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A sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the logistic function , which is defined by the formula: [ 1 ]
The swish family was designed to smoothly interpolate between a linear function and the ReLU function. When considering positive values, Swish is a particular case of doubly parameterized sigmoid shrinkage function defined in [2]: Eq 3 . Variants of the swish function include Mish. [3]
The standard logistic function is the logistic function with parameters =, =, =, which yields = + = + = / / + /.In practice, due to the nature of the exponential function, it is often sufficient to compute the standard logistic function for over a small range of real numbers, such as a range contained in [−6, +6], as it quickly converges very close to its saturation values of 0 and 1.
The generalized logistic function or curve is an extension of the logistic or sigmoid functions. Originally developed for growth modelling, it allows for more flexible S-shaped curves. The function is sometimes named Richards's curve after F. J. Richards, who proposed the general form for the family of models in 1959.
In mathematics, the sign function or signum function (from signum, Latin for "sign") is a function that has the value −1, +1 or 0 according to whether the sign of a given real number is positive or negative, or the given number is itself zero.
In mathematics, S-function may refer to: sigmoid function; Schur polynomials; A function in the Laplace transformed 's-domain' In computer science, It may be member of a series of graph parameters, see Treewidth § Hadwiger number and S-functions; In physics, it may refer to: action functional; In MATLAB, it may refer to:
The activation function of a node in an artificial neural network is a function that calculates the output of the node based on its individual inputs and their weights. Nontrivial problems can be solved using only a few nodes if the activation function is nonlinear .
S-curve (math), a characteristic S-shaped curve of a sigmoid function; S-curve corset, an Edwardian corset style; S-Curve Records, a record company label; Reverse curve, or "S" curve, in civil engineering