Limitations of Perceptrons

As described so far, we can use a perceptron to implement AND, NAND, and OR logic gates. In this next section, you will consider an XOR gate.

XOR Gate

An XOR gate is a gate circuit that is also called an exclusive OR. As shown in Figure 2.5, the output is 1 when either x1 or x2 is 1 ("exclusive" means "limited to only one person"). What should be the value of the weights to realize the XOR gate by using a perceptron?

Figure 2.5: Truth table of an XOR gate

In fact, we cannot build this XOR gate by using the perceptron that we have learned about so far. Why can we not build XOR even though we can build AND and OR gates?

First, let's examine the behavior of an OR gate visually. An OR gate satisfies the truth table in Figure 2.5 when the weight parameters are (b, w1, w2) = (-0.5, 1.0, 1.0), for example. In this case, the perceptron is represented by equation (2.3):

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