Abstract: We will explore the interesting methodological task for constructing new 2–parametric deterministic activation function – (2PDAF). We prove upper and lower estimates for the Hausdorff approximation of the sign function by means of this new activation functions. Numerical examples, illustrating our results are given.

Keywords: 2–parametric deterministic activation function – (2PDAF), Sign function, Hausdorff distance, Upper and lower bounds.