neural network - What kind can be the function of artificial neurone? -

i have whole thing structured in head want confirm it.

we have neural network 3 layers.

1. we input xs , weights ws (we choose ws on random @ beginning).
2. the neurone sums x*w inputs (or can there different function in here , if yes why need it, in scenario).
3. we pass sum activation function , pass output of function next neurones in next layer.
4. while training network use back-propagation (if have nn without hidden layers) , wait train.

so question sum function, can different , if yes why?

also quick question if want train nn solve a*x^2 +b*x+c=y , have random values x , corresponding y design of network? how many layers need?

regarding 2).that's more function more used, nonlinear weighted sum, in more general form f(x) = sum(w*g(x)) g(x) function. can change f(x) , g(x) won't recommended unless have reason that. pass result of f(x) activation function. advise read activation function available , why use 1 of another, maybe you: https://stats.stackexchange.com/questions/35776/choice-of-neural-net-hidden-activation-function

for number of hidden layers: https://stats.stackexchange.com/questions/181/how-to-choose-the-number-of-hidden-layers-and-nodes-in-a-feedforward-neural-netw

depens on data basically.

i think question belong site cross-validated.

cheers!