The Soboleva modified hyperbolic tangent, also known as (parametric) Soboleva modified hyperbolic tangent activation function (
MHTAF),
is a special S-shaped
function
Function or functionality may refer to:
Computing
* Function key, a type of key on computer keyboards
* Function model, a structured representation of processes in a system
* Function object or functor or functionoid, a concept of object-oriente ...
based on the
hyperbolic tangent
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points form a circle with a unit radius, the points form the right half of the u ...
, given by
:
This function was originally proposed as "modified hyperbolic tangent"
by Elena V. Soboleva () as a utility function for
multi-objective optimization
Multi-objective optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, multiattribute optimization or Pareto optimization) is an area of multiple criteria decision making that is concerned with ...
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 transistor
The field-effect transistor (FET) is a type of transistor that uses an electric field to control the flow of current in a semiconductor. FETs ( JFETs or MOSFETs) are devices with three terminals: ''source'', ''gate'', and ''drain''. FETs cont ...
s and
light-emitting diode
A light-emitting diode (LED) is a semiconductor device that emits light when current flows through it. Electrons in the semiconductor recombine with electron holes, releasing energy in the form of photons. The color of the light (co ...
s,
to design
antenna feeders,
and analyze
plasma temperatures and densities in the
divertor
In nuclear fusion power research, a divertor is a device within a tokamak or a stellarator that allows the online removal of waste material from the plasma while the reactor is still operating. This allows control over the buildup of fusion pro ...
region of
fusion reactor
Fusion power is a proposed form of power generation that would generate electricity by using heat from nuclear fusion reactions. In a fusion process, two lighter atomic nuclei combine to form a heavier nucleus, while releasing energy. Devices ...
s.
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
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points form a circle with a unit radius, the points form the right half of the un ...
(''x'') function, whereas for ''a'' = ''b'' = 1 and ''c'' = ''d'' = 0, the term becomes equal to
sinh(''x'').
See also
*
Activation function
In artificial neural networks, the activation function of a node defines the output of that node given an input or set of inputs.
A standard integrated circuit can be seen as a digital network of activation functions that can be "ON" (1) or " ...
*
e (mathematical constant)
The number , also known as Euler's number, is a mathematical constant approximately equal to 2.71828 that can be characterized in many ways. It is the base of the natural logarithms. It is the limit of as approaches infinity, an expressi ...
*
Equal incircles theorem, based on sinh
*
Hausdorff distance In mathematics, the Hausdorff distance, or Hausdorff metric, also called Pompeiu–Hausdorff distance, measures how far two subsets of a metric space are from each other. It turns the set of non-empty compact subsets of a metric space into a me ...
*
Inverse hyperbolic function
In mathematics, the inverse hyperbolic functions are the inverse functions of the hyperbolic functions.
For a given value of a hyperbolic function, the corresponding inverse hyperbolic function provides the corresponding hyperbolic angle. Th ...
s
*
List of integrals of hyperbolic functions
*
Poinsot's spirals
*
Sigmoid function
A sigmoid function is a mathematical function having a characteristic "S"-shaped curve or sigmoid curve.
A common example of a sigmoid function is the logistic function shown in the first figure and defined by the formula:
:S(x) = \frac = \ ...
Notes
References
Further reading
* (20 pages
{{DEFAULTSORT:Modified Hyperbolic Tangent
Elementary special functions
Exponentials
Analytic functions
Functions and mappings
Artificial neural networks