A probabilistic study of neural complexity

Abstract : G. Edelman, O. Sporns, and G. Tononi have introduced the neural complexity of a family of random variables, defining it as a specific average of mutual information over subfamilies. We show that their choice of weights satisfies two natural properties, namely exchangeability and additivity, and we call any functional satisfying these two properties an intricacy. We classify all intricacies in terms of probability laws on the unit interval and study the growth rate of maximal intricacies when the size of the system goes to infinity. For systems of a fixed size, we show that maximizers have small support and exchangeable systems have small intricacy. In particular, maximizing intricacy leads to spontaneous symmetry breaking and failure of uniqueness.
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Pré-publication, Document de travail
minor edits. 2009
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Soumis le : vendredi 18 décembre 2009 - 22:19:03
Dernière modification le : mercredi 29 novembre 2017 - 16:31:50
Document(s) archivé(s) le : jeudi 23 septembre 2010 - 18:14:55

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  • HAL Id : hal-00409143, version 3
  • ARXIV : 0908.1006

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Jerome Buzzi, Lorenzo Zambotti. A probabilistic study of neural complexity. minor edits. 2009. 〈hal-00409143v3〉

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