out of these affine mapping formulas so there's a lot of applications for complexity measures for example you might want to compare two deep networks one which has a very complicated prediction function the other that solves the same task but has a much simpler prediction function Occam's razor type idea we might also want to apply a complexity measure as a penalty directly to our to our learning process right so there's a large literature of deriving different complexity measures and complexity penalties for deep nets all this point