Flexible Memory Networks

Carina Curto; Anda Degeratu; Vladimir Itskov

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arXiv · 1009.4958

Flexible Memory Networks

Carina Curto·Anda Degeratu·Vladimir Itskov

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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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Carina Curto, Anda Degeratu, Vladimir Itskov. 2010-09-24. Flexible Memory Networks. https://arxiv.org/abs/1009.4958

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