Lines and Xor

• Note that (using a linear transfer function), a perceptron reduces the dimension from 2 (or n) to 1.
• Using a step function, it is a linear classifier.
• It returns true if the input is on one side of a line, and false if it's on the other.
• You can of course have three inputs, and it's a planar separator, and four or more gives a hyperplaner separator.
• However, a line cannot solve the xor problem.
• Thus a perceptron cannot solve the xor problem.
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• Indeed any number of perceptrons together do the same thing.
• However, if you put the perceptrons in layers, you can.
• The input from one layer of perceptrons goes into a second layer.