Mathematical Tractability of Neural Nets

[slehar@bucasb.bu.edu]

Thank you for your lengthy reply to my posting.  I do  not dispute the
variability of functional   organization between individuals'  brains,
and I am intrigued by the organizational differences based on language
that you pointed  out.  My point was  not that  brains  are  identical
enough that pinpointing a lesion  can necessarily lead  to an accurate
prediction of deficits (although admittedly that is what I said).

What  I meant  to say is  that the  functionality   of areas has  been
identified to   a level  of detail   that would surprise  many "neural
network" modellers.  The fact that the 'task'  of  speech, for example
is functionally divided  into the components  generally   performed by
Brocca's area   (grammar  and   articulation),   Wernicke's (meaning),
angular gyrus (vocabulary), right hemisphere (prosidy),  frontal areas
(initiation of speech),  motor strip  (execution  of  speech) etc.  is
extremely interesting to the neural modeler, as it gives a clue  as to
how a parallel speech system can be organized, while  leaving open the
tantalizing question of  the  fine level microstructure  required  for
such a   system to  be   actually  implemented.  It   is the  specific
functionality  of each area that has  been mapped  in such detail, not
the physical location of that area  in any particular individual.  (In
other words, if Broccas area is pinpointed in a particular individual,
then lesion of that area will produce predictable deficits)

In fact the very variability of the actual locations of such  areas is
equally interesting, and  provides further clues  as to the underlying
mechanisms.  The fact  that a lesion  nearby  can induce a  functional
area like  Broccas area to  'move  over' to an adjacent  region really
emphasizes the adaptability and  variability of the system, and  until
we  duplicate that type of adaptability,  we  will not have duplicated
the functionality either.

Thank you for all your references to interesting work- I will preserve
them for future reading.

Steve Lehar