Feed-Forward neural networks using hermite polynomial activation functions

Authors:
Gerasimos G. Rigatos;Spyros G. Tzafestas
Affiliations:
Industrial Systems Institute, Unit of Industrial Automation, Rion Patras, Greece;Dept. of Electrical and Computer Engineering, National Technical University of Athens, Athens, Greece
Venue:
SETN'06 Proceedings of the 4th Helenic conference on Advances in Artificial Intelligence
Year:
2006

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Abstract

In this paper feed-forward neural networks are introduced where 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, and (ii) the basis functions are the eigenstates of the quantum harmonic oscillator, and stem from the solution of Schrödinger's diffusion equation. The proposed neural networks demonstrate the particle-wave nature of information and can be used in nonparametric estimation. Possible applications of neural networks with Hermite basis functions include system modelling and image processing.