Sparse sign-consistent Johnson–Lindenstrauss matrices: Compression with neuroscience-based constraints
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Allen-Zhu-2014-Sparse sign-consiste.pdf
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Author(s)
Allen-Zhu, Zeyuan
Gelashvili, Rati
Micali, Silvio
Shavit, Nir N.
Date Issued
November 2014
Journal
Proceedings of the National Academy of Sciences
Publisher
National Academy of Sciences (U.S.)
Citation
Allen-Zhu, Zeyuan, Rati Gelashvili, Silvio Micali, and Nir Shavit. “Sparse Sign-Consistent Johnson–Lindenstrauss Matrices: Compression with Neuroscience-Based Constraints.” Proceedings of the National Academy of Sciences 111, no. 47 (November 10, 2014): 16872–16876.
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Final published version
Abstract
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 all nonnegative or all nonpositive), and the fact that any given neuron connects to a relatively small subset of other neurons implies that the JL matrix should be sparse. We construct sparse JL matrices that are sign consistent and prove that our construction is essentially optimal. Our work answers a mathematical question that was triggered by earlier work and is necessary to justify the existence of JL compression in the brain and emphasizes that inhibition is crucial if neurons are to perform efficient, correlation-preserving compression.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1073/pnas.1419100111
