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Flexible Memory Networks

Bulletin of Mathematical Biology volume 74, pages 590–614 (2012)Cite this article

Abstract

Networks of neurons in some brain areas are flexible enough to encode new memories quickly. Using a standard firing rate model of recurrent networks, we develop a theory of flexible memory networks. Our main results characterize networks having the maximal number of flexible memory patterns, given a constraint graph on the network’s connectivity matrix. Modulo a mild topological condition, we find a close connection between maximally flexible networks and rank 1 matrices. The topological condition is H 1(X;ℤ)=0, where X is the clique complex associated to the network’s constraint graph; this condition is generically satisfied for large random networks that are not overly sparse. In order to prove our main results, we develop some matrix-theoretic tools and present them in a self-contained section independent of the neuroscience context.

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Authors and Affiliations

  1. Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE, USA

    Carina Curto & Vladimir Itskov

  2. Max Planck Institute for Gravitational Physics, Golm, Germany

    Anda Degeratu

Authors
  1. Carina Curto
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  2. Anda Degeratu
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  3. Vladimir Itskov
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Correspondence to Carina Curto.

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Curto, C., Degeratu, A. & Itskov, V. Flexible Memory Networks. Bull Math Biol 74, 590–614 (2012). https://doi.org/10.1007/s11538-011-9678-9

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  • DOI: https://doi.org/10.1007/s11538-011-9678-9

Keywords

  • Neural networks
  • Memory
  • Learning
  • Clique complex
  • Low rank