On Kolmogorov's superpositions and Boolean functions
Abstract
The paper overviews results dealing with the approximation capabilities of neural networks, as well as bounds on the size of threshold gate circuits. Based on an explicit numerical (i.e., constructive) algorithm for Kolmogorov's superpositions they will show that for obtaining minimum size neutral networks for implementing any Boolean function, the activation function of the neurons is the identity function. Because classical AND-OR implementations, as well as threshold gate implementations require exponential size (in the worst case), it will follow that size-optimal solutions for implementing arbitrary Boolean functions require analog circuitry. Conclusions and several comments on the required precision are ending the paper.
- Authors:
- Publication Date:
- Research Org.:
- Los Alamos National Lab., Space and Atmospheric Div., NM (US)
- Sponsoring Org.:
- USDOE Assistant Secretary for Management and Administration, Washington, DC (US)
- OSTI Identifier:
- 314133
- Report Number(s):
- LA-UR-98-2883; CONF-981210-
ON: DE99001742; TRN: US200304%%281
- DOE Contract Number:
- W-7405-ENG-36
- Resource Type:
- Conference
- Resource Relation:
- Conference: Brazilian symposium on neural networks, Belo Horizonte (BR), 12/09/1998--12/11/1998; Other Information: Supercedes report DE99001742; PBD: [1998]; PBD: 31 Dec 1998
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ACCURACY; ALGORITHMS; NERVE CELLS; NEURAL NETWORKS
Citation Formats
Beiu, V. On Kolmogorov's superpositions and Boolean functions. United States: N. p., 1998.
Web.
Beiu, V. On Kolmogorov's superpositions and Boolean functions. United States.
Beiu, V. 1998.
"On Kolmogorov's superpositions and Boolean functions". United States. https://www.osti.gov/servlets/purl/314133.
@article{osti_314133,
title = {On Kolmogorov's superpositions and Boolean functions},
author = {Beiu, V},
abstractNote = {The paper overviews results dealing with the approximation capabilities of neural networks, as well as bounds on the size of threshold gate circuits. Based on an explicit numerical (i.e., constructive) algorithm for Kolmogorov's superpositions they will show that for obtaining minimum size neutral networks for implementing any Boolean function, the activation function of the neurons is the identity function. Because classical AND-OR implementations, as well as threshold gate implementations require exponential size (in the worst case), it will follow that size-optimal solutions for implementing arbitrary Boolean functions require analog circuitry. Conclusions and several comments on the required precision are ending the paper.},
doi = {},
url = {https://www.osti.gov/biblio/314133},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Thu Dec 31 00:00:00 EST 1998},
month = {Thu Dec 31 00:00:00 EST 1998}
}