Neural Structures Using the Eigenstates of a Quantum Harmonic Oscillator

Authors:
Gerasimos Rigatos;Spyros Tzafestas
Affiliations:
Unit of Industrial Automation, Industrial Systems Institute, Rion Patras, Greece 26504;Department of Electrical and Computer Engineering, National Technical University of Athens, Zografou Athens, Greece 15773
Venue:
Open Systems & Information Dynamics
Year:
2006

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Abstract

The main result of the paper is the use of orthogonal Hermite polynomials as the basis functions of feedforward neural networks. 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 demonstrate the particle-wave nature of information and can be used in nonparametric estimation. Possible applications of the proposed neural networks include function approximation, image processing and system modelling.