Combined Model and Task Learning, and Other Mechanisms - Computational Explorations in Cognitive Neuroscience - page 186

of adapting weights going from the context to the hid-
den layer that can adapt to a fixed (or slowly updating)
transformation of the hidden layer representations by
the context layer. This point will be important for the
possible biological implementation of context.
Although it is not essential that the context layer be
a literal copy of the hidden layer, it is essential that the
context layer be updated in a very controlled manner.
For example, an alternative idea about how to imple-
ment a context layer (one that might seem easier to
imagine the biology implementing using the kinds of
network dynamics described in chapter 3) would be to
just have an additional layer of “free” context units,
presumably recurrently connected amongst themselves
to enable sustained activation over time, that somehow
maintain information about prior states without any spe-
cial copying operation. These context units would in-
stead just communicate with the hidden layer via stan-
dard bidirectional connections. However, there are a
couple of problems with this scenario.
First, there is a basic tradeoff for these context units.
They must preserve information about the prior hidden
state as the hidden units settle into a new state with a
new input, but then they must update their representa-
tions to encode the new hidden state. Thus, these units
need to be alternately both stable and updatable, which
is not something that generic activation functions do
very well, necessitating a special context layer that is
updated in a controlled manner rather than “free” con-
text units. Second, even if free context units could strike
a balance between stability and updating through their
continuous activation trajectory over settling, the error-
driven learning procedure (GeneRec) would be limited
because it does not take into account this activation tra-
jectory; instead, learning is based on the final activation
states. Controlled updating of the context units allows
both preserved and updated representations to govern
learning. For these reasons, the free context representa-
tion does not work, as simulations easily demonstrate.
For most of our simulations, we use a simple copy-
ing operation to update the context representations. The
equation for the update of a context unit cj is:

Output

Hidden

(copy)

Input Context

Figure 6.12: Simple recurrent network (SRN), where the
context layer is a copy of the hidden layer activations from
the previous time step.

networks. The category that includes both models is
known as a simple recurrent network or SRN ,which
is the terminology that we will use. The context repre-
sentation in an SRN is contained in a special layer that
acts just like another input layer, except that its activity
state is set to be a copy of the prior hidden or output unit
activity states for the Elman and Jordan nets, respec-
tively (figure 6.12). We prefer the hidden state-based
context layer because it gives the network considerable
flexibility in choosing the contents of the context rep-
resentations, by learning representations in the hidden
layer. This flexibility can partially overcome the essen-
tially Markovian copying procedure.
We adopt the basic SRN idea as our main way of
dealing with sequential tasks. Before exploring the ba-
sic SRN, a couple of issues must be addressed. First,
the nature of the context layer representations and their
updating must be further clarified from a computational
perspective. Then we need to examine the biological
plausibility of such representations. We then explore a
simulation of the basic SRN.

6.6.1 Computational Considerations for Context

Representations

In the standard conception of the SRN, the context layer
is a literal copy of the hidden layer. Although this is
computationally convenient, it is not necessary for the
basic function performed by this layer. Instead, the
context layer can be any information-preserving trans-
formation of the hidden layer, because there is a set

(6.2)

( t )= fm
hid

( t ￿ 1) + fm
prv

( t ￿ 1)

where the parameter fm hid (meaning “from hidden,” a