VC dimension bounds for product unit networks

Author

Schmitt, Michael

Author_Institution

Lehrstuhl Math. & Inf., Ruhr-Univ., Bochum, Germany

Volume

4

fYear

2000

fDate

2000

Firstpage

165

Abstract

A product unit is a formal neuron that multiplies its input values instead of summing them. Furthermore, it has weights acting as exponents instead of being factors. We investigate the complexity of learning for networks containing product units. We establish bounds on the Vapnik-Chervonenkis (VC) dimension that can be used to assess the generalization capabilities of these networks. In particular, we show that the VC dimension for these networks is not larger than the best known bound for sigmoidal networks. For higher-order networks we derive upper bounds that are independent of the degree of these networks. We also contrast these results with lower bounds

Keywords

computational complexity; feedforward neural nets; generalisation (artificial intelligence); learning (artificial intelligence); Vapnik-Chervonenkis dimension; feedforward neural networks; generalization; learning; lower bounds; product unit networks; sigmoidal networks; upper bounds; Artificial neural networks; Biological system modeling; Biology computing; Computer networks; Explosions; Neural networks; Neurons; Polynomials; Upper bound; Virtual colonoscopy;

fLanguage

English

Publisher

ieee

Conference_Titel

Neural Networks, 2000. IJCNN 2000, Proceedings of the IEEE-INNS-ENNS International Joint Conference on

Conference_Location

Como

ISSN

1098-7576

Print_ISBN

0-7695-0619-4

Type

conf

DOI

10.1109/IJCNN.2000.860767

Filename

860767