A Vector Space Model for Neural Network Functions: Inspirations From Similarities Between the Theory of Connectivity and the Logarithmic Time Course of Word Production

Ortwin Fromm; Fabian Klostermann; Felicitas Ehlen

doi:10.3389/fnsys.2020.00058

A Vector Space Model for Neural Network Functions: Inspirations From Similarities Between the Theory of Connectivity and the Logarithmic Time Course of Word Production

Front Syst Neurosci. 2020 Aug 28:14:58. doi: 10.3389/fnsys.2020.00058. eCollection 2020.

Authors

Ortwin Fromm¹, Fabian Klostermann^{1

2}, Felicitas Ehlen^{1

3}

Affiliations

¹ Motor and Cognition Group, Department of Neurology, Charité - Universitätsmedizin Berlin, Berlin, Germany.
² Berlin School of Mind and Brain, Humboldt-Universität zu Berlin, Berlin, Germany.
³ Department of Psychiatry, Jüdisches Krankenhaus Berlin, Berlin, Germany.

Abstract

The present report examines the coinciding results of two study groups each presenting a power-of-two function to describe network structures underlying perceptual processes in one case and word production during verbal fluency tasks in the other. The former is theorized as neural cliques organized according to the function N = 2 ⁱ - 1, whereas the latter assumes word conglomerations thinkable as tuples following the function N = 2 ⁱ . Both theories assume the innate optimization of energy efficiency to cause the specific connectivity structure. The vast resemblance between both formulae motivated the development of a common formulation. This was obtained by using a vector space model, in which the configuration of neural cliques or connected words is represented by a N-dimensional state vector. A further analysis of the model showed that the entire time course of word production could be derived using basically one single minimal transformation-matrix. This again seems in line with the principle of maximum energy efficiency.

Keywords: connectivity; energy efficiency; neural clique; neural network; vector space; word production.