Artificial Neural Networks

Artificial Neural Networks, known affectionately as "networks", constitute a class of signal processing algorithms 1 that bear some, however remote, resemblance to wetware neural networks, such as the nervous systems of animals (like the human brain). Still, this is not really artificial intelligence, at least not on its own, and this is not a good mathematical model of actual physico-chemical brains.
Several scientific communities 2 contribute to the theory of artificial neural networks, and most of these have their own viewpoints on them.

Artificial neural networks have proven to be practical, robust tools, that are used in many applications: distinguishing bombs and weapons from alarm-clocks in semi-automatic airport x-ray, translating spoken words into computer commands and the control of autonomous robots to mention a few. Some of the network theory helps by defining a conceptual vocabulary that enables scientists to more accurately describe the vastly more complex phenomenon that we observe in e g our own brains.

As usual, there are problems as well. Even if you have a nice network that does its job, it is almost impossible to tell just how it does it. This goes along the same lines as asking a natural talent how she does whatever she is good at. They just do it. Artificial neural networks also typically involve the use of non-linear optimisation (explained later), and are then largely dependent on the performance of this rather difficult procedure.