Universal Approximators

[john kolen]

Question:
	How important are "universal approximator" results?

Hornik, Stinchcombe, and White [1] demonstrate that a single hidden
layer that uses an arbitrary squashing function can appoximate any
Borel measurable function (i.e. has a countable number of
discontinuities).  They do this by showing the functions computable by
this class of networks is dense in the set of Borel measurable
functions.  Great, but so are polynomials, or any sigma-algebra over
the input space for that matter.  

[1] K. Hornik, M. Stinchcombe, H. White.  "Multi-Layer Feedforward
Networks are Universal Approximators".  in press, Neural Networks.
----------------------------------------------------------------------
John Kolen (kolen-j at cis.ohio-state.edu)|computer science - n. A field of study 
Computer & Info. Sci. Dept.	       |somewhere between numerology and
The Ohio State Univeristy	       |astrology, lacking the formalism of the
Columbus, Ohio	43210	(USA)	       |former and the popularity of the later.