6.3 Computer Science - Pattern Recognition

An approach to solving the XOR function is to map the problem to three dimensions, by including a third input, x3, which moves the point at x_1 = 1, x_2 = 1 along a third dimension but does not change the result when it is looked at using a projection into the x_1, x_2 plane. This allows a linear plane (the 2D analog of a straight line) to separate the points. (a) Construct a truth table for XOR with three inputs, (b) plot a decision plane in a 3D diagram and (c) show how this could be implemented with a neural network.