Depth efficient neural networks for division and related problems

Author

Siu, Kai Yeung ; Bruck, Jehoshua ; Kailath, Thomas ; Hofmeister, Thomas

Author_Institution

Dept. of Electr. & Comput. Eng., California Univ., Irvine, CA, USA

Volume

39

Issue

3

fYear

1993

fDate

5/1/1993 12:00:00 AM

Firstpage

946

Lastpage

956

Abstract

An artificial neural network (ANN) is commonly modeled by a threshold circuit, a network of interconnected processing units called linear threshold gates. It is shown that ANNs can be much more powerful than traditional logic circuits, assuming that each threshold gate can be built with a cost that is comparable to that of AND/OR logic gates. In particular, the main results indicate that powering and division can be computed by polynomial-size ANNs of depth 4, and multiple product can be computed by polynomial-size ANNs of depth 5. Moreover, using the techniques developed, a previous result can be improved by showing that the sorting of n n-bit numbers can be carried out in a depth-3 polynomial-size ANN. Furthermore, it is shown that the sorting network is optimal in depth

Keywords

digital arithmetic; neural nets; polynomials; threshold logic; artificial neural network; depth efficient neural networks; depth-3 polynomial-size ANN; division; linear threshold gates; multiple product; powering; sorting network; threshold circuit; Analog computers; Arithmetic; Artificial neural networks; Computer networks; Concurrent computing; Integrated circuit interconnections; Logic circuits; Neural networks; Polynomials; Sorting;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.256501

Filename

256501