Is there a way to understand, for instance, a multi-layered perceptron without hand-waving about them being similar to brains, etc?
For example, it is obvious that what a perceptron does is approximating a function; there might be many other ways, given a labelled dataset, to find the separation of the input area into smaller areas that correspond to the labels; however, these ways would probably be computationally rather ineffective, which is why they cannot be practically used. However, it seems that the iterative approach of finding such areas of separation may give a huge speed-up in many cases; then, natural questions arise why this speed-up may be possible, how it happens and in which cases.
One could be sure that this question was investigated. If anyone could shed any light on the history of this question, I would be very grateful.
So, why are neural networks useful and what do they do? I mean, from the practical and mathematical standpoint, without relying on the concept of "brain" or "neurons" which can explain nothing at all.