On the overlap dynamics of multi-state neural networks with a finite number of patterns

Autor:	Désiré Bollé, Patrick Dupont, B Vinck
Rok vydání:	1992
Předmět:	Lyapunov function Artificial neural network Time evolution General Physics and Astronomy Statistical and Nonlinear Physics Fixed point Stability (probability) Combinatorics symbols.namesake Hebbian theory symbols Statistical physics Absolute zero Finite set Mathematical Physics Mathematics
Zdroj:	Journal of Physics A: Mathematical and General. 25:2859-2872
ISSN:	1361-6447 0305-4470
DOI:	10.1088/0305-4470/25/10/014
Popis:	Neural networks with multi-state neurons are studied in the case of low loading. For symmetric couplings satisfying a certain positivity condition, a Lyapunov function is shown to exist in the space of overlaps between the instantaneous microscopic state of the system and the learned patterns. Furthermore, an algorithm is derived for zero temperature to determine all the fixed points. As an illustration, the three-state model is worked out explicitly for Hebbian couplings. For finite temperature the time evolution of the overlap is studied for couplings which need not be symmetric. The stability properties are discussed in detail for the three-state model. For asymmetric couplings limit-cycle behaviour is shown to be possible.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::2946a2e74c34b27991faef92810053c4 https://doi.org/10.1088/0305-4470/25/10/014 Zobrazit plný text záznamu