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The activation function of a node in an artificial neural network is a function that calculates the output of the node based on its ... Hyperbolic tangent ...
Derivative of the function is defined by the formula: ′ + + + The following conditions are keeping the function limited on y-axes: a ≤ c, b ≤ d.. A family of recurrence-generated parametric Soboleva modified hyperbolic tangent activation functions (NPSMHTAF, FPSMHTAF) was studied with parameters a = c and b = d. [9]
A wide variety of sigmoid functions including the logistic and hyperbolic tangent functions have been used as the activation function of artificial neurons. Sigmoid curves are also common in statistics as cumulative distribution functions (which go from 0 to 1), such as the integrals of the logistic density , the normal density , and Student's ...
A widely used type of composition is the nonlinear weighted sum, where () = (()), where (commonly referred to as the activation function [3]) is some predefined function, such as the hyperbolic tangent, sigmoid function, softmax function, or rectifier function. The important characteristic of the activation function is that it provides a smooth ...
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t , sin t ) form a circle with a unit radius , the points (cosh t , sinh t ) form the right half of the unit hyperbola .
[13] [14] In 2011, [4] ReLU activation enabled training deep supervised neural networks without unsupervised pre-training, compared to the widely used activation functions prior to 2011, e.g., the logistic sigmoid (which is inspired by probability theory; see logistic regression) and its more practical [15] counterpart, the hyperbolic tangent.
The Gudermannian function is a sigmoid function, and as such is sometimes used as an activation function in machine learning. The (scaled and shifted) Gudermannian function is the cumulative distribution function of the hyperbolic secant distribution. A function based on the Gudermannian provides a good model for the shape of spiral galaxy arms ...
where is the hyperbolic tangent function, is the carrying capacity, and both and > jointly determine the growth rate. In addition, the parameter γ {\displaystyle \gamma } represents acceleration in the time course.