Special Topics: Simple Recurrent Networks

Simple recurrent networks (SRNs) are similar to standard feed-forward networks in that information propagates all the way through the network during the forward pass on each tick. In such networks, groups are updated in the order in which they appear in the network's group array. A group update in this case consists of computing its inputs and immediately computing its outputs. This differs from fully recurrent networks which have all groups update their inputs and then have all groups compute their outputs. Therefore, we say that continuous networks have synchronous update and standard or simple recurrent networks have sequential update.

An SRN is just a feed-forward network with one or more ELMAN type groups. An Elman context group is affiliated with a source group that has the same number of units. The context group should have the type ELMAN, but the source group can have any type.

When the context group computes its output, each unit increments its output by the output of the corresponding unit in the source group. If ELMAN_CLAMP is the only output function, this essentially copies the outputs of the source group. Ordinarily, the context group should appear before the source group in the group order. In this case, the values copied will be the output of the source group from the previous tick. Therefore, the context group is able to provide a bit of history.

It is customary to create a normal projection from the context group back to the source group, but this need not be the case. You might chain context groups together to get a history of length two or three ticks. If the source group is the output layer and the context group projects to a hidden layer, you will have a Jordan network.

During training, standard networks, including SRNs, perform a backpropagation sweep on each tick immediately after the forward pass. Continuous networks, on the other hand, perform a single backprop sweep that runs from the end of the example to the beginning of the example. You can extend the backpropagation phases of an SRN by increasing the backpropTicks parameter. A value of 3 will mean that, after each tick, the error will be backpropagated across the current tick and the previous two ticks. This can help SRNs learn long or difficult sequences. However, the training time of the network will increase in proportion to the backpropTicks.

An alternative is to use a simple recurrent backprop through time (SRBPTT) network. This is similar to an SRN in that it uses sequential updating. But it is similar to a continuous backprop through time network in that it uses a single backward sweep that runs from the end of the example to the beginning. It is like having the number of backpropTicks always equal to the number of ticks in the example, but much more efficient because there is just a single backward pass, rather than one for each tick.

Building SRNs

A simple SRN can be constructed as follows:

    addNet srn -i 5
    addGroup input   4  INPUT
    addGroup hidden  10
    addGroup context 10 ELMAN
    addGroup output  4  OUTPUT
    connectGroups {input context} hidden output
    elmanConnect  hidden  context
    orderGroups bias input context hidden output

This is a network with 5 time intervals, but only 1 tick per time interval. We normally would not want a tick per time interval value other than 1 for an SRN. We give the context group the type ELMAN. Given that basic type, the default will be to have no input function, no bias inputs, and an ELMAN_CLAMP output function. Note that, in the group order, the context group must appear before its source group and all groups the context projects to. The orderGroups step could be avoided if the context group was initially created before the hidden group.

The addNet command is also able to construct Elman networks provided that the context group has full connectivity back into its source. The above network could have been built with this one command:

    addNet srn -i 5 4 10 ELMAN 4

Notice that there are only three groups specified in the group list to the addNet command. If the ELMAN type is used for a group, two groups will actually be created. The groups will have the same size but one will be a hidden (or output) layer with all of the specified types except -ELMAN and the other will be a context layer of type ELMAN. The context layer will precede the source layer in the group list and there will be an Elman connection from source to context and a full projection from context to source.

Unit Output Initialization

Before running the first tick of each example, any group with type RESET_ON_EXAMPLE (which is the default) will reset its outputs to the initOutput. If a source group is reset in this way, its context group will copy those initialized values. This is probably desirable if no information should be maintained from one example to the next.

However, if the examples form a sequence, you may want the context to carry from the end of one example to the beginning of the next. This can be done by giving the source groups the flag -RESET_ON_EXAMPLE when you specify its type. To save some time, you can change this flag in the call to elmanConnect with the "-reset" option. You can also set the source group's initOutput using the "-initOutput" option.

You can reset the source group on demand using the resetUnitValues command.

Extended Context Groups

It is possible to chain context groups together to get context that extends back in time more than one tick. To do this, just create more than one context group and elmanConnect the first to the second and so on. However, it is important to note that the groups must appear in reverse order in the group list so that information does not propagate all the way through them on a single tick. Here is an example of how to create a hidden layer with context from the previous three ticks:

    addGroup hidden 10
    addGroup context1 10 ELMAN
    addGroup context2 10 ELMAN
    addGroup context3 10 ELMAN
    elmanConnect hidden   context1
    elmanConnect context1 context2
    elmanConnect context2 context3
    connectGroups {context1 context2 context3} hidden
    orderGroups input context3 context2 context1 hidden output

Partial Simple Recurrent Backprop Through Time

In the basic SRN algorithm, the network learns to produce correct outputs on the current tick given whatever information happens to be in the context groups. However, there is no pressure to store particular representations in the context groups that will best aid in later outputs. Thus, standard SRNS can have trouble learning difficult temporal tasks.

To help remedy this problem, Lens provides an extension of the SRN algorithm that will backpropagate error across multiple ticks. This allows the weights to be adjusted based on the derivative of future error w.r.t. the weights, which can lead to significant performance improvements.

The backpropTicks parameter controls how far back error is propagated. The default value is 1, which acts like a normal SRN. A value of 3 would cause the error to be propagated back through 2 ticks prior to the current one.

Unless the hidden groups are reset at the start of each example, the backprop phase will wrap around from the start of the current example to the end of the previous example. In order for this to work properly, the historyLength should be at least as long as the backpropTicks. Therefore, if you are using a minimal history length, to set backpropTicks to 4, you will want to do:

    setObj backpropTicks 4
    setTime -h 4

In doing the extended backpropagation, only relevant groups are involved. Therefore, if your network has a small recurrent projection but a very large hidden to output projection, this could be relatively cheap because the hidden to output projection is ignored in the backpropagation. Using partial simple recurrent backprop through time can result in significant performance improvements.

Full Simple Recurrent Backprop Through Time

If you need to use very large backpropTicks values to learn a particular problem, the network could be rather slow to train. A better solution is provided by the simple recurrent backprop through time network. This is similar to an SRN in that it uses sequential updating. But it is similar to a continuous backprop through time network in that it uses a single backward sweep that runs from the end of the example to the beginning. The backpropagation does not extend from the start of an example to the end of the previous example. An SRBPTT network must be given the type SRBPTT when it is created, as in:

    addNet foo SRBPTT 10 20 ELMAN 10

The backpropTicks parameter does not affect SRBPTT networks. However, the historyLength should be as long as the maximum number of ticks per example for it to work properly.

Douglas Rohde
Last modified: Sat Nov 11 15:54:37 EST 2000