Perception and Attention - Computational Explorations in Cognitive Neuroscience - page 244

this brightness/dimness feature to evaluate to what ex-
tent these V2 units encode conjunctions of features (re-
sponding only when the features are present together),
and to what extent they exhibit spatial invariance (re-
sponding to a feature or features in a range of different
locations).
We first consider conjunctions of features. If a unit
responds only when two features are present together,
thus representing the conjunction of these features, the
unit will have a bright encoding of those features. For
example, the unit in column 5, row 7, has two bright
vertical lines, and the unit at 1, 3 has two bright horizon-
tal lines, suggesting that each of these units represents
the conjunction of their respective features. In contrast,
if a unit had responded to one feature in one input and
the other feature in another input (thus not representing
the conjunction of those features), then the lines would
be dimmer, due to the diluting of the activation based
receptive field. Thus, we see some evidence for con-
junctive representations in the V2 units in the multiple
bright features encoded by some of the units.
We next consider spatial invariance. If a unit re-
sponds to the same feature in a number of different lo-
cations (across inputs), thus representing that feature in
a spatially invariant manner, the unit will have a dim
encoding of the feature in each of those locations. The
dim receptive fields are produced by the process of aver-
aging across different inputs, with activation based re-
ceptive fields becoming more diluted the more a unit
responds to different inputs (the less selective the unit
is). For example, the unit at 5, 5 has several dim verti-
cal lines, suggesting that the unit represents this feature
across those different locations. Thus, we see some ev-
idence of spatially invariant encoding in the V2 units
in these dimmer receptive fields for the same feature in
different locations.

Figure 8.14: V2 activation-based receptive fields from off-
center LGN inputs. Layout is the same as the previous figure.

You should observe a clear correspondence between
the receptive field patterns for the on- and off-center in-
puts, indicating that the V2 neurons have encoded the
linear elements represented in the on-center fields, and
also where these lines should end as represented in the
off-center fields.

Now press Open in the next file selection window to
view the outputlayer receptive fields for these same V2
units (figure 8.15).
This enables you to see which objects the units par-
ticipate in representing. You may notice there does not
appear to be a correlation between input and output se-
lectivity — units with highly selective input coding par-
ticipated in the representation of many objects, and vice
versa. You might have expected that highly selective in-
put tuning would make units highly selective for what
objects they represent, but in fact they are representing
shared features of objects and so can participate in the
representation of multiple objects.

Question 8.4 Explain the significance of the level of
conjunctive representations and spatial invariance ob-
served in the V2 receptive fields, in terms of the overall
computation performed by the network.

Press Open in the file selection window to bring up
the next receptive field display, which shows the input
receptive fields from the off-center LGN input layer (fig-
ure 8.14). Again put aside the next dialog for a moment.