Long Term Memory and the Densest K-Subgraph Problem

Robert Legenstein, Wolfgang Maass, Christos H. Papapdimitriou, Santosh S. Vempala

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Abstract

In a recent experiment [9], 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 [14] and a “birthday paradox”, while (3) the strength of these connections is enhanced through Hebbian plasticity.
Original languageEnglish
Title of host publication9th Innovations in Theoretical Computer Science Conference (ITCS 2018)
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH
Pages57:1–57:15
Volume94
DOIs
Publication statusPublished - 2018

Publication series

NameLIPIcs-Leibniz International Proceedings in Informatics
PublisherSchloss Dagstuhl--Leibniz-Zentrum fuer Informatik

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Data storage equipment
Graph theory
Plasticity
Experiments

Keywords

  • Brain computation
  • long term memory
  • assemblies
  • association

Cite this

Legenstein, R., Maass, W., Papapdimitriou, C. H., & Vempala, S. S. (2018). Long Term Memory and the Densest K-Subgraph Problem. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018) (Vol. 94, pp. 57:1–57:15). [57] (LIPIcs-Leibniz International Proceedings in Informatics ). Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH. https://doi.org/10.4230/LIPIcs.ITCS.2018.57

Long Term Memory and the Densest K-Subgraph Problem. / Legenstein, Robert; Maass, Wolfgang; Papapdimitriou, Christos H. ; Vempala, Santosh S. .

9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Vol. 94 Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH, 2018. p. 57:1–57:15 57 (LIPIcs-Leibniz International Proceedings in Informatics ).

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Legenstein, R, Maass, W, Papapdimitriou, CH & Vempala, SS 2018, Long Term Memory and the Densest K-Subgraph Problem. in 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). vol. 94, 57, LIPIcs-Leibniz International Proceedings in Informatics , Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH, pp. 57:1–57:15. https://doi.org/10.4230/LIPIcs.ITCS.2018.57
Legenstein R, Maass W, Papapdimitriou CH, Vempala SS. Long Term Memory and the Densest K-Subgraph Problem. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Vol. 94. Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH. 2018. p. 57:1–57:15. 57. (LIPIcs-Leibniz International Proceedings in Informatics ). https://doi.org/10.4230/LIPIcs.ITCS.2018.57
Legenstein, Robert ; Maass, Wolfgang ; Papapdimitriou, Christos H. ; Vempala, Santosh S. . / Long Term Memory and the Densest K-Subgraph Problem. 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Vol. 94 Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH, 2018. pp. 57:1–57:15 (LIPIcs-Leibniz International Proceedings in Informatics ).
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