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

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.

Unexpected Aspects of Expectancy in Music

“…For example, a new, unfamiliar piece of music that is 10 minutes long will initially have no mental representation it can activate, particularly if there is nothing familiar about the context in which the piece is situated. However, there may be portions of the piece that are familiar or can otherwise be processed fluently (Huron, 2013;Reber et al, 2004), meaning that 'higher level' or 'superordinate' (Fromm et al, 2020;Rendeiro et al, 2014) cell-assemblies can become activated during those musical events. The segmentation can be applied to 'vertical' features, such as timbre or harmony at any given time (as in the pitch to chord activation, and other semantic and contextual nodes -see Bharucha & Stoeckig, 1987), or as short musical episodes, which are in Western music of the common practice period frequently conceived in a time-scale based hierarchy from (shortest to longest, or events to episodes) pitch-rhythm combinations (or motifs), to subphrases, to phrases, to periods, to sections, to movements, to an entire work (Benward & White, 1997;Drabkin, 2001;Jackendoff & Lerdahl, 1983, p. 8;Ratner, 2001;Schubert, 2021).…”