Sigmoid Function(Activation Function In Neural Network)

A Sigmoid Activation Function is a fine function which has a characteristic S- shaped wind. There are a number of common sigmoid functions, similar as the logistic function, the hyperbolic digression, and the arctangent.

sigmoid function is commonly used to relate specifically to the logistic function, also called the logistic sigmoid function. 

 All sigmoid functions have the property that they collude the exclusive opus line into a small range similar as between 0 and 1, or-1 and 1, so one use of a sigmoid function is to convert a real value into bone that can be explicated as a probability. 



Sigmoid functions have come popular in deep literacy because they can be used as an activation function in an artificial neural network. They were inspired by the activation eventuality in natural neural networks.

Sigmoid functions are also useful for numerous machine literacy operations where a real number needs to be converted to a probability. A sigmoid function placed as the last subcaste of a machine literacy model can serve to convert the model's affair into a probability score, which can be easier to work with and interpret.


Sigmoid functions are an important part of a logistic retrogression model. Logistic retrogression is a revision of direct retrogression for two- class bracket, and converts one or further real- valued inputs into a probability, similar as the probability that a client will buy a product. The final stage of a logistic retrogression model is frequently set to the logistic function, which allows the model to affair a probability.



Sigmoid Function Formula

All sigmoid functions are monotonic and have a bell- shaped first outgrowth. There are several sigmoid functions and some of the best- known are presented below.


Logistic Sigmoid Function Formula

One of the commonest sigmoid functions is the logistic sigmoid function. This is often referred to as the Sigmoid Function in the field of machine learning. The logistic sigmoid function is defined as follows:

Mathematical definition of the logistic sigmoid function, a common sigmoid function

The logistic function takes any real-valued input, and outputs a value between zero and one.

Hyperbolic Tangent Function Formula

Another common sigmoid function is the hyperbolic function. This maps any real- valued intake to the pasture between-1 and 1.


Arctangent Function Formula

A third volition sigmoid function is the arctangent, which is the antipode of the digression function.


Now Look What Is Activation Function In Neural Network?

Activation function in neural network decides, whether a neuron should be actuated or not by calculating weighted sum and farther adding bias with it. The purpose of the activation function is to introduce non-linearity into the affair of a neuron.

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