Is Wikipedia's page on the sigmoid function incorrect?
It states that:
A common example of a sigmoid function is the logistic function
From my knowledge of machine learning, I thought that "the sigmoid function" is defined as the logistic function, $$\sigma(z) = \frac {1} {\left(1 + e^{-z}\right)}\text{.}$$ I have never seen or heard the phrasing that the logistic function is a type of sigmoid function.
Furthermore, that Wikipedia page says that other examples of a sigmoid function are the tanh and arctan functions. Again, I've never seen tanh nor arctan described as a type of sigmoid function.
These functions are considered to be peers, usually in a context like:
We can use various non-linear functions in this neural network, such as the sigmoid, tanh, and ReLU activation functions.
What am I missing here? Is the Wikipedia article correct or incorrect? I find that Wikipedia is usually accurate for math terms.
Best Answer
The unsatisfying answer is "It depends who you ask." "Sigmoid", if you break it into parts, just means "S-shaped".
The logistic sigmoid function is so prevalent that people tend to gloss over the word "logistic". For machine learning folks, it's become the exemplar of the class, and most call it the sigmoid function. (Is it myopia to call it the sigmoid function?) Still, there are other communities that use S-shaped functions.