|
NeuroCOLT
Technical Report NC-TR-00-071
VC
Dimension Bounds for Product Unit Networks
Michael
Schmitt
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.
Download
Compressed Postscript
|