Soboleva modified hyperbolic tangent  The Soboleva modified hyperbolic tangent, also known as (parametric) Soboleva modified hyperbolic tangent activation function ([P]SMHTAF), is a special S-shaped function based on the hyperbolic tangent, given by  This function was originally proposed as "modified hyperbolic tangent" by Elena V. Soboleva () as a utility function for multi-objective optimization and choice modelling in decision-making. It has since been introduced into neural network theory and practice. The function was also used to approximate current-voltage characteristics of field-effect transistors and light-emitting diodes, to design antenna feeders, and analyze plasma temperatures and densities in the divertor region of fusion reactors. A family of recurrence-generated parametric Soboleva modified hyperbolic tangent activation functions (NPSMHTAF, FPSMHTAF) was studied with parameters "a" = "c" and "b" = "d". With parameters "a" = "b" = "c" = "d" = 1 the modified hyperbolic tangent function reduces to the conventional tanh("x") function, whereas for "a" = "b" = 1 and "c" = "d" = 0, the term becomes equal to sinh("x").