In this book, we introduce the parametrized, deformed and general activation function of neural networks. The parametrized activation function kills much less neurons than the original one. The asymmetry of the brain is best expressed by deformed activation functions. Along with a great variety of activation functions, general activation functions are also engaged. Thus, in this book, all presented is original work by the author given at a very general level to cover a maximum number of different kinds of neural networks: giving ordinary, fractional, fuzzy and stochastic approximations. It…mehr
In this book, we introduce the parametrized, deformed and general activation function of neural networks. The parametrized activation function kills much less neurons than the original one. The asymmetry of the brain is best expressed by deformed activation functions. Along with a great variety of activation functions, general activation functions are also engaged. Thus, in this book, all presented is original work by the author given at a very general level to cover a maximum number of different kinds of neural networks: giving ordinary, fractional, fuzzy and stochastic approximations. It presents here univariate, fractional and multivariate approximations. Iterated sequential multi-layer approximations are also studied. The functions under approximation and neural networks are Banach space valued.
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Inhaltsangabe
Abstract ordinary and fractional neural network approximations based on Richard's curve.- Abstract Multivariate Neural Network Approximation based on Richard's curve.- Parametrized hyperbolic tangent based Banach space valued basic and fractional neural network approximations.- Parametrized hyperbolic tangent induced Banach space valued multivariate multi layer neural network approximations.- Banach space valued neural network approximation based on a parametrized arctangent sigmoid function.- Parametrized arctangent activated Banach space valued multi layer neural network multivariate approximation.- Banach space valued Ordinary and Fractional neural networks approximations based on the parametrized Gudermannian function.- Parametrized Gudermannian activation function based Banach space valued neural network multivariate approximation.- Banach space valued univariate neural network approximation based on parametrized error activation function.- Banach space valued multivariate multi layer neural network approximation based on parametrized error activation function.- Hyperbolic Tangent Like based univariate Banach space valued neural network approximation.- Banach space valued neural network multivariate approximation based on hyperbolic tangent like activation function.- Banach space valued ordinary and fractional neural network approximations based on q-deformed hyperbolic tangent activation function.- Banach space valued multivariate multi layer neural network approximation based on q-deformed hyperbolic tangent activation function.- Banach space valued multivariate multi layer neural network approximation based on q-deformed and -parametrized A-generalized logistic function.- Banach space valued ordinary and fractional neural network approximation based on q-deformed and -parametrized A-generalized logistic function.- Banach space valued multivariate multi layer neural network approximation based on q-deformed and -parametrized hyperbolic tangent function.- q-Deformed and -parametrized hyperbolic tangent based Banach space valued ordinary and fractional neural network approximation.- Banach space valued multivariate multi layer neural network approximation based on q-Deformed and parametrized half hyperbolic tangent.- Banach space valued ordinary and fractional neural network approximation based on q-deformed and beta-parametrized half hyperbolic tangent.- General sigmoid relied Banach space valued neural network approximation.- General sigmoid induced Banach space valued neural network multivariate approximation.- Fuzzy basic and fractional general sigmoid function generated neural network approximation.- Multivariate Fuzzy Approximation by Neural Network Operators induced by a general sigmoid function.- Multivariate Fuzzy-Random and stochastic general sigmoid activation function generated Neural Network Approximations.- Voronovskaya type asymptotic expansions for general sigmoid functions induced quasi-interpolation neural network operators.- Multiple general sigmoids activated Banach space valued neural network multivariate approximation.- Quantitative Approximation by Multiple sigmoids KantorovichChoquet quasi-interpolation neural network operators.- Degree of Approximation by Multiple sigmoids KantorovichShilkret quasi-interpolation neural network operators.- Approximation by Neural Networks of Brownian Motion.- Neural Networks Approximation of Time Separating Stochastic Processes.- Fractional Calculus between Banach spaces together with Ostrowski and Gr¨uss kind of inequalities.- Sequential Fractional Calculus between Banach spaces and corresponding Ostrowski and Gr¨uss kind of inequalities.
Abstract ordinary and fractional neural network approximations based on Richard's curve.- Abstract Multivariate Neural Network Approximation based on Richard's curve.- Parametrized hyperbolic tangent based Banach space valued basic and fractional neural network approximations.- Parametrized hyperbolic tangent induced Banach space valued multivariate multi layer neural network approximations.- Banach space valued neural network approximation based on a parametrized arctangent sigmoid function.- Parametrized arctangent activated Banach space valued multi layer neural network multivariate approximation.- Banach space valued Ordinary and Fractional neural networks approximations based on the parametrized Gudermannian function.- Parametrized Gudermannian activation function based Banach space valued neural network multivariate approximation.- Banach space valued univariate neural network approximation based on parametrized error activation function.- Banach space valued multivariate multi layer neural network approximation based on parametrized error activation function.- Hyperbolic Tangent Like based univariate Banach space valued neural network approximation.- Banach space valued neural network multivariate approximation based on hyperbolic tangent like activation function.- Banach space valued ordinary and fractional neural network approximations based on q-deformed hyperbolic tangent activation function.- Banach space valued multivariate multi layer neural network approximation based on q-deformed hyperbolic tangent activation function.- Banach space valued multivariate multi layer neural network approximation based on q-deformed and -parametrized A-generalized logistic function.- Banach space valued ordinary and fractional neural network approximation based on q-deformed and -parametrized A-generalized logistic function.- Banach space valued multivariate multi layer neural network approximation based on q-deformed and -parametrized hyperbolic tangent function.- q-Deformed and -parametrized hyperbolic tangent based Banach space valued ordinary and fractional neural network approximation.- Banach space valued multivariate multi layer neural network approximation based on q-Deformed and parametrized half hyperbolic tangent.- Banach space valued ordinary and fractional neural network approximation based on q-deformed and beta-parametrized half hyperbolic tangent.- General sigmoid relied Banach space valued neural network approximation.- General sigmoid induced Banach space valued neural network multivariate approximation.- Fuzzy basic and fractional general sigmoid function generated neural network approximation.- Multivariate Fuzzy Approximation by Neural Network Operators induced by a general sigmoid function.- Multivariate Fuzzy-Random and stochastic general sigmoid activation function generated Neural Network Approximations.- Voronovskaya type asymptotic expansions for general sigmoid functions induced quasi-interpolation neural network operators.- Multiple general sigmoids activated Banach space valued neural network multivariate approximation.- Quantitative Approximation by Multiple sigmoids KantorovichChoquet quasi-interpolation neural network operators.- Degree of Approximation by Multiple sigmoids KantorovichShilkret quasi-interpolation neural network operators.- Approximation by Neural Networks of Brownian Motion.- Neural Networks Approximation of Time Separating Stochastic Processes.- Fractional Calculus between Banach spaces together with Ostrowski and Gr¨uss kind of inequalities.- Sequential Fractional Calculus between Banach spaces and corresponding Ostrowski and Gr¨uss kind of inequalities.
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