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Johnson-Lindenstrauss (JL) matrices implemented by sparse random synaptic connections are thought to be a prime candidate for how convergent pathways in the brain compress information. However, to date, there is no complete mathematical support for such implementations given the constraints of real neural tissue. The fact that neurons are either excitatory or inhibitory implies that every so implementable JL matrix must be sign-consistent (i.e., all entries in a single column must be either alldoi:10.1073/pnas.1419100111 pmid:25385619 pmcid:PMC4250157 fatcat:aoulhcj4vzdo3nf5sqmg6ya6xy