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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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