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
$$\operatorname{mtanh}x = \frac {e^{ax} - e^{-bx}} {e^{cx} + e^{-dx}}.$$
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).
See also
- Activation function
- e (mathematical constant)
- Equal incircles theorem, based on sinh
- Hausdorff distance
- Inverse hyperbolic functions
- List of integrals of hyperbolic functions
- Poinsot's spirals
- Sigmoid function
Further reading
(5 pages)
(20 pages) 1