\( \newcommand{\matr}[1] {\mathbf{#1}} \newcommand{\vertbar} {\rule[-1ex]{0.5pt}{2.5ex}} \newcommand{\horzbar} {\rule[.5ex]{2.5ex}{0.5pt}} \)
deepdream of a sidewalk
Show Question
Logistic sigmoid


$\sigma(x) = \frac{1}{1+e^{-x}}$

The logistic sigmoid:


The logistic function is a special case sigmoid function.

A sigmoid function is a mathematical function having an "S" shaped curve (sigmoid curve). A wide variety of sigmoid functions have been used as the activation function of artifical neurons. They are used to produce the $\phi$ parameter of a Bernoulli distribution.

A collection of sigmoid functions, normalized to have a gradient of 1 at the origin: