Combined Model and Task Learning, and Other Mechanisms - Computational Explorations in Cognitive Neuroscience - page 183

a)

Question 6.3 (a) What do you notice about the gen-
eral shape of the standard backpropagation (BP) learn-
ing curve (SSE over epochs) in figure 6.9 compared to
that of the PURE_ERR Leabra network you just ran?
Pay special attention to the first 30 or so epochs of
learning. (b) Given that one of the primary differ-
ences between these two cases is that the PURE_ERR
network has inhibitory competition via the kWTA func-
tion, whereas BP does not, speculate about the possible
importance of this competition for learning based on
these results (also note that the BP network has a much
larger learning rate, .39 vs .01). (c) Now, compare the
PURE_ERR case with the original HEBB_AND_ERR
case (i.e., where do the SSE learning curves (red lines)
start to diverge, and how is this different from the BP
case)? (d) What does this suggest about the role of
Hebbian learning? (Hint: Error signals get smaller as
the network has learned more.)

100−

Pure Hebb

90−

80−

70−

60−

50−

Pure Err

40−

30−

20−

10−

Hebb & Err

0−

0 102030405060708090100

Epochs

b)

60−

Pure Err

55−

50−

Pure Hebb

45−

40−

35−

Hebb & Err

30−

25−

0 102030405060708090100
Epochs

Figure 6.10: Graph log display showing both errors (a) And
cycles (b) Over epochs of training for the three different net-
work learning parameters: pure error driven learning (Pure
Err), pure Hebbian learning (Pure Hebb) and combined Heb-
bian and error-driven learning (Hebb & Err), which performs
the best.

To get a sense of how learning has shaped the trans-
formations performed by this network to emphasize rel-
evant similarities, we can do a cluster plot of the hid-
den unit activity patterns over all the inputs. Let'sdoa
comparison between the initial clusters and those after
learning for the default network.

First, press ReInit on the overall control panel to
reinitialize the weights. Then, press Cluster .
After a bit (it tests all 100 patterns, so be patient), a
cluster plot window will appear. We will compare this
cluster plot to one for the trained network.

see this by loading the graph log for a network trained
for 100 epochs.

, !

Select LogFile/Load File in the graph log, and
choose family_trees.pure_hebb.epc.log .
Although Hebbian model learning is useful for help-
ing error-driven learning, the graph shows that it is sim-
ply not capable of learning tasks like this on its own.
We next compare all three cases with each other.

, !

Go to the network window and select from the
menu at the upper left: Object/Load , and then se-
lect family_trees.hebb_err.00.041.net.gz (or
the network that you saved). Do Cluster again.
Your results should look something like figure 6.11.
There are many ways in which people who appear to-
gether can be justifiably related, so you may think there
is some sensibility to the initial plot. However, the fi-
nal plot has a much more sensible structure in terms of
the overall nationality difference coming out as the two
largest clusters, and individuals within a given genera-
tion tending to be grouped together within these overall
clusters. The network is able to solve the task by trans-
forming the patterns in this way.

, !

Load the family_trees.all.epc.log log file.
This log display has the three runs overlaid on each
other (figure 6.10). You can identify the lines based on
what epoch they end on (40 = HEBB_AND_ERR ,80=
PURE_ERR , and 100 = PURE_HEBB ). It is interesting
to note that the orange line (average settling cycles) is
fairly well correlated with the training error, and only
the combined Hebb and error network achieves a sig-
nificant speedup in cycles. You might also note that the
pure Hebb case starts out with very quick settling in the
first few epochs, and then slows down over training.

, !