On Kolmogorov's superpositions and Boolean functions
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.
- Research Organization:
- Los Alamos National Lab., Space and Atmospheric Div., NM (US)
- Sponsoring Organization:
- USDOE Assistant Secretary for Management and Administration, Washington, DC (US)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 314133
- Report Number(s):
- LA-UR--98-2883; CONF-981210--; ON: DE99001742
- Country of Publication:
- United States
- Language:
- English
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