THE COMBINATORIAL CODE AND THE GRAPH RULES OF DALE NETWORKS

Nikola Milićević, Vladimir Itskov

Research output: Contribution to journalArticlepeer-review

Abstract

We describe the combinatorics of equilibria and steady states of neurons in threshold-linear networks that satisfy Dale's law. The combinatorial code of a Dale network is characterized in terms of two conditions: (i) a condition on the network connectivity graph, and (ii) a spectral condition on the synaptic matrix. We find that in the weak coupling regime the combinatorial code depends only on the connectivity graph, and not on the particulars of the synaptic strengths. Moreover, we prove that the combinatorial code of a weakly coupled network is a sublattice, and we provide a learning rule for encoding a sublattice in a weakly coupled excitatory network. In the strong coupling regime we prove that the combinatorial code of a generic Dale network is intersection-complete and is therefore a convex code, as is common in some sensory systems in the brain.

Original languageEnglish (US)
Pages (from-to)2522-2544
Number of pages23
JournalSIAM Journal on Applied Mathematics
Volume84
Issue number6
DOIs
StatePublished - 2024

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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