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{{Short description|Mathematical function having a characteristic S-shaped curve or sigmoid curve}}
{{Use dmy dates|date=July 2022|cs1-dates=y}}
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[[File:Logistic-curve.svg|thumb|320px|right|The [[logistic curve]]]]
[[File:Error Function.svg|thumb|right|320px|Plot of the [[error function]]]]
A '''sigmoid function'''
:<math>\sigma(x) = \frac{1}{1 + e^{-x}} = \frac{e^x}{1 + e^x} = 1 - \sigma(-x).</math>▼
In many fields, especially in the context of [[Neural network (machine learning)|artificial neural networks]], the term "sigmoid function" is correctly recognized as a synonym for the logistic function. While other S-shaped curves, such as the [[Gompertz function|Gompertz curve]] or the [[Ogee|ogee curve]], may resemble sigmoid functions, but they are distinct mathematical functions with different properties and applications.
▲:<math>\sigma(x) = \frac{1}{1 + e^{-x}} = \frac{e^x}{1 + e^x}=1-\sigma(-x).</math>
Sigmoid functions, particularly the logistic function, have a domain of all [[Real number|real numbers]] and typically produce output values in the range from 0 to 1, although some variations, like the [[Hyperbolic functions|hyperbolic tangent]], output values between −1 and 1. These functions are commonly used as [[Activation function|activation functions]] in artificial neurons and as [[Cumulative distribution function|cumulative distribution functions]] in [[statistics]]. The logistic sigmoid is also invertible, with its inverse being the [[Logit|logit function]].
== Definition ==
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{{Commons category|Sigmoid functions}}
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