In this example, the network learns to add binary numbers. Using an SRN, we feed the two numbers in bit-by-bit, starting with the lowest-order bits. On each step, the network must output the corresponding bit of the sum.

This is actually like an extension of the XOR problem. On the first pair of bits the network must compute an XOR and possibly retain a carry. On subsequent bits, the network must add the two bits and the carry and output their parity.

Because this is so related to the XOR problem, it should not be surprising that the network sometimes fails to learn. Try training several times. You should find that the network masters the task about half the time. When the network does succeed, you'll usually see that learning didn't occur in a smooth progression. It tends to reach plateaus on which it slowly reorganizes its internal representations before achieving a breakthrough.

Try examining the representations and link structure of a network that has mastered the task. Can you figure out how the network is solving it? Try examining the context-to-hidden projection to see how the carry is represented and used.

Can you get the network to learn the task 100% of the time? Try putting the example set in PERMUTED mode using the exampleSetMode command. Now use a smaller batch size, around 10 or 20. This can have the effect of adding a little noise in the system. Full batches aren't always the best way to learn.

Douglas Rohde Last modified: Fri Nov 17 15:24:40 EST 2000