Neural networks are a computational paradigm inspired by the architecture of the human brain. The intuition is that since brains are good at solving problems, machines built in the same way should be, too.
The basic computational component of the brain is a neuron, a simple unit that produces a non-linear, weighted sum of its inputs, which are connections from other neurons. Neural networks are weighted digraphs with neurons as vertices and weights on edges denoting the connection strength of the pair.
Brains are very good at learning and recognizing certain patterns. Learning in brains seems to work by adding connections between different pairs of neurons and changing the strengths of the connections. Modifying connection strength in response to training examples provides a natural way to ``teach'' a neural network.
Although there have been attempts to apply neural networks to solving combinatorial optimization problems, the successes have been rather limited. Simulated annealing is a much more straightforward and efficient approach to optimization.
Neural networks have been more successful in classification and forecasting applications, such as optical character recognition, gene prediction, and stock-market time-series prediction. A set of features for the given patterns is selected, and each training example is represented in terms of its features. The network is trained on a series of positive and negative examples, with the strengths of the connections adjusted to recognize these examples. Output cells for each class of item are provided and the strength of these cells on a given input used to determine the classification. Once the network is trained, feature vectors corresponding to unknown items can be entered and a classification made.
Because neural networks are black boxes, with the strength of edges
adjusted only by the training examples,
there is usually no way to figure out exactly why they
are making the decisions that they are.
A particularly amusing instance where this led to trouble
is reported in Section 
.
Still, they can be useful in certain pattern-recognition applications.