# Which functions can be activation functions?

What are the required characteristics of an activation function (in a neural network)? Which functions can be activation functions?

For example, which of the functions below can be used as an activation function?

$$f(x) = \frac{2}{\pi} \tan^{-1}(x)$$

which looks like

or

$$f(x) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{x} e^{-\frac{t^2}{2}} dt$$

which looks

• the derivative of the activation function should be easy to compute , so the first one is better than the second. – riemann77 Jun 5 '18 at 11:06