A new class activation functions with application in the theory of impulse technics

Abstract

In this note we define the new activation functions, based on the well-known hyperbolic tangent and half--hyperbolic tangent activation functions. We consider the Hausdorff distance between the ''double step'' function $\sigma^{\ast}(t)$ (resp. function $\sigma^{\ast \ast}(t)$) and the new classes of activation functions. The results have independent significance in the study of issues related to neural networks and impulse techniques. Numerical examples, illustrating our results are presented using programming environment Mathematica.

Keywords

• ''double step'' function $\sigma^{\ast}(t)$
• $\sigma^{\ast \ast}(t)$--function
• emitting chart
• hausdorff distance