f(x) = 1
1 + e
when e is the exponential function
and B is a parameter to adjust the steepness.
This function has the following properties:
One practical application of this function is the firing function in multi-layer perceptron neural networks.
It is used because of its simple derivative:
f'(x) = -Bx
( 1 + e )
= B f(x) (1 - f(x))