Universal Approximator Results

[Arun Jagota]

A question was raised some time back that since universal approximator 
results establish no new bounds on computability (one result is as good 
as another in a computability sense), what then is their significance.
Don't such results for k-hidden layer networks show, additionally,
that the represented function can be _evaluated_ on a point in it's
domain in 

(k+1)  inner-product       +        k    hidden-layer function eval
steps on a suitable abstract machine.

Doesn't that provide a strong result on the running time,
as compared with Church's thesis which says, that any algorithm
(effective procedure) can be programmed on a Turing m/c but doesn't
put a bound on the running time.

Arun Jagota
jagota at cs.buffalo.edu

[I don't wish to be accused of starting a fresh round of value-less 
discussions (if so perceived), so I prefer receiving responses by mail.
I suggest using 'mail' instead of 'R' or 'r']