Introduction and Overview - Computational Explorations in Cognitive Neuroscience - page 7

erating at the level of individual neurons to explain
even relatively complex, high-level cognitive phenom-
ena. This raises the question as to why these basic
neural mechanisms should have any relevance to un-
derstanding something that is undoubtedly the product
of millions or even billions of neurons — certainly we
do not include anywhere near that many neurons in our
simulations! This scaling issue relates to the way in
which we construct a scaled-down model of the real
brain. It is important to emphasize that the need for
scaling is at least partially a pragmatic issue having to
do with the limitations of currently available computa-
tional resources. Thus, it should be possible to put the
following arguments to the test in the future as larger,
more complex models can be constructed. However,
scaled-down models are also easier to understand, and
are a good place to begin the computational cognitive
neuroscience enterprise.
We approach the scaling problem in the following
ways.

a) b)

Figure 1.3: Illustration of scaling as performed on an image
— the original image in (a) was scaled down by a factor of
8, retaining only 1/8th of the original information, and then
scaled back up to the same size and averaged (blurred) to pro-
duce (b), which captures many of the general characteristics
of the original, but not the fine details. Our models give us
something like this scaled-down, averaged image of how the
brain works.

or down along this content dimension, but it seems rea-
sonable to allow that some important properties might
be relatively scale invariant. For example, one could
plausibly argue that each major area of the human cor-
tex could be reduced to handle only a small portion of
the content that it actually does (e.g., by the use of a

The target cognitive behavior that we expect (and ob-
tain) from the models is similarly scaled down com-
pared to the complexities of actual human cognition.

We show that one of our simulated neurons (units)
in the model can approximate the behavior of many
real neurons, so that we can build models of multi-
ple brain areas where the neurons in those areas are
simulated by many fewer units.

pixel retina instead of 16 million x 16 million
pixels), but that some important aspects of the essential
computation on any piece of that information are pre-
served in the reduced model. If several such reduced
cortical areas were connected, one could imagine hav-
ing a useful but simplified model of some reasonably
complex psychological phenomena.
The second argument can perhaps be stated most
clearly by imagining that an individual unit in the model
approximates the behavior of a population of essentially
identical neurons. Thus, whereas actual neurons are dis-
cretely spiking, our model units typically (but not ex-
clusively) use a continuous, graded activation signal.
We will see in chapter 2 that this graded signal pro-
vides a very good approximation to the average num-
ber of spikes per unit time produced by a population of
spiking neurons. Of course, we don't imagine that the
brain is constructed from populations of identical neu-
rons, but we do think that the brain employs overlapping
distributed representations, so that an individual model
unit can represent the centroid of a set of such repre-

16 x 16

We argue that information processing in the brain
has a fractal quality, where the same basic proper-
ties apply across disparate physical scales. These ba-
sic properties are those of individual neurons, which
“show through” even at higher levels, and are thus
relevant to understanding even the large-scale behav-
ior of the brain.

The first argument amounts to the idea that our neu-
ral network models are performing essentially the same
type of processing as a human in a particular task, but
on a reduced problem that either lacks the detailed in-
formation content of the human equivalent or represents
a subset of these details. Of course, many phenomena
can become qualitatively different as they get scaled up