This is similar to the adder2.in example, except that the network must now add base-10 numbers. Two networks have been created: adder-a and adder-b.

Let's start with the adder-a network. This is a standard SRN. You will probably find that the network learns the task fairly consistently, although the learning gets slow near the end and you may need 1000 or 1500 updates to get really good performance.

The adder-b network has an architecture specifically designed for this task. There is a single "carry" unit that feeds back into the hidden layer. We're hoping the network will be able to learn to use this unit to represent the carry.

Compare the training curve of adder-b to that of adder-a. You'll probably find that adder-b settles into a local minimum. If you watch the value in the carry group, it isn't doing much, and the network is hedging its bets about whether there is a carry and guessing two digits in the output.

Why can't this network learn? We'll, lets think about the SRN learning rule for a minute. The standard SRN backprop phase only occurs over the current tick. It does not extend backward in time. So, in fact, there is no teaching signal for the hidden-to-carry weights. Those weights never change and the network can't learn to use its carry unit effectively.

We can make things easier for the network by setting the backpropTicks to 2. This will extend the backprop phase backward one tick in time. This is enough to provide a training signal for the hidden-to-carry units that will allow it to learn. Try setting the backpropTicks to 2 and increasing the learning rate to 0.2. Has the network learned to use the carry group as a carry or anti-carry?

Douglas Rohde Last modified: Fri Nov 17 16:23:18 EST 2000