No subject

networks,   it  is  easy to  see  that  an "instantaneous" multi-layer
network  combined  with delays/integrators  in  the feedback  loop can
approximate arbitrary discrete/continuous-time dynamical systems.
A question  of interest is whether  it can be done  when all the units
have  intrinsic delays/integrators. The answer  is  yes,  if we use  a
distributed representation of the state space. (6 pages)

----It is a simple problem someone might have already solved.
    I appreciate any reference to previous works.

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	      Bifurcations of Recurrent Neural Networks
		     in Gradient Descent Learning
			   Kenji Doya, UCSD

Asymptotic   behavior   of   a   recurrent   neural  network   changes
qualitatively at certain  points  in the   parameter space, which  are
known as ``bifurcation points''.  At bifurcation points, the output of
a network can change discontinuously with the change of parameters and
therefore   convergence  of    gradient  descent  algorithms   is  not
guaranteed.  Furthermore, learning equations  used for error  gradient
estimation can  be unstable. However,  some  kinds of bifurcations are
inevitable  in  training a recurrent  network as  an  automaton or  an
oscillator. Some   of  the factors underlying successful   training of
recurrent networks   are  investigated, such  as  choice    of initial
connections, choice of input patterns, teacher forcing,  and truncated
learning equations. (11 pages)

----It is (to be) an extended version of "doya.bifurcation.ps.Z".

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	   Dimension Reduction of Biological Neuron Models
		    by Artificial Neural Networks
	       Kenji Doya and Allen I. Selverston, UCSD

An   artificial neural  network approach for   dimension reduction  of
dynamical systems is proposed and  applied to conductance-based neuron
models. Networks with  bottleneck  layers of continuous-time dynamical
units could  make a 2-dimensional  model from the trajectories  of the
Hodgkin-Huxley model and  a 3-dimensional model from the  trajectories
of a 6-dimensional bursting neuron model.  Nullcline analysis of these
reduced  models  revealed the   bifurcations  of the neuronal dynamics
underlying firing and bursting behaviors. (17 pages)

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FTP INSTRUCTIONS

     unix% ftp archive.cis.ohio-state.edu (or 128.146.8.52)
     Name: anonymous
     Password: neuron
     ftp> cd pub/neuroprose
     ftp> binary
either
     ftp> get doya.universality.ps.Z
     ftp> get doya.bifurcation2.ps.Z
     ftp> get doya.dimension.ps.Z
or
     ftp> mget doya.*
rehtie
     ftp> bye
     unix% zcat doya.universality.ps.Z | lpr
     unix% zcat doya.bifurcation2.ps.Z | lpr
     unix% zcat doya.dimension.ps.Z | lpr

These files are also available for anonymous ftp from
crayfish.ucsd.edu (132.239.70.10), directory "pub/doya".