TR: Fixed Points in Two--Neuron Discrete Time Recurrent Networks:

[Lee Giles]

The following Technical Report is available via the University of Maryland 
Department of Computer Science and the NEC Research Institute archives:

_____________________________________________________________________________



        "Fixed Points in Two--Neuron Discrete Time Recurrent Networks:
                Stability and Bifurcation Considerations"


   UNIVERSITY OF MARYLAND TECHNICAL REPORT UMIACS-TR-95-51 and CS-TR-3461

            Peter Tino[1,2], Bill G. Horne[2], C. Lee Giles[2,3]  
   [1] Dept. of Informatics and Computer Systems, Slovak Technical University,
                Ilkovicova 3, 812 19 Bratislava, Slovakia
    [2] NEC Research Institute, 4 Independence Way, Princeton, NJ  08540
         [3] UMIACS, University of Maryland, College Park, MD 20742
          
                   {tino,horne,giles}@research.nj.nec.com
                

The position, number and stability types of fixed points of a two--neuron recurrent net
work with nonzero weights are investigated. Using simple geometrical arguments in 
the space of derivatives of the sigmoid transfer function with respect to the weighted 
sum of neuron inputs, we partition the network state space into several regions corre
sponding to stability types of the fixed points. If the neurons have the same mutual 
interaction pattern, i.e. they either mutually inhibit or mutually excite themselves, a 
lower bound on the rate of convergence of the attractive fixed points towards the satu
ration values, as the absolute values of weights on the self--loops grow, is given. The 
role of weights in location of fixed points is explored through an intuitively appealing 
characterization of neurons according to their inhibition/excitation performance in the 
network. In particular, each neuron can be of one of the four types: greedy, enthusias
tic, altruistic or depressed. Both with and without the external inhibition/excitation 
sources, we investigate the position and number of fixed points according to character 
of the neurons. When both neurons self-excite themselves and have the same mutual 
interaction pattern, the mechanism of creation of a new attractive fixed point is shown 
to be that of saddle node bifurcation.

-------------------------------------------------------------------------

http://www.neci.nj.nec.com/homepages/giles.html
http://www.cs.umd.edu/TRs/TR-no-abs.html

or

ftp://ftp.nj.nec.com/pub/giles/papers/UMD-CS-TR-3461.two.neuron.recurrent.nets.ps.Z

--------------------------------------------------------------------------


--                                 
C. Lee Giles / NEC Research Institute / 4 Independence Way
Princeton, NJ 08540, USA / 609-951-2642 / Fax 2482
URL  http://www.neci.nj.nec.com/homepages/giles.html
==