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

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.

6 pages, 5 figures

References in corpus (1)

• Prevalence of unstable attractors in networks of pulse-coupled oscillators

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