Individual Neurons - Computational Explorations in Cognitive Neuroscience - page 55

display both the weights and the current input pattern. As a result of working through the above questions,

you should now have a detailed understanding of how
the net excitatory input to the neuron reflects the degree
of match between the input pattern and the weights. You
have also observed how the activation value can ignore
much of the graded information present in this input
signal. Now, we will explore how we can change how
much information is conveyed by the activation signal.
We will manipulate the leak current ( g_bar_l ), which
has a default value of 7, which is sufficient to oppose the
strength of the excitatory inputs for all but the strongest
(best fitting) input pattern (the 8).

First click on the act button (this will probably al-
ready be selected, but just make sure). Then, select the
r.wt as before, except this time use the middlemouse
button (or hold down the shift key and use the left but-
ton). Then, select the receiving unit (it may already have
been selected, in which case you can either do nothing,
or click twice because your first click will deselect it).
You should now see each unit in the display divided
into two, with the left half displaying the activation, and
the right half displaying the weight value. Note that ac-
tivations provided by the environment are clipped to a
maximum of .95, so you can use this to tell the differ-
ence between the weights (which are at 1) and the acti-
vations.

Locate the detect_ctrl control panel. Notice the
g_bar_l variable there, with its default value of 7. Re-
duce g_bar_l to 6. (Note that you can just hit the Run
button in the control panel to both apply the new value
of g_bar_l and run the epoch process for one sweep
through the digits).

Now Step to present the digit 0 again.

Question 2.7 (a) For each digit, report the number of
input units where there is a weight of 1 and the input
unit is also active. This should be easily visually per-
ceptible in the display. You should find some variability
in these numbers across the digits. (b) Why does the
activation value of the receiving unit not reflect any of
this variability? (c) What would be a better variable
to examine in order to view this underlying variability,
and why?

Question 2.9 (a) What happens to the pattern of re-
ceiving unit activity when you reduce g_bar_l to 6?
(b) What happens with g_bar_l values of 4, 1, and
8? (c) Explain the effect of changing g_bar_l in
terms of the point neuron activation function. (d) What
might the consequences of these different response pat-
terns have for other units that might be listening to the
output of this receiving unit? Try to give some possi-
ble advantages and disadvantages for both higher and
lower values of g_bar_l .

Now, click on the net variable in the GraphLog win-
dow, to display the net input of the receiving unit in re-
sponse to each of the digit inputs.

Question 2.8 (a) What is the general relationship be-
tween the plot of the net input and the numbers you com-
puted in the previous question? (b) Use equation 2.15
in section 2.5.1 to explain exactly how the net input is
computed such that it results in the values plotted in the
graph for each digit — verify this for a couple of digits.
Remember that you can click on the line in the graph
to obtain exact numerical values to check your work.
The ￿ k for the input layer projection has been set to 1 35 .
(You can use the simplified equation 2.15 rather than
equation 2.16, because we are looking at the asymptotic
values after settling rather than time-averaging, net is
the same as g e (t)g e ,but g e is set to the default of 1 in
this case, and the bias weights are 0 and can be ignored
(i.e, ￿ =0 ).)

It is clearly important how responsive the neuron is to
its inputs. However, there are tradeoffs associated with
different levels of responsivity. The brain solves this
kind of problem by using many neurons to code each
input, so that some neurons can be more “high thresh-
old” and others can be more “low threshold” types,
providing their corresponding advantages and disadvan-
tages in specificity and generality of response. The bias
weights can be an important parameter in determining
this behavior. As we will see in the next chapter, our
tinkering with the value of the leak current g_bar_l
is also partially replaced by the inhibitory input, which
plays an important role in providing a dynamically ad-
justed level of inhibition for counteracting the excita-
tory net input. This ensures that neurons are generally