Comment by eru

Huh? Who says anything about 'precise functions'? And what's a precise function in the first place?

I am saying that training (at least for conventional neural nets) only fiddles with some parameters. But it does not change the shape of the network, no new nodes nor different connections. (Which is almost equivalent to saying training doesn't change the abstract syntax tree, if you were to write the network out as a procedure in, say, Python.)

The geometric shape you get when you print out the function changes, yes.