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A quick look at neural systems..
A typical neural network is composed of layers of neurons, with mesh-like connections between consecutive layers. Each neuron assumes a single value per activation, but this value may affect all the neurons in the next layer differently, according to the weights assigned to the connections between that neuron and the neurons in the next layer. Often a bias neuron is added, whose value is always 1.
For instance, a neural net with 10 input neurons (plus a bias unit), no hidden (intermediate) layers, and 10 output neurons, would typically have 110 connections, with each connection being an adjustable (Learnt) weight.