Parameter Estimation of Sigmoid Superpositions: Dynamical System Approach

Details Parameter Estimation of Sigmoid Superpositions: Dynamical System Approach Parameter Estimation of Sigmoid Superpositions: Dynamical System Approach

2002-07-09

arxiv.org/abs/math/0207075v2

Neural Computation, 15, 2419-2455 (2003)

Mathematics

Optimization and Control

30 pages, 7 figures

Scientific paper

Superposition of sigmoid function over a finite time interval is shown to be equivalent to the linear combination of the solutions of a linearly parameterized system of logistic differential equations. Due to the linearity with respect to the parameters of the system, it is possible to design an effective procedure for parameter adjustment. Stability properties of this procedure are analyzed. Strategies shown in earlier studies to facilitate learning such as randomization of a learning sequence and adding specially designed disturbances during the learning phase are requirements for guaranteeing convergence in the learning scheme proposed.

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