Artificial Intelligence By Example

The XOR limit of a linear model, such as the original perceptron

A linear model cannot solve the XOR problem expressed as follows in a table:

Value of x1	Value of x2	Output
1	1	0
0	0	0
1	0	1
0	1	1

 

The following graph shows the linear inseparability of the XOR function represented by one perceptron:

The values of the table represent the Cartesian coordinates in this graph. The circle with a cross at (1,1) and (0,0) cannot be separated from the circles at (1,0) and (0,11). That's a huge problem. It means that Frank Rosenblatt's f(x,w) perceptron cannot separate, and thus not classify, these dots into clouds and trees; an object ...