VC Dimension of Sigmoidal and General Pfaffian Neural Networks
| Title | VC Dimension of Sigmoidal and General Pfaffian Neural Networks |
| Publication Type | Technical Report |
| Year of Publication | 1995 |
| Authors | Karpinski, M., & Macintyre A. |
| Other Numbers | 1005 |
| Keywords | Boolean Computation, neural networks, Pfaffian Activation Functions and Formulas, Sparse Networks, VC Dimension |
| Abstract | 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. |
| URL | http://www.icsi.berkeley.edu/ftp/global/pub/techreports/1995/tr-95-065.pdf |
| Bibliographic Notes | ICSI Technical Report TR-95-065 |
| Abbreviated Authors | M. Karpinski and A. Macintyre |
| ICSI Publication Type | Technical Report |