Dynamics of the Amari-Takeuchi competitive learning model

Author

Troyer, Todd

Author_Institution

Dept. of Math., California Univ., Berkeley, CA, USA

fYear

1991

fDate

8-14 Jul 1991

Firstpage

237

Abstract

A rigorous analysis of an analog version of the Amari-Takeuchi (1978) theory of self-organization of category detecting nerve cells is given. Convergence of the learning is proven by constructing a Lyapunov function for the learning dynamics in a convenient set of coordinates. This function has separate terms reflecting the Hebbian learning and lateral inhibition components of the theory. This facilitates a theoretic characterization of the categories formed by the model. Also proposed is a different network interpretation of the equations, with the outputs implicit functions of the inputs

Keywords

Lyapunov methods; brain models; learning systems; neural nets; self-adjusting systems; Amari-Takeuchi; Hebbian learning; Lyapunov function; brain model; category characterisation; category detecting nerve cells; competitive learning model; convergence; lateral inhibition components; learning dynamics; neural nets; self-organization; Brain modeling; Convergence; Differential equations; Electronic mail; Hebbian theory; Lyapunov method; Mathematical model; Mathematics; Neurons; Nonlinear equations;

fLanguage

English

Publisher

ieee

Conference_Titel

Neural Networks, 1991., IJCNN-91-Seattle International Joint Conference on

Conference_Location

Seattle, WA

Print_ISBN

0-7803-0164-1

Type

conf

DOI

10.1109/IJCNN.1991.155344

Filename

155344