Add some more input/output examples and re-train the network. Does this make it generalize better on new examples, or does it perform worse?

Restart the kernal, and then change the network so that it outputs the SUM of the two inputs, instead of the product. What do you have to change in order to do that?

Now make a new network that takes in four numbers (a, b, c and d). It should compute the sum of a and b (a + b) and the product of c and d (c * d). What changes are needed to make that happen?

Write down a few problems that you see in work or school that might be able to be solved with this type of neural network. What would the input matrix be? What would the output matrix be? How would you go about collecting that data?

Bonus: Actually go collect that data, and train a neural network on it!