Magic number 7+/-2 in networks of threshold dynamics.
Information processing by random feed-forward networks consisting of units with a 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 less or similar to 7, while for M greater or similar to 7, chaotic dynamics arises, resulting in a continuous distribution of outputs. This universality of the critical number M approximately 7 is explained by a combinatorial explosion, i.e., the dominance of factorial over exponential increase. The relevance of the result to biological problems is briefly discussed.
Ishihara
Shuji
S
Department of Pure and Applied Sciences, University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8902, Japan. shuiji@complex.c.u-tokyo.ac.jp
Kaneko
Kunihiko
K
D000818:Animals; D003198:Computer Simulation; D004056:Differential Threshold / Q000502:physiology*; D006801:Humans; D008959:Models, Neurological; D015233:Models, Statistical; D009415:Nerve Net / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics; D009435:Synaptic Transmission / Q000502:physiology*