The Sigmoid Neural Network Activation Function and its Connections to Airy’s and the Nield-Kuznetsov Functions

Author:

Hamdan M. H.1,Roach D. C.2

Affiliation:

1. Department of Mathematics and Statistics University of New Brunswick 100 Tucker Park Road, Saint John, New Brunswick, E2L 4L5 CANADA

2. Department of Engineering University of New Brunswick 100 Tucker Park Road, Saint John, New Brunswick, E2L 4L5 CANADA

Abstract

Analysis and solution of Airy’s inhomogeneous equation, when its forcing function is the sigmoid neural network activation function, are provided in this work. Relationship between the Nield-Kuznetsov, the Scorer, the sigmoid, the polylogarithm and Airy’s functions are established. Solutions to initial and boundary value problems, when the sigmoid function is involved, are obtained. Computations were carried out using Wolfram Alpha.

Publisher

World Scientific and Engineering Academy and Society (WSEAS)

Subject

General Mathematics,General Mathematics,Rheumatology,Molecular Biology,Cell Biology,Genetics,Molecular Biology,Histology,Biochemistry,Biophysics,General Materials Science,General Medicine,Virology,Microbiology,General Medicine,Maternity and Midwifery,Pharmacology (nursing)

Reference22 articles.

1. Skapura, D.M., Building Neural Networks. ACM Press, New York, NY, 1996.

2. Haykin, S., Neural Networks: A Comprehensive Foundation, 2/e. Prentice-Hall, Inc., 1999.

3. von Seggern, D., CRC Standard Curves and Surfaces with Mathematics, 2nd ed. Boca Raton, FL: CRC Press, 2007.

4. Wood, T., Sigmoid Function. Retrieved March 8, 2022. https://deepai.org/machinelearning-glossary-and-terms/sigmoid-function.

5. Roach, D.C. and Hamdan, M.H., On the Sigmoid Function as a Variable Permeability Model for Brinkman Equation, Trans. on Applied and Theoretical Mechanics, WSEAS, Vol. 17, 2022, pp. 29-38.

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