Some Implications of Interval Approach to Dimension for Network Complexity

Authors: Věra Kůrková
Publication year: 2022
Publication type: Kapitola v monografii
Periodical: Computational Intelligence and Mathematics for Tackling Complex Problems 2
Projects: Capabilities and limitations of shallow and deep networks
Bibliographic citation: KŮRKOVÁ, Věra. Some Implications of Interval Approach to Dimension for Network Complexity. In: CORNEJO, M. E., KÓCZY, L. T., MEDINA-MORENO, J., MORENO-GARCÍA, J., eds. Computational Intelligence and Mathematics for Tackling Complex Problems 2. Cham: Springer, 2022, S. 113-119. Studies in Computational Intelligence, 955. ISBN 978-3-030-88816-9
Dostupné z: doi:10.1007/978-3-030-88817-6_13
DOI: 10.1007/978-3-030-88817-6_13
ID: 549873

Abstract

An interval approach to the concept of dimension is presented. Implications of exponentially growing quasiorthogonal dimension for estimates of network complexity are analyzed. Bounds on correlations of computational tasks represented by high-dimensional vectors are derived. Network complexity is explored from the point of view of the concentration of measure phenomenon.