Steve Lehar slehar at park.bu.edu
Sat Aug 3 09:34:28 EST 1991

> There was nothing  in here so I thought  I'd  write  something so that
> this file doesn't feel lonely.

Indeed, what  a  shame that   there   is no  discussion   on such   an
interesting topic!  How   about a   discussion of  the   computational
aspects of  neural  mechanisms?   There  are three  elements of neural
computation   that  seem  to    differ   from  artificial computation-
distributiveness, analog, and feedback.

Distributiveness   is the way  that  neurons   tend  to branch  out so
abundantly, receiving  input from and sending  output to  thousands of
other cells.  This is very different from computer systems, but we are
beginning  to   understand the  significance  of parallel  distributed
processing, and     how it  affords   fault  tolerance     and  robust

Analog  computation: the frequency of spiking  is  an analog quantity,
despite the fact that the individual spikes are  essentially binary in
nature,  and  of  course  non-spiking  neurons are  completely analog.
Analog computation has  been largely abandoned by   man  after a brief
spate of popularity  in the 50's and  60's, so why  does the brain use
it?  The  reason we abandoned it was  because   of it's complexity and
chaotic tendancies.  The reason the brain  uses it is because  of it's
complexity and chaotic tendancies.  I use, of course, the mathematical
meaning of  the  word chaos- i.e. any  signal that is neither periodic
nor completely random.

Feedback: For years it was a mystery  why the pathway from the lateral
geniculate nucleus (first stage in the visual  pathway) to the primary
visual  cortex (second stage)  is  actually  SMALLER than a reciprocal
pathway  from visual cortex  BACK to   the lateral geniculate!  Indeed
throughout the brain we see multiple  feedback  pathways.  What is the
significance of these backwards connections?   Grossberg proposes that
the  feedback allows for a resonant  matching  between lower level and
higher level representations.  At each level of representation (within
each neural  layer) there are  certain  computational constraints that
are   expressed within    that  layer   by excitatory or    inhibitory
interactions.  For simple cells  in  visual  cortex, for instance,  an
edge found at  one location at, say, 30  degrees, is inconsistant with
an edge found at that SAME  location but a  different orientation, say
60   degrees.     The   cells   that  represent   these    conflicting
representations experience a  mutually inhibitory relationship so that
only one can  remain active even when both   receive some stimulation.
At a higher level of computation, complex cells of  adjacent locations
boost  each  other if they  find themselves along the same  line, i.e.
they detect two  simple edges that are both  parallel and aligned with
one   another.     The constraints  felt   individually at  each level
(competition in the lower level, and cooperation at the  higher level)
must interact with  each other in  a large feedback  loop (Grossberg's
cooperative / competitive loop) so that  the multiple constraints felt
at each level are optimally satisfied by the whole system.

It is kind of like a system of balls connected  by springs, where each
spring  represents a  spatial  constraint  linking two   balls.  Short
springs  between nearby balls enforce  local  constraints, while  long
springs between whole groups of balls enforce more global constraints.
Given certain inputs (some balls  clamped into specific positions) the
rest of the network will  wiggle and jiggle until  it  finally relaxes
into a global stability where the total energy  of the  system (sum of
tensions on the springs) has reached a minimum.
(O)((O))(((               slehar at park.bu.edu               )))((O))(O)
(O)((O))(((    Steve Lehar Boston University Boston MA     )))((O))(O)
(O)((O))(((    (617) 424-7035 (H)   (617) 353-6741 (W)     )))((O))(O)

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