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[JANSSEN Jacques]

          IS BEHAVIORAL LIMIT CYCLING SURPRISING?
 
I have a question I would like to pose to theorists of neural net
dynamics. A behavioral phenomenon has cropped up in my work which surprised
me and I would like to know if this phenomenon is to be expected by NN
dynamics theorists or not. Before describing the phenomenon, I need to
give some technical background. I work in the field of "Genetic
Programming", i.e. using the Genetic Algorithm (GA) to build/evolve
systems which function, but are (probably) too complex to analyse
mathematically. I have applied these GP techniques to building artificia
nervous systems and artificial embryos. To build an artificial nervous
system, I evolve the weights of fully connected neural nets (GenNets),
such that their time dependent outputs control some process e.g. the
angles of legs on a simulated artificial creature. This way one can
evolve behaviours of the creature, e.g. to get it to walk straight
ahead, choose the GA fitness to be the distance covered over a
given number of cycles. To get it to turn, choose the fitness to be
the angle rotated etc. The surprise comes when one tries to combine
these motions. To do so, take the output of one GenNet (with its set
of weights) and input it into the second GenNet. For example, if one
wants the creature to walk straight ahead and later to turn right,
then use the GenNet evolved for straight ahead walking for the time
you want. Then take the output of this first GenNet and input it
into the second GenNet which was evolved to get the creature to turn.
What I found was that INDEPENDENTLY of the state of the creatures
legs i.e. their angles (which are proportional to the output values),
which were input into the second GenNet, one got the desired qualitative
behaviour, i.e. it turned. I find this extremely useful phenomenon
puzzling. It can be used for smooth transitions between behaviours, but
why does it work? It looks as though the GenNet has evolved a sort of
limit cycle in its behaviour, so that no matter what the starting state
(i.e. the initial input values to the GenNet) the desired limit cycle
behaviour will occur (e.g. straight ahead walking or turning etc). I
call this phenomenon "Behavioral Limit Cycling" (BLC). Is this
phenomenon to be expected? Is it old-hat to the theorists or have I
stumbled onto something new and exciting? (I will certainly be able
to use it when switching between behavioral GenNets amongst a whole
GenNet library. This library constitutes an artificial nervous system
and will be useful in forging a link between the two fields of
neural networks (i.e. multi networks, not just one, which is what most
NN papers are about) and the hot new field of Artificial Life).
 
I pose this question for open discussion.
 
Cheers, Hugo de Garis,
University of Brussels &
George Mason University VA.
email  CADEPS at BBRNSF11.BITNET