SIR: shift invariant recognition

[Hans-Otto Carmesin]

Dear Rolf and Jerry.

The question raised by Rolf Wurtz is, how SIR ( shift invariant
recognition) might be processed in 
the visual system. 
There is a biologically reasonable candidate network:
I proposed it for experiments on so-called stroboscopic alternative
motion (SAM). The most simple instance is established by TWO light
dots, one of which is elicited at a time in an alternating manner.
At adequate frequency an observer perceives ONE dot moving back and
forth.
The experiment becomes quite non-trivial with four dots at the corners
of a square, two elicited at a time at diagonal positions and in an
alternating manner. An observer perceives either two dots moving
horizontally or two dots moving vertically (roughly speaking).
The network represents each dot by a formal neuron; these neurons
project to inner neurons that tend to fire in accordance with the
stimulation and that are coupled with rapid formal couplings (similar
to dynamic 
links) with a local coupling dynamics reminescent of the Hebb-rule [1-4].
A motion percept is established by the emerging nonzero couplings.
It turns out that each active neuron at a time t is coupled to
exactly one active neuron at a later time, t+t' say.
Moreover there are prestabilized coupling weights (modeling synaptic
densities) that prefer short distances in space and time.
As a result: If a pattern is presented at a time t and a shifted
pattern is presented at a time t+t', then the dots of the first
pattern are coupled to the corresponding dots of the second pattern.

This network is understood very well [3,4]:
It can be solved analytically and exhibits an effective potential 
dynamics in coupling space.
I predicted [3] a continuous phase transition and measured it together
with experimental psychologists later.
Another indication of biological relevance: Formally the network is
very similar to networks with retinotopy emergence [5].


References:
[1] H.-O. Carmesin:
Statistical neurodynamics: A model for universal properties of
EEG-data and perception.
Acta Physica Slovaca, 44:311--330, 1994.

[2] H.-O. Carmesin and S. Arndt:
Neuronal self-organization of motion percepts.
Technical Report 6/95, ZKW Universitt Bremen, Bremen, 1995.

[3] H.-O. Carmesin: Theorie neuronaler Adaption.
(Kster, Berlin, 1994. ISBN 3-89574-020-9).

[4] H.-O. Carmesin: Neuronal Adaptation Theory.
(Peter Lang, Frankfurt am Main, 1996. ISBN 3-631-30039-5).

[5] H.-O. Carmesin: Topology preservation emergence by Hebb rule with
  infinitesimal short range signals. Phys. Rev. E, 53(1):993--1003, 1996.



For details see:
WWW: http://schoner.physik.uni-bremen.de/~carmesin/