A Wavelet View for Unifying Boolean Discrete Functions and Neural Nets through Haar Transform

Masatoshi SEKINE  

IEICE TRANSACTIONS on Electronics   Vol.E80-C   No.7   pp.1003-1009
Publication Date: 1997/07/25
Online ISSN: 
Print ISSN: 0916-8516
Type of Manuscript: Special Section PAPER (Special Issue on New Concept Device and Novel Architecture LSIs)
Category: Neural Networks and Chips
synthesis,  wavelet neural net,  significant variable,  multi-valued function,  spectral transform,  

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Spectral transform methods have been widely studied for classification and analysis of logic functions. Spectral methods have also been used for logic synthesis, and by use of BDDs, practical-sized synthesis problems have been solved. Wavelet theory has recently attracted the attention of researchers in the signal processing field. The Haar function is used in both spectral methods and in signal processing to obtain spectral coefficients of logic functions of signals. In this paper spectral transform-based analysis of neural nets verifying signal processing and discrete function is presented. A neural net element is defined as a discrete function with multi-valued input signals and multi-valued or binary outputs. The multi-valued variable is realized as a variable (V, W) formed by a pair of a binary value and a multi-value pulse width. The multi-valued encoding is used with the multi-valued Haar function to give meanings to the wavelet coefficients from the view of Boolean algebra. A design example shows that these conceptually different concepts are closely related.