What's inside a deep neural network

Say you have a cutting-edge gadget that can crack any safe in the world--but you haven't got a clue how it works. You could take a much older safe-cracking tool--a trusty crowbar, perhaps. You could use that lever to pry open your gadget, peek at its innards, and try to reverse-engineer it. As it happens, that's what scientists have just done with mathematics. Researchers have examined a deep neural network--one type of artificial intelligence, a type that's notoriously enigmatic on the inside--with a well-worn type of mathematical analysis that physicists and engineers have used for decades.