DocumentCode :
2350967
Title :
On Kolmogorov´s superpositions and Boolean functions
Author :
Beiu, Valeriu
Author_Institution :
Space & Atmos. Div., Los Alamos Nat. Lab., NM, USA
fYear :
1998
fDate :
9-11 Dec 1998
Firstpage :
55
Lastpage :
60
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 we show that for obtaining minimum size neural networks for implementing any Boolean function, the activation function of the neurons is the identity function. Since classical AND-OR implementations, as well as threshold gate implementations which require exponential size (in the worst case), it follows that size-optimal solutions for implementing arbitrary Boolean functions require analog circuitry. Conclusions and several comments on the required precision are presented
Keywords :
Boolean functions; feedforward neural nets; function approximation; logic gates; threshold logic; Boolean functions; Kolmogorov superpositions; activation function; feedforward neural networks; function approximation; logic gates; threshold gate circuits; Boolean functions; Circuits; Computer networks; Independent component analysis; Laboratories; Neural networks; Neurofeedback; Neurons; Optical computing; Postal services;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Neural Networks, 1998. Proceedings. Vth Brazilian Symposium on
Conference_Location :
Belo Horizonte
Print_ISBN :
0-8186-8629-4
Type :
conf
DOI :
10.1109/SBRN.1998.730994
Filename :
730994
Link To Document :
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