Convergence (was Re: Mathematical Tractability of Neural Nets)

[mesard@BBN.COM]

> This comes from my idea that if the cerebral activity
> in a human did converge, he would have stopped thinking. While this
> might be the goal of the devout follower of eastern philosophy, I
> think it is impossible.

There are two assumptions made in the case of artificial neural nets [or
a large class of them anyway] that don't generally hold for a brain:

1) The set of input patterns is finite.

2) There is no random neural activity (aside from an random initial
   state).

Remove these assumptions, and an ANN can quite easily be made to never
converge.  Impose these assumptions on a brain, and it would very likely
stop thinking.  (In fact, even one assumption may be enough to produce
a sort of convergence.  Consider the effects of solitary confinement, etc.)
-- 
void Wayne_Mesard();   Mesard at BBN.COM   Bolt Beranek and Newman, Cambridge, MA