“In the last couple of years, deep learning techniques have transformed the world of artificial intelligence. One by one, the abilities and techniques that humans once imagined were uniquely our own have begun to fall to the onslaught of ever more powerful machines. Deep neural networks are now better than humans at tasks such as face recognition and object recognition. They’ve mastered the ancient game of Go and thrashed the best human players.
But there is a problem. There is no mathematical reason why networks arranged in layers should be so good at these challenges.” […]
“Now that we finally understand why deep neural networks work so well, mathematicians can get to work exploring the specific mathematical properties that allow them to perform so well.”