On Kolmogorov's superpositions and Boolean functions

被引：4

作者：

Beiu, V ^{[1
]}

机构：

[1] Univ Calif Los Alamos Natl Lab, Space & Atmospher Div NIS1, Los Alamos, NM 87545 USA

来源：

VTH BRAZILIAN SYMPOSIUM ON NEURAL NETWORKS, PROCEEDINGS | 1998年

关键词：

neural networks; Kolmogorov's superpositions; Boolean circuits; threshold gate circuits; analog circuits; size; precision;

D O I：

10.1109/SBRN.1998.730994

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

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 will show that for obtaining minimum size neural 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 she-optimal solutions for implementing arbitrary Boolean functions require analog circuitry. Conclusions and several comments on the required precision are ending the paper.

引用

页码：55 / 60

页数：6