The Power of Extra Analog Neuron

Authors: Jiří Šíma
Publication year: 2014
Publication type: Konferenční příspěvek (mezinárodní konf.)
Periodical: Theory and Practice of Natural Computing
Projects: NoSCoM: Non-Standard Computational Models and Their Applications in Complexity, Linguistics, and Learning
Bibliographic citation: ŠÍMA, Jiří. The Power of Extra Analog Neuron. In: DEDIU, A.H., LOZANO, M., MARTÍN-VIDE, C., eds. Theory and Practice of Natural Computing. Cham: Springer, 2014, S. 243-254. Theoretical Computer Science and General Issues, 8890. ISBN 978-3-319-13748-3. ISSN 0302-9743
Dostupné z: doi:10.1007/978-3-319-13749-0_21
DOI: 10.1007/978-3-319-13749-0_21
ID: 431209

Abstract

In the effort to refine the analysis of computational power of neural nets between integer and rational weights we study a hybrid binary-state network with an extra analog unit. We introduce a finite automaton with a register which is shown to be computationally equivalent to such a network. The main result is a sufficient condition for a language accepted by this automaton to be regular which is based on the new concept of a quasi-periodic power series. These preliminary results suggest an interesting connection with the active research field on the expansions of numbers in non-integer bases which seems to be a fruitful area for further research including many important open problems.