Interpolation representation of feedforward neural networks

Authors:
Hong-Xing Li;Ling-Xia Li;Jia-Yin Wang
Affiliations:
Department of Mathematics, Beijing Normal University Beijing 100875, P.R. China and Department of Mathematics, Sichuan Normal University Chengdu 610066, P.R. China and Department of Automation, Ts ...;Department of information Systems and Decision Sciences Old Dominion University, Norfolk, VA 23529-0223, U.S.A.;Department of Mathematics, Beijing Normal University Beijing 100875, P.R. China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2003

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Abstract

Mathematical essence and structures of feedforward neural networks are researched in detail in this paper. First of all, interpolation mechanism of Feedforward neural networks is exposed, so we can more clearly understand why a feedforward network is of approximation. For example, a well-known conclusion for arbitrarily a continuous function, there exists a three-layer forward neural network such that the network can approximate the function to within any given precision. It, in fact, is regarded as a natural result of interpolation representation. Then the learning algorithms of feedforward neural networks are discussed by some new ideas.