformed and λ-parameterized hyperbolic tangent activation sigmoid function. The convergences are pointwise and uniform. The associated feed-forward neural networks are with one hidden layer. Full article
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