Networks of Neurons - Computational Explorations in Cognitive Neuroscience - page 109

Species Name Color Size Food Toy

Cat Morris Orange Small Grass String

Socks Black & White Small Bugs Feather

Sylvester Black & White Small Grass String

Garfield Orange Medium Scraps String

Fuzzy White Medium Grass Feather

Dog Rex Black Large Scraps Bone

Fido Brown Medium Shoe Shoe

Spot Black & White Medium Scraps Bone

Snoopy Black & White Medium Scraps Bone

Butch Brown Large Shoe Shoe

Tab le 3 . 1 : Feature values for the individual cats and dogs used in this exploration.

This lower harmony reflects the fact that the more con-
straints you impose externally, the less likely the net-
work will be able to satisfy them as well. Put another
way, Cat is an easy constraint to satisfy, so the result-
ing harmony is large. Cat plus Orange is harder to
satisfy because it applies to fewer things, so the har-
mony is lower.
There are a seemingly infinite number of different
ways that you can query the network — go ahead and
present different input patterns and see what kinds of
responses the network gives you. Most of them will we
hope be recognizable as a reasonable response to the set
of constraints provided by the input pattern.
It is sometimes interesting to try to figure out how the
activation spreads through the network as it settles. You
can open up a GridLog for this purpose. It shows the
state of the network every grid_interval (default
= 5) cycles of updating.

a) b) c)

Figure 3.28: Necker cube a) , which can be seen as looking
down on it b) or looking up at it c) .

use is the Necker cube , which is shown in figure 3.28,
and can be viewed as a cube in one of two orientations.
People tend to oscillate back and forth between view-
ing it one way versus the other. However, it is very rare
that they view it as both at the same time — in other
words, they tend to form a consistent overall interpre-
tation of the ambiguous stimulus. This consistency re-
flects the action of a constraint satisfaction system that
favors interpretations that maximize the constraints im-
posed by the possible interpretations. Alternatively, we
can say that there are two stable attractors, one for each
interpretation of the cube, and that the network will be
drawn into one or the other of these attractor states.

Press View and select GRID_LOG to open the grid

log.
Have fun experimenting!

, !

Go to the PDP++Root window. To continue on to
the next simulation, close this project first by selecting
.projects/Remove/Project_0 . Or, if you wish to
stop now, quit by selecting Object/Quit .

, !

Open the project necker_cube.proj.gz in
chapter_3 to begin. Press the Init button in the net-
work window (located in the group of buttons on the left
of the window).
This should update the display (figure 3.29) so that
you can see two “cubes” with units at each vertex, with
each cube representing one of the two possible interpre-

, !

3.6.5 Explorations of Constraint Satisfaction:

Necker Cube

Now, lets explore the use of constraint satisfaction in
processing ambiguous stimuli. The example we will