Yeah.
Um. I mean , it seems to me , if you have exactly the right thing then it 's better to do it without the net because otherwise you 're asking the net to learn this  you know , say if you wanted to learn how to do multiplication.
Mm - hmm.
I mean you could feed it a bunch of s you could feed two numbers that you wanted to multiply into a net and have a bunch of nonlinearities in the middle and train it to get the product of the output and it would work. But , it 's kind of crazy , cuz we know how to multiply and you  you 'd be you know much lower error usually  if you just multiplied it out. But suppose you don't really know what the right thing is. And that 's what these sort of dumb machine learning methods are good at. So. Um. Anyway. It 's just a thought.