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 paperpeer-review


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
Publication statusPublished - 2018

Publication series

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


  • Brain computation
  • long term memory
  • assemblies
  • association


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