Polynomial Nets

[ananth sankar]

I am sorry to be reposting this but I forgot to put the subject in my last
message. Sincere apologies to all.


A neural network basically classifies training and testing samples
into different regions in an n dimensional space. By generating the output
of the network for all possible points in the space one constructs a n + 1
dimensional surface with n independent variables. A polynomial can be
generated to approximate this surface. 

It should be possible to construct a "polynomial neural network" that can do
this job. The neurons individually may implement simple polynomials (using
sigma-pi units maybe). I would really appreciate any pointers to any research
on this (published or unpublished). The work that I am aware of dates to
the late 60's--A.G. Ivakhnenko and Donald Specht--though they did not
model their systems as nn's.

I would also like feedback on what the potential use of such nets may be
over typical work like back prop.

Thanks in anticipation

Ananth Sankar
Dept. of Electrical Engg.
Rutgers University
NJ