n 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.
Author(s): George A. Anastassiou
Series: Studies in Computational Intelligence
Publisher: Springer Nature Switzerland
Year: 2023
Language: English
Pages: 854
Cover
Front Matter
1. Abstract Ordinary and Fractional Neural Network Approximations Based on Richard’s Curve
2. Abstract Multivariate Neural Network Approximation Based on Richard’s Curve
3. Parametrized Hyperbolic Tangent Based Banach Space Valued Basic and Fractional Neural Network Approximations
4. Parametrized Hyperbolic Tangent Induced Banach Space Valued Multivariate Multi Layer Neural Network Approximations
5. Banach Space Valued Neural Network Approximation Based on a Parametrized Arctangent Sigmoid Function
6. Parametrized Arctangent Activated Banach Space Valued Multi Layer Neural Network Multivariate Approximation
7. Banach Space Valued Ordinary and Fractional Neural Networks Approximations Based on the Parametrized Gudermannian Function
8. Parametrized Gudermannian Activation Function Based Banach Space Valued Neural Network Multivariate Approximation
9. Banach Space Valued Univariate Neural Network Approximation Based on Parametrized Error Activation Function
10. Banach Space Valued Multivariate Multi Layer Neural Network Approximation Based on Parametrized Error Activation Function
11. Hyperbolic Tangent Like Based Univariate Banach Space Valued Neural Network Approximation
12. Banach Space Valued Neural Network Multivariate Approximation Based on Hyperbolic Tangent Like Activation Function
13. Banach Space Valued Ordinary and Fractional Neural Network Approximations Based on q-Deformed Hyperbolic Tangent Activation Function
14. Banach Space Valued Multivariate Multi Layer Neural Network Approximation Based on q-Deformed Hyperbolic Tangent Activation Function
15. Banach Space Valued Multivariate Multi Layer Neural Network Approximation Based on q-Deformed and -Parametrized A-Generalized Logistic Function
16. Banach Space Valued Ordinary and Fractional Neural Network Approximation Based on q-Deformed and -Parametrized A-Generalized Logistic Function
17. Banach Space Valued Multivariate Multi Layer Neural Network Approximation Based on q-Deformed and -Parametrized Hyperbolic Tangent Function
18. q-Deformed and -Parametrized Hyperbolic Tangent Based Banach Space Valued Ordinary and Fractional Neural Network Approximation
19. Banach Space Valued Multivariate Multi Layer Neural Network Approximation Based on q-Deformed and Parametrized Half Hyperbolic Tangent
20. Banach Space Valued Ordinary and Fractional Neural Network Approximation Based on q-Deformed and -Parametrized Half Hyperbolic Tangent
21. General Sigmoid Relied Banach Space Valued Neural Network Approximation
22. General Sigmoid Induced Banach Space Valued Neural Network Multivariate Approximation
23. Fuzzy Basic and Fractional General Sigmoid Function Generated Neural Network Approximation
24. Multivariate Fuzzy Approximation by Neural Network Operators Induced by a General Sigmoid Function
25. Multivariate Fuzzy-Random and Stochastic General Sigmoid Activation Function Generated Neural Network Approximations
26. Voronovskaya Type Asymptotic Expansions for General Sigmoid Functions Induced Quasi-Interpolation Neural Network Operators
27. Multiple General Sigmoids Activated Banach Space Valued Neural Network Multivariate Approximation
28. Quantitative Approximation by Multiple Sigmoids Kantorovich-Choquet Quasi-interpolation Neural Network Operators
29. Degree of Approximation by Multiple Sigmoids Kantorovich-Shilkret Quasi-interpolation Neural Network Operators
30. Approximation by Neural Networks of Brownian Motion
31. Neural Networks Approximation of Time Separating Stochastic Processes
32. Fractional Calculus Between Banach Spaces Together with Ostrowski and Grüss Kind of Inequalities
33. Sequential Fractional Calculus Between Banach Spaces and Corresponding Ostrowski and Grüss Kind of Inequalities
34. Advanced Fractional Inequalities Over a Line Segment of a Banach Space
Back Matter
