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and Field (1996). Recall from chapter 4 that the sequen-
tial PCA algorithm (SPCA) does not produce the ap-
propriate edge detector representations, giving instead
the “blob” representation and its orthogonal subcompo-
nents as shown in figure 4.8. However, the conditional
PCA (CPCA) Hebbian algorithm should self-organize
representations of the appropriate conditional correla-
tional structure present in image edges.
Because we use only Hebbian model learning in this
case, we are effectively treating the very earliest levels
of perceptual processing as sufficiently removed from
any particular task that error-driven learning does not
play a major role. Put another way, we assume that the
statistical structure of the input (visual images) is suf-
ficiently strong to constrain the nature of the represen-
tations developed by a purely model learning system,
without the need for extra task-based constraints. The
success of the model in producing realistic-looking re-
ceptive fields justifies this assumption to some extent.
We will see in the next model that even the next layer
up in the network benefits from a combination of model
and task learning.
The model focuses on several important properties
of V1 representations — orientation, position, size, and
polarity — that have been emphasized to varying ex-
tents in existing models. For each of these properties
or dimensions , the model develops coarse coding repre-
sentations that cover the space of possible values along
each dimension, as with actual V1 neurons. For exam-
ple, in the case of orientation, the units have a preferred
orientation where they respond maximally, and progres-
sively weaker responses for increasingly different orien-
tations. Further, individual units have a particular tun-
ing value along each of these dimensions (e.g., coding
for a low spatial frequency (large) edge with dark-light
polarity at 45 degrees in a given location). Finally, we
explore the topographic arrangement of these dimen-
sions (with neighboring units representing similar val-
ues) that is produced by having excitatory lateral con-
nectivity within V1.
Hidden
Input_pos
Input_neg
Figure 8.7: V1 receptive field network, showing both on- and
off-center LGN inputs and the single V1 hidden layer with
lateral excitatory connectivity.
venience, we have organized these two different types
of inputs into two separate layers (figure 8.7), which
may actually be a characteristic of LGN inputs. V1 it-
self is modeled as a single layer, which actually corre-
sponds to the hidden layer of this area (cortical layers
2, 3), because many of the input layer neurons (cortical
layer 4) have basically the same unoriented on- and off-
center receptive fields as the LGN (and retina). Thus,
the inputs in our model could probably be viewed as ei-
ther the cortical input layer or the LGN, but we refer to
them as LGN inputs.
The network was presented with images of natural
scenes (mountains, plants, etc.) that had been prepro-
cessed by Olshausen and Field (1996) to mimic the ef-
fects of contrast enhancement in the retina (using a spa-
tial filtering that approximates the effects of the center-
surround processing). Because the units in the Ol-
shausen and Field (1996) network had both positive and
negative weights and activations (which is biologically
implausible), they did not separate on- and off-center
components. However, we must separate these com-
ponents because our activations and weights obey the
biological constraints. We do this separation by pre-
senting the positive-valued processed image pixels in
the “on-center” input layer, and the absolute values of
8.3.1
Basic Properties of the Model
The inputs to the model are based on the on- and off-
center neurons of the LGN that project to V1. For con-
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