License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.ITCS.2019.57
URN: urn:nbn:de:0030-drops-101506
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Papadimitriou, Christos H. ; Vempala, Santosh S.

Random Projection in the Brain and Computation with Assemblies of Neurons

LIPIcs-ITCS-2019-57.pdf (0.7 MB)


It has been recently shown via simulations [Dasgupta et al., 2017] that random projection followed by a cap operation (setting to one the k largest elements of a vector and everything else to zero), a map believed to be an important part of the insect olfactory system, has strong locality sensitivity properties. We calculate the asymptotic law whereby the overlap in the input vectors is conserved, verifying mathematically this empirical finding. We then focus on the far more complex homologous operation in the mammalian brain, the creation through successive projections and caps of an assembly (roughly, a set of excitatory neurons representing a memory or concept) in the presence of recurrent synapses and plasticity. After providing a careful definition of assemblies, we prove that the operation of assembly projection converges with high probability, over the randomness of synaptic connectivity, even if plasticity is relatively small (previous proofs relied on high plasticity). We also show that assembly projection has itself some locality preservation properties. Finally, we propose a large repertoire of assembly operations, including associate, merge, reciprocal project, and append, each of them both biologically plausible and consistent with what we know from experiments, and show that this computational system is capable of simulating, again with high probability, arbitrary computation in a quite natural way. We hope that this novel way of looking at brain computation, open-ended and based on reasonably mainstream ideas in neuroscience, may prove an attractive entry point for computer scientists to work on understanding the brain.

BibTeX - Entry

  author =	{Christos H. Papadimitriou and Santosh S. Vempala},
  title =	{{Random Projection in the Brain and Computation with Assemblies of Neurons}},
  booktitle =	{10th Innovations in Theoretical Computer Science  Conference (ITCS 2019)},
  pages =	{57:1--57:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-095-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{124},
  editor =	{Avrim Blum},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-101506},
  doi =		{10.4230/LIPIcs.ITCS.2019.57},
  annote =	{Keywords: Brain computation, random projection, assemblies, plasticity, memory, association}

Keywords: Brain computation, random projection, assemblies, plasticity, memory, association
Collection: 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)
Issue Date: 2018
Date of publication: 08.01.2019

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