Paper on stability conditions for design of linear threshold recurrent networks

[Heiko Wersing]

Dear Connectionists,


the following paper has recently been accepted
for publication in Neural Computation.

It can be downloaded from my university homepage at

http://www.techfak.uni-bielefeld.de/~hwersing/

Comments and questions are highly appreciated.

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"Dynamical stability conditions for 
recurrent neural networks with unsaturating 
piecewise linear transfer functions"

by Heiko Wersing, Wolf-Juergen Beyn, and Helge Ritter.

Abstract:

We establish two conditions which ensure the non-divergence of 
additive recurrent networks with unsaturating piecewise linear
transfer functions, also called linear threshold or semilinear
transfer functions. As was recently shown by Hahnloser (Nature 405, 
2000) networks of this type can be efficiently built in silicon and 
exhibit the coexistence of digital selection
and analogue amplification in a single circuit. To obtain this
behaviour, the network must be multistable and non-divergent and our
conditions allow to determine the regimes where this can be achieved
with maximal recurrent amplification. The first condition can be
applied to nonsymmetric networks and has a simple interpretation of
requiring that the strength of local inhibition must match the sum
over excitatory weights converging onto a neuron. The second
condition is restricted to symmetric networks, but can also take
into account the stabilizing effect of non-local inhibitory
interactions. We demonstrate the application of the conditions on a
simple example and the orientation-selectivity model of 
Ben-Yishai et al. (1995).  We show that the conditions can be used
to identify in their model regions of maximal orientation-selective
amplification and symmetry breaking.
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Best wishes


-- 
Heiko Wersing
Future Technology Research
HONDA R&D EUROPE (DEUTSCHLAND) GmbH
Carl-Legien-Str. 30
63073 Offenbach /Main
Germany
Tel.: +49-69-89011741
Fax:  +49-69-89011749
e-mail: heiko.wersing at hre-ftr.f.rd.honda.co.jp