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I. Introduction to Neural Networks A simple mathematical representation of a neuron is shown in Figure 2. The notation to be used denotes the inputs as x, the weights as w, the summed output (pre-threshold) as yin, and the final output as y. Subscripts follow these letters where necessary to distinguish among multiple inputs, weights, etc. Thus, for the single neuron shown with N inputs, the inputs are denoted by x1, x2, ..., xN with corresponding weights w1, w2, ..., wN. The pre-threshold output yin is a sum of each input multiplied by the weight on its line. The threshold function will arbitrarily produce binary outputs for y - i.e. zero if the sum is less than a defined threshold value θ, or one if yin is equal to or exceeds the threshold.For supervised learning, neural networks are trained to map input patterns to desired outputs (i.e. target values). A modified threshold function, which proves more useful with various learning algorithms, produces bipolar (-1 or +1) rather than binary outputs. Also, an additional fixed input of +1 may be provided with the weight on the connecting line referred to as a bias value (b). This allows flexibility is setting of the threshold value θ.
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