A New Class of Activation Functions Based on the Correcting Amendments of Gompertz–makeham Type

Abstract

We will explore the interesting methodological task for constructing new activation functions using "correcting amendments" of "Gompertz-Makehamtype" (GMAF). We also define the new family of recurrence generated activation functions based on "Gompertz-Makeham correction" -(RGGMAF).We prove upper and lower estimates for the Hausdorff approximation of the sign function by means of this new class of parametric activation functions -(RGGMAF). Numerical examples, illustrating our results are given.

Reaction networks reveal new links between Gompertz and Verhulst growth functions

“…Remark. In the special case k 1 = 1, we obtain dynamical system (17), if k 2 = 1 we obtain system (18), and if k 1 = k 2 we obtain dynamical system (19).…”

“…Gompertz models find application in software reliability models (GSRM, GMSRM) [28], [27], [23]. Gompertz-type modeling and data fitting problems stimulate various mathematical and computational studies, such as applications of new cumulative distribution functions, transformations (type I-type III) to construct families of sigmoidal functions and new activation functions using 'correcting amendments' [17], [18], [19]. For other related works the reader may consult [11]- [14].…”

Some Notes on the Omega Distribution and the Pliant Probability Distribution Family

“…The study can be very useful for specialists that are working in several scientific fields like insurance, financial mathematics, analysis, approximation of data sets in various modeling problems and others. Application of the Hausdorff metrics in different approximation problems is topic for many science works (for example see articles [1][2][3][4][5][6][7][8], some monographs [9][10][11][12][13][14][15][16][17][18] and references there in). Definition 1.…”