Paper:
Language: English:

Feed-Forward Neural Networks Based on the Eigenstates of the Quantum Harmonic Oscillator

Gerasimos Rigatos

Unit of Industrial Automation, Industrial Systems Institute, 26504, Rion Patras, Greece

Received: September 1, 2005

Accepted: January 30, 2006

Keywords: feed-forward neural networks, quantum harmonic oscillator, Schrödinger’s diffusion equation, Gauss-Hermite expansion, Hermite polynomials

Journal ref: Journal of Advanced Computational Intelligence and Intelligent Informatics, Vol.10, No.4 pp. 567-577, 2006

Abstract

The paper introduces feed-forward neural networks where the hidden units employ orthogonal Hermite polynomials for their activation functions. The proposed neural networks have some interesting properties: (i) the basis functions are invariant under the Fourier transform, subject only to a change of scale, (ii) the basis functions are the eigenstates of the quantum harmonic oscillator, and stem from the solution of Schrödinger’s diffusion equation. The proposed feed-forward neural networks belong to the general category of nonparametric estimators and can be used for function approximation, system modelling and image processing.

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