Hierarchical Function Approximation with a Neural Network Model

Hierarchical Function Approximation with a Neural Network Model

Luis F. de Mingo (Universidad Politécnica de Madrid, Spain), Nuria Gómez (Universidad Politécnica de Madrid, Spain), Fernando Arroyo (Universidad Politécnica de Madrid, Spain) and Juan Castellanos (Universidad Politécnica de Madrid, Spain)
DOI: 10.4018/jssci.2009070105
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Abstract

This article presents a neural network model that permits to build a conceptual hierarchy to approximate functions over a given interval. Bio-inspired axo-axonic connections are used. In these connections the signal weight between two neurons is computed by the output of other neuron. Such architecture can generate polynomial expressions with lineal activation functions. This network can approximate any pattern set with a polynomial equation. This neural system classifies an input pattern as an element belonging to a category that the system has, until an exhaustive classification is obtained. The proposed model is not a hierarchy of neural networks; it establishes relationships among all the different neural networks in order to propagate the activation. Each neural network is in charge of the input pattern recognition to any prototyped category, and also in charge of transmitting the activation to other neural networks to be able to continue with the approximation.

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