As you can see in what I just posted about an inch below this, my point is that the process of training a NN does not involve adjusting any parameter to any non-linear functions. What goes into an activation function is a pure sum of linear multiplications and an add, but there's no "tunable" parameter (i.e. adjusted during training) that's fed into the activation function.
If course they do exist. A parameterized activation function is the most obvious thing to try in NN design, and has certainly been invented/studied by 1000s of researchers.
