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Long Term Memory and the Densest K-Subgraph Problem

Authors Robert Legenstein, Wolfgang Maass, Christos H. Papadimitriou, Santosh S. Vempala

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  • Brain computation
  • long term memory
  • assemblies
  • association

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Abstract

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.

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

Author Details

Robert Legenstein
Wolfgang Maass
Christos H. Papadimitriou
Santosh S. Vempala

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