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Bar-Cohen : Biomimetics: Biologically Inspired Technologies DK3163_c003 Final Proof page 117 21.9.2005 11:41pm

Mechanization of Cognition 117

coding a single active symbol (assumed fact) on a lexicon, essentially anywhere in cortex, always
fire at about the same signal level (namely, the maximum possible) when they are implementing a
link, we can consider this link input signal as constant. Thus, for the purposes of discussing
elementary confabulation (the process of reaching conclusions based upon sets of assumed facts),
we need not worry about this issue here. Another issue that can be ignored is the influence of the
many nonstrengthened synapses impinging on target lexicon symbol neurons. This effect can be
ignored because the inputs due to this prolific, but unreliable, source is very uniformly distributed
across all neurons of all symbols and so it affects them all equally. In other words, this input acts as
a low-variance, roughly constant, uniform ‘‘background noise.’’
The main conclusion of the above argument is that those neurons which represent answer
lexicon symbol l, which happen to receive a sufficient number of c transponder neuron inputs to
allow them to respond, will all have about the same response to that input; namely a response
proportional to a þ log b (p(cjl)).
Recall from the discussion of Figure 3.A.6 that the number of neurons of each answer lexicon
symbol which receive sufficient synaptic inputs from the transponder neurons of a source symbol c
are about the same for each knowledge link and each symbol. You may wonder why only l neurons
having this maximum number of synapses from c transponders will respond. It has to do with the
events of the confabulation process. As the operate command input rises, these ‘‘sufficient’’ neurons
will become active first. In the operation of the feature attractor (which is very fast) only those
neurons with a sufficient number of inputs from an assumed fact will be able to participate in the
dynamical convergence process. Another good question is why the variance in this number of
synapses turns out to be small. This is because the binomial statistics of random transponder neuron
axons make it such that neurons with unusually large numbers of synapses are extremely unlikely.
Otherwise put, binomial (or Poisson) probability distributions have ‘‘thin tails.’’ Thus, the set of all
l neurons which have strengthened synapses — the ones which participate in the (strength-
weighted) excitation of l — are those that lie in a narrow range at the top end of the Poisson
density right before it plummets.
The binomial statistics of the locally random cortical connections also keep the number of target
symbol neurons with near-maximum complements of input synapses very close to being constant
for all symbols. Let this number of neurons be K. Then the total excitation of the K neurons which
represent answer lexicon symbol l that are receiving input from c symbol transponders (where c is
one of the assumed facts) is proportional to K[a þ log b (p(cjl)] (again, with a universal constant of
proportionality that is the same for all the symbols of one module).
Finally, since the subsets of l-representing neurons which receive inputs from different links
typically do not overlap, the total excitation of the entire set of neurons representing answer lexicon
symbol l (assuming that l is receiving knowledge link inputs from assumed facts a, b, g, and d)is
approximately proportional to (again, with a universal constant of proportionality) the total input
excitation sum I(l):

I(l) K [a þ log (p(ajl))] þ K [a þ log (p(bjl))]
b b
þ K [a þ log (p(gjl))] þ K [a þ log (p(djl))]
b b
¼ 4K a þ K log [p(ajl) p(bjl) p(gjl) p(djl)] (3A:4)
b
Recall from the discussion of Section 3.A.2, that when the answer lexicon feature attractor is
operated (and yields only one winning symbol), all of the neurons representing the winning symbol
(which will be the one with the highest total input excitation) are left in the active state and all other
symbol neurons are left inactive. By virtue of the above formula, we see that this winning symbol
will be the symbol l with the highest confabulation product p(ajl) p(bjl) p(gjl) p(djl) value
(e.g., in the specific case of Figure 3.A.6, this will be symbol e). This is the theory’s explanation for
how thalamocortical modules can carry out confabulation.