Flexible Memory Networks

TL;DR

This paper develops a theoretical framework for flexible memory networks in recurrent neural models, characterizing the maximum number of memory patterns based on network connectivity and topology.

Contribution

It introduces a novel theory linking network flexibility to rank 1 matrices and topological conditions, expanding understanding of memory encoding in neural networks.

Findings

Maximal flexible memory patterns relate to rank 1 matrices.

A topological condition H_1(X;Z)=0 is key for network flexibility.

Results apply to large, not overly sparse random networks.

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.