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### Paper:

TR95-055 | 24th November 1995 00:00

#### VC Dimension of Sigmoidal and General Pfaffian Networks

TR95-055
Authors: Marek Karpinski, Angus Macintyre
Publication: 27th November 1995 10:47
Keywords:

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.

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