Machine learning works spectacularly well, but mathematicians aren’t sure why
In addition to "We need a cluster for deep learning", the second most popular mostly untrue thing I hear is "We have no idea how neural networks learn".However, there are many papers that explore various ways to make a network learn, and they keep improving on performance, suggesting they're on to something. There are also many papers that discuss possible theoretical implications of experimental results.But what does Knowing Why The Network Works mean exactly? "It works because universal approximation and gradient descent", but that's not a very satisfactory answer. "It works because it starts at a general solution and, over the course of many iterations, takes many small steps in an ever changing direction defined by a gradient approximation generated by looking at the difference between an average error and a target output (which should trend towards 0)".What would a satisfactory "why" even look like exactly? As in, what form might it take compared to some other scientific discipline where we do know what's going on?Personally, I think the whole thing is a red herring -- people in the field have some idea of how neural nets work, and there are many disciplines considered by many to be mature sciences that are far from settled on a grand theoretical scale.That said, the theory I'm most interested in is recent attempts to connect a memory module to neural networks so they can "learn" to store important/complex/distributed information that can be recalled with high accuracy later. That will make it easier to do things like ask a neural network to remember your name, or where you left your keys, or whatever.