Mathematical Tractability of Neural Nets

[slehar@bucasb.bu.edu]

I agree with  your   comment about  mathematically  tractable   neural
models.  I am currently taking  courses  on  neuropsychology and I  am
amazed  at the depth of  knowledge available about brain functionality
from the medical  point of view.  Lesion  studies show in great detail
how  specific brain areas  interact  to  perform   various  tasks, and
neurologists can  predict  with  great accuracy   what the effects  of
different   lesions would be  in  specific  locations.  This level  of
understanding must be exploited in our neural models.

The  problem    is that this  global  level  of understanding  is very
heuristic, and cannot be directly implemented  in a  neural model.  In
order to bring together the low level mathematical models and the high
level  neurological  knowledge we   must   advance both  sciences   in
converging directions.   In  other words, neurologists  must study the
microscopic origins of the observed macroscopic phenomena,  and neural
modelers  must design neural   models to duplicate specific anatomical
structures or behavioral elements.

This  is the  primary  thrust of  Grossbergs work.  Grossberg's neural
models   are based on   neurological  findings,   and  are designed to
duplicate behavioral data.  This, it seems to  me, is the way to bring
together the two sciences.