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Magic number 7 $\pm$ 2 in networks of threshold dynamics

Shuji Ishihara·Kunihiko Kaeko
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Abstract

Information processing by random feed-forward networks consisting of units with sigmoidal input-output response is studied by focusing on the dependence of its outputs on the number of parallel paths M. It is found that the system leads to a combination of on/off outputs when $M \lesssim 7$, while for $M \gtrsim 7$, chaotic dynamics arises, resulting in a continuous distribution of outputs. This universality of the critical number $M \sim 7$ is explained by combinatorial explosion, i.e., dominance of factorial over exponential increase. Relevance of the result to the psychological magic number $7 \pm 2$ is briefly discussed.

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Shuji Ishihara, Kunihiko Kaeko. 2004-09-19. Magic number 7 $\pm$ 2 in networks of threshold dynamics. https://doi.org/10.1103/physrevlett.94.058102

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