The "somehow" part reminds me of studying differential equations. A lot of them can't be solved step-by-step analytically, like the equation for an RLC circuit, but some really smart guy figured them out through guesswork. Same goes for deep learning. A lot of these setups like the "Inception" framework and LeNet5 seem like a lot of clever guesswork and intuition. However, unlike differential equations, you can't know that you've actually solved the problem perfectly once you've figured out the answer. It's always just good enough util the next paper comes out claiming a better solution on whatever the latest canonical benchmark is.