paper available:Lorentzian Neural Nets

[Joerg_Lemm]

          FTP-host: archive.cis.ohio-state.edu
          FTP-filename: /pub/neuroprose/giraud.lorentz.ps.Z

The file giraud.lorentz.ps.Z is now available for
copying from the Neuroprose repository:
(27 pages, compressed file size 215K)

TITLE:
                   LORENTZIAN NEURAL NETS
AUTHORS:
                         B.G.Giraud
          Service Physique Theorique, DSM, C.E.Saclay,
          91191 Gif/Yvette, France,

                    A.Lapedes and L.C.Liu
          Theoretical Division, Los Alamos National Laboratory,
          87545 Los Alamos, NM, USA,

                         J.C.Lemm
          Institut fuer Theoretische Physik I, Muenster University,
          48149 Muenster, Germany

ABSTRACT:
We consider neural units whose response functions are Lorentzians rather
than the usual sigmoids or steps. This consideration is justified by the fact
that neurons can be paired and that a suitable difference of the sigmoids 
of the paired neurons can create a window response function.
Lorentzians are special cases of such windows and we take advantage of their
simplicity to generate polynomial equations for several problems such as:
i)   fixed points of a completely connected net,
ii)  classification of operational modes,
iii) training of a feedforward net,
iv)  process signals represented by complex numbers.
                                                                
Keywords: Neural Networks, Window-like response functions,
Lorentzians and rational fractions, Integer coefficients, Training by solving
polynomial systems, Processing of complex numbers,
Fixed number of solutions, Classification of operational modes.

URL:
ftp://archive.cis.ohio-state.edu/pub/neuroprose/giraud.lorentz.ps.Z