The XOr, or “exclusive or”, the problem is a classic problem in ANN research. It is the main problem of using a neural network to predict the outputs of XOr logic gates given two binary inputs. A XOr function should return a true value if the two inputs are not equal and a false value if they are equal. All the possible inputs and their predicted outputs are shown below:
Like all ANNs, the perceptron is composed of a network of units, which are analogous to biological neurons. A unit can receive input from other units. In doing so, it takes the sum of all values received and decides whether it is going to forward a signal on to other units to which it is connected. This is called activation. The activation function helps to reduce the sum of input values to a 1 or a 0 (or a value very close to a 1 or 0) in order to represent activation or lack thereof. Another form of unit, known as a bias unit, always activates, typically sending a hardcoded 1 to all units to which it is connected.
Perceptrons include a single layer of input units including one bias unit and a single output unit (as seen below). Here a bias unit is depicted by a dashed circle, while other units are shown as blue circles. There are two non-bias input units representing the two binary input values for XOr. Any number of input units can be included.
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