Perception and Attention - Computational Explorations in Cognitive Neuroscience - page 234

stead, we will use a single display of all of the receptive
fields at one time.

space of possible values (and combinations of values)
is reasonably well covered.
One of the most interesting aspects of the topography
of these representations (in the network as well as in V1
neurons) are pinwheels , where the orientation of the re-
ceptive fields varies systematically around 360 degrees
in the topographic space of the units.
Start at the hidden unit located 3 rows from the top in
column number 7, and note the orientation of the units
as you progress around a circle several units wide in
the surrounding units — they progress around the circle
of orientations. This structure can be seen as a conse-
quence of having smoothly varying neighborhood rela-
tionships — if each unit has an orientation coding simi-
lar but distinct from its neighbor, then one would expect
that they might proceed around the circle as one goes
further away.
The unit at the middle of the pinwheel represents a
singularity , which does not smoothly relate to neighbor-
ing unit values. Singularities also occur where there are
relatively abrupt changes in orientation mapping across
a short distance in the hidden unit topographic space.
Both of these phenomena are found in the topographic
representations of real V1 neurons, and provide an im-
portant source of data that models must account for to
fully simulate the real system (Swindale, 1996; Erwin
et al., 1995).
We can directly examine the weights of the simulated
neurons in our model, but not in the biological system.
Thus, more indirect measures must be taken to map
the receptive field properties of V1 neurons. One com-
monly used methodology is to measure the activation
of neurons in response to simple visual stimuli that vary
in the critical dimensions (e.g., oriented bars of light).
Using this technique, experimenters have documented
all of the main properties we observe in our simulated
V1 neurons — orientation, polarity, size, and location
tuning, and topography. We will simulate this kind of
experiment now.

To view this display, press View , RFIELDS in the
control panel, and select v1rf.rfs.log in response
to the file dialog that appears (you should be able to just
press Open ).
You will now see a grid log that presents the pat-
tern of receiving weights for each hidden unit, which
should look just like figure 8.8 (note that this is the same
as figure 4.9). To make it easier to view, this display
shows the off-center weights subtracted from the on-
center ones, yielding a single plot of the receptive field
for each hidden unit. Positive values (in red tones going
to a maximum of yellow) indicate more on-center than
off-center excitation, and vice versa for negative values
(in blue tones going to a maximum negative magnitude
of purple). The receptive fields for each hidden unit are
arranged to correspond with the layout of the hidden
units in the network. To verify this, look at the same
3 units that we examined individually, which are along
the upper left of the grid log. You should see the same
features we described above, keeping in mind that this
grid log represents the difference between the on-center
and off-center values. You should clearly see the topo-
graphic nature of the receptive fields, and also the full
range of variation among the different receptive field
properties.

Question 8.2 Which different properties of edges are
encoded differently by different hidden units? In other
words, over what types of properties or dimensions do
the hidden unit receptive fields vary? There are four
main ones, with one very obvious one being orientation
— different hidden units encode edges of different orien-
tations (e.g., horizontal, vertical, diagonal). Describe
three more such properties or dimensions.

You should observe that the topographic organization
of the different features, where neighboring units usu-
ally share a value along at least one dimension (or are
similar on at least one dimension). Keep in mind that
the topography wraps around, so that units on the far
right should be similar to those on the far left, and so
forth. You should also observe that a range of different
values are represented for each dimension, so that the

First, do View , PROBE_ENV in the control panel to
bring up the probe stimuli.
This will bring up an environment containing 4
events, each of which represents an edge at a different
orientation and position.