Sigmoid Function
Sigmoid Function
\[y = \frac{a}{1+e^{-bx}}\]
Variables
y = function value
a = upper limit value
b = growth steepness constant
x = independent variable
Description
What is this formula?
This formula represents a sigmoid function, an S-shaped curve commonly used to model smooth transitions between two states.
When to use it
Use this formula when modeling gradual activation, saturation effects or bounded growth processes.
Example
For:
a=1
b=2
x=1
y=1/(1+(℮^(-2*1)))
y≈0.881
Applications
Artificial neural networks
Machine learning
Population models
Control systems
Biological processes
Probability models
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