Deriving Composite Functions as Activation Function for Neural Networks or for Wavenets

Abstract

   This study present new idea in way to more future wonderful ideas, exploiting mathematical side of specific, through several ways employing very wide resources of mathematical functions and their properties that with natural in improve features of activation function, from these studies this study which drive an activation function through compose two (and more) functions with properties to be continuous and drivable.

     We can drive membership function under fuzzy logic by this as composite function on wavelet function or vice versa, and for many different functions (as future work).

      Also there idea to compose wavelets from families such SLOG mother wavelets with RASP or POLYWOG wavelets, that specifically arises from NNs representation and classification problems ,which also drivable .Each one from these functions have derivative which also can be composed to get an other activation function .