Examples: rand10x40.in

This is a fairly simple feed-forward mapping task. There are 40 examples, each requiring the network to map from a random input to a random output. Although this could be solved with a standard feed-forward network, we have used a continuous network here to get you acquainted with them.

A continuous network generally has units that integrate their outputs over time, and thus adapt gradually to changes in their input. We have created a continuous network in this case by giving it the type CONTINUOUS.

When the network was created, we also specified that the network can run for at most 4.0 time intervals. You should think of a time interval as a unit of real time, like a second. So the network can process an example for at most four seconds. However, when we simulate the network, we can't actually run it continually like an analog system. We have to simulate it in discrete steps. Ideally, our grain size is small enough that we get a good approximation to the true continuous behavior.

The discrete steps at which we simulate the network are called ticks. When we defined the network, we specified that there should be 5 ticks per time interval. Thus, if we think of a time interval as representing a second, then we are simulating the network at a grain size of 200 milliseconds.

By default, the groups in a continuous network are given the OUT_INTEGR type. This integrates the units' outputs over time using the following formula:

    output += dt * (instantOutput - output);

The instant output is the output that the unit would have if we just computed its input and output without integrating. The integration function exchanges a certain percentage of this instant output for a percentage of the old output. The percentage is given by dt. If dt is small, the network will adapt slowly to new input. If dt is 1, the integrator will have no effect.

By default, the dt is set to the inverse of the number of ticks per time interval. In our case, dt will default to 0.2. You can change it if you would like the units to adapt more or less quickly. Each group also has a dtScale parameter which is multiplied by the network's dt to compute the actual dt used by the group. In this way, you can have one group that adapts at a different rate than the others, but still be able to adjust the dt of the whole system by just changing the network's value.

Once the network is constructed, it is possible to change the maximum number of intervals or the ticks per time interval using the setTime command. This will recalculate dt for you. If you want a different dt, you will have to change dt again afterwards, or use the -dtfixed parameter with setTime.

The Input group in this network will not be given a default integrator, because it is an INPUT group. For the Hidden group, we specified an IN_INTEGR, or input integrator. This is similar to the output integrator but does the integration on the input. Because we specified this, an output integrator will not be added. But we did not specify an integrator for the Output group, so it defaults to OUT_INTEGR.

Open the Unit Viewer and step through some examples. You can use the arrow buttons in the upper right to step through the ticks on the current example. Make sure you are looking at the training set and that the training set is set1. Don't worry about set2 yet.

You should notice a few things. On the initial tick, there are no inputs or targets. All of the units of groups with type RESET_ON_EXAMPLE, which is the default, are set to their default values. This is normal in a continuous network. For the next interval, or five ticks, there are inputs but no targets. This is because we have set the default graceTime of the example set to 1.0. The grace time is the delay, in time intervals, between input presentation and target presentation. It is frequently used in training continuous networks because it gives the network a chance to reach its targets before it is penalized.

On the next tick, 1:1 in event time or 1:2 in example time, the targets appear and they remain on. The examples will last at least 1.0 intervals, as determined by the minTime, and no more than 4.0 intervals, as determined by either the network's timeIntervals value or the example set's maxTime parameter.

Now open a graph of the error and train the network. You should see that it masters the task. Step through the examples again. Does it get the right outputs? Does it start heading in the righ direction even before the targets have appeared?

Now open a graph of the output of the first output unit, Output:0.output, and have it update every tick. Click on some examples. This shows you a profile of the unit activations. Since this is a simple task, they should be pretty smooth and monotone. Try changing the network's dt. You should see the curves change.

Now let's turn to set2. This one has slightly more complicated examples. In this case, the examples have two events. The first is the same as before, but it only lasts 2 intervals. The next event has the same targets but removes the input. Can the network maintain its activations when the inputs disappear? You will probably find that it can't. Now try training the network some more using set2. If you haven't reset the network since training on set1, the error will jump up a bit and then quickly fall away again. Now the network should be pretty good at maintaining its activations.

Take a look at the example file for set2, rand10x40b.ex, and see if you understand how it was specified. You may need to refer to the manual section on example files.

As is the default in a continuous network, the Output group has been given the STANDARD_CRIT criterion function. During testing, if every unit's output is within the testGroupCrit of its target at the end of each event, the example is considered correct. Try testing the network. At the end it tells you the percentage of examples for which the criterion was reached. If the network has been trained well, you should find that the network gets most examples correct with a testGroupCrit of 0.1 and all correct within a range of 0.2.

The output criterion is also used in continuous networks for deciding when to go on to the next event. If the event has gone past its minTime and all output units are within the trainGroupCrit of their targets, the network will immediately go on to the next event. Try setting the trainGroupCrit to 0.1.

Now click on an example in set2. Step through the example. You should see that as soon as all of the output units are within 0.1 of their target (and the event has lasted for its minTime), the next event begins.

Douglas Rohde
Last modified: Tue Nov 21 15:25:08 EST 2000