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".<p>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 <i>something</i>. There are also many papers that discuss possible theoretical implications of experimental results.<p>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)".<p>What would a satisfactory "why" even look like exactly? As in, what form might it take compared to some other scientific discipline where we <i>do</i> know what's going on?<p>Personally, I think the whole thing is a red herring -- people in the field have <i>some idea</i> 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.<p>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.