Exercise 7.6 Suppose that, in the output of a neural network, we assign any value greater than 0.5 to be true and any less than 0.5 to be false (i.e., any positive value before the activation function is true, and a negative value is false).

Run the AIspace.org neural network learning applet on the data of Figure 7.9

(page 309) for a neural network with two hidden nodes. Given the final parameter settings found, give a logical formula (or a decision tree or a set of rules) that represents the Boolean function that is the value for the hidden units and the output units. This formula or set of rules should not refer to any real numbers.

[Hint: One brute-force method is to go through the 16 combinations of values for the inputs to each hidden unit and determine the truth value of the output. A better method is to try to understand the functions themselves.]

Does the neural network learn the same function as the decision tree?