Perception and Attention - Computational Explorations in Cognitive Neuroscience - page 250

across all possible locations and sizes, and object 19
had 34 percent errors (66% correct). Considering that
the network had been trained on only 72 out of 1024
possible input images (7%), that is quite a good gen-
eralization result. The network performed correctly on
roughly twelve times as many images as it was trained
on for object 18, and 9.4 times for object 19. We
also note that there was some evidence of interference
from the training on some of the other objects, which
can be observed in detail by comparing this file with
objrec.swp_pre.err (table 8.1).
Looking specifically at the size generalization perfor-
mance, the network generalized to object 18 in the novel
sizes (which show up as sizes 1 and 3 in the table) at a
level of 27d percent and 13 percent errors, which is not
wildly different from the trained sizes (10% and 12%).
Similar results held for object 19, which had 40 percent
and 37 percent errors in the novel sizes, compared to 48
percent and 13 percent for the trained ones. Thus, there
is good evidence that the network was able to generalize
its learning on one set of sizes to recognizing objects at
different sizes that it had never seen before. Note also
that the smaller sizes produced many more errors, be-
cause they are near the level of acuity of the model (i.e.,
object features are basically the same size as the individ-
ual oriented line detectors in V1). Thus, we would ex-
pect better performance overall from a larger network.
To determine where the learning primarily occurred,
we can examine the difference between the pregener-
alization and postgeneralization training weights (i.e.,
for each weight, we subtracted its value before gener-
alization training from its value after training, and then
saved that value as the weight value for the connection
in question). We can load these weight differences into
the network where they will appear instead of the nor-
mal weight values, and can thus be viewed using our
standard weight viewing technique.

other layers lower in the network, it is clear that this
is where the primary learning occurred. Nevertheless,
there is evidence of some weight change in the other
units, which probably accounts for the observed inter-
ference. This kind of interference is probably inevitable
because learning will constantly be jostling the weights.
To summarize, these generalization results demon-
strate that the hierarchical series of representations can
operate effectively on novel stimuli, as long as these
stimuli possess structural features in common with
other familiar objects. The network has learned to rep-
resent combinations of these features in terms of in-
creasingly complex combinations that are also increas-
ingly spatially invariant. In the present case, we have
facilitated generalization by ensuring that the novel ob-
jects are built out of the same line features as the other
objects. Although we expect that natural objects also
share a vocabulary of complex features, and that learn-
ing would discover and exploit them to achieve a simi-
larly generalizable invariance mapping, this remains to
be demonstrated for more realistic kinds of objects. One
prediction that this model makes is that the generaliza-
tion of the invariance mapping will likely be a function
of featural similarity with known objects, so one might
expect a continuum of generalization performance in
people (and in a more elaborate model).

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 .

, !

8.4.3 Summary and Discussion

This model achieves two important objectives for a bi-
ologically realistic model of object recognition. First,
the response properties of the units in the different lay-
ers of the model provide a good qualitative fit to those of
corresponding areas in the ventral visual pathway. Sec-
ond, the model does a good job of discriminating be-
tween different objects regardless of what position or
size they appeared in. Furthermore, this ability to per-
form spatially invariant object recognition generalized
well to novel objects. All of this was achieved with rel-
atively minimal built-in constraints through the use of
the generic learning principles of the Leabra algorithm.

Do Actions/Read Weights in the NetView win-
dow, and select objrec.diff.wts.gz (this is what
the LoadNet button does, but it loads the trained
weights). Click on r.wt , and then click on objects 18
and 19 in the output layer.
You should see that the magnitude of the weight
changes from V4 to these units was about .25 or so.
Now, if you compare that with other output units and