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

2006 ◽  
Vol 10 (4) ◽  
pp. 567-577
Author(s):  
Gerasimos Rigatos ◽  
Keyword(s):  
Neural Networks ◽  
Harmonic Oscillator ◽  
Hermite Polynomials ◽  
Basis Functions ◽  
System Modelling ◽  
General Category ◽  
Quantum Harmonic Oscillator ◽  
Feed Forward ◽  
Change Of Scale ◽  
Feed Forward Neural Networks

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.

Neural Structures Using the Eigenstates of a Quantum Harmonic Oscillator

2006 ◽  
Vol 13 (01) ◽  
pp. 27-41 ◽  
Author(s):  
Gerasimos Rigatos ◽  
Spyros Tzafestas
Keyword(s):  
Neural Networks ◽  
Harmonic Oscillator ◽  
Hermite Polynomials ◽  
Feedforward Neural Networks ◽  
Basis Functions ◽  
System Modelling ◽  
Quantum Harmonic Oscillator ◽  
Wave Nature ◽  
Change Of Scale ◽  
The Fourier Transform

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.

An Evolutionary Approach to the Use of Neural Networks in the Segmentation of Handwritten Numerals

1997 ◽  
Vol 11 (05) ◽  
pp. 717-734 ◽  
Author(s):  
J. M. Westall ◽  
M. S. Narasimha
Keyword(s):  
Neural Networks ◽  
Production System ◽  
Background Noise ◽  
Evolutionary Approach ◽  
Feed Forward ◽  
Feed Forward Neural Networks ◽  
Decision Functions

Neural networks are now widely and successfully used in the recognition of handwritten numerals. Despite their wide use in recognition, neural networks have not seen widespread use in segmentation. Segmentation can be extremely difficult in the presence of connected numerals, fragmented numerals, and background noise, and its failure is a principal cause of rejected and incorrectly read documents. Therefore, strategies leading to the successful application of neural technologies to segmentation are likely to yield important performance benefits. In this paper we identify problems that have impeded the use of neural networks in segmentation and describe an evolutionary approach to applying neural networks in segmentation. Our approach, based upon the use of monotonic fuzzy valued decision functions computed by feed-forward neural networks, has been successfully employed in a production system.

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