Example of convex activation function For a particular task, I need a convex activation function with the following properties:


f''(x) > 0
0 &lt;=    f(x) &lt;=  1
f(x) is monotonic
f(x) is not "exploding" i.e. avoiding functions such as f(x) = x²


The only example I have in mind for this is the softplus activation function. Would you have anything else in mind?
There is no such function.

A convex function defined on all of $\mathbb{R}$ with bounded range is constant.