License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2018.57
URN: urn:nbn:de:0030-drops-83593
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Legenstein, Robert ; Maass, Wolfgang ; Papadimitriou, Christos H. ; Vempala, Santosh S.

Long Term Memory and the Densest K-Subgraph Problem

LIPIcs-ITCS-2018-57.pdf (0.7 MB)


In a recent experiment, a cell in the human medial temporal lobe (MTL) encoding one sensory stimulus starts to also respond to a second stimulus following a combined experience associating the two. We develop a theoretical model predicting that an assembly of cells with exceptionally high synaptic intraconnectivity can emerge, in response to a particular sensory experience, to encode and abstract that experience. We also show that two such assemblies are modified to increase their intersection after a sensory event that associates the two corresponding stimuli. The main technical tools employed are random graph theory, and Bernoulli approximations. Assembly creation must overcome a computational challenge akin to the Densest K-Subgraph problem, namely selecting, from a large population of randomly and sparsely interconnected cells, a subset with exceptionally high density of interconnections. We identify three mechanisms that help achieve this feat in our model: (1) a simple two-stage randomized algorithm, and (2) the "triangle completion bias" in synaptic connectivity and a "birthday paradox", while (3) the strength of these connections is enhanced through Hebbian plasticity.

BibTeX - Entry

  author =	{Robert Legenstein and Wolfgang Maass and Christos H. Papadimitriou and Santosh S. Vempala},
  title =	{{Long Term Memory and the Densest K-Subgraph Problem}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{57:1--57:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Anna R. Karlin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-83593},
  doi =		{10.4230/LIPIcs.ITCS.2018.57},
  annote =	{Keywords: Brain computation, long term memory, assemblies, association}

Keywords: Brain computation, long term memory, assemblies, association
Collection: 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)
Issue Date: 2018
Date of publication: 12.01.2018

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