VC Dimension of Sigmoidal and General Pfaffian Neural Networks

TitleVC Dimension of Sigmoidal and General Pfaffian Neural Networks
Publication TypeTechnical Report
Year of Publication1995
AuthorsKarpinski, M., & Macintyre A.
Other Numbers1005
KeywordsBoolean Computation, neural networks, Pfaffian Activation Functions and Formulas, Sparse Networks, VC Dimension

We introduce a new method for proving explicit upper bounds on the VC Dimension of general functional basis networks, and prove as an application, for the first time, that the VC Dimension of analog neural networks with the sigmoidal activation function sigma(y)=1/1+e^{-y} is bounded by a quadratic polynomial O((lm)^2) in both the number l of programmable parameters, and the number m of nodes. The proof method of this paper generalizes to much wider class of Pfaffian activation functions and formulas, and gives also for the first time polynomial bounds on their VC Dimension. We present also some other applications of our method.

Bibliographic Notes

ICSI Technical Report TR-95-065

Abbreviated Authors

M. Karpinski and A. Macintyre

ICSI Publication Type

Technical Report