ECCC-Report TR00-002https://eccc.weizmann.ac.il/report/2000/002Comments and Revisions published for TR00-002en-usFri, 14 Jan 2000 15:56:59 +0200
Paper TR00-002
| Lower Bounds on the Complexity of Approximating Continuous Functions by Sigmoidal Neural Networks |
Michael Schmitt
https://eccc.weizmann.ac.il/report/2000/002 We calculate lower bounds on the size of sigmoidal neural networks
that approximate continuous functions. In particular, we show that
for the approximation of polynomials the network size has to grow
as $\Omega((\log k)^{1/4})$ where $k$ is the degree of the polynomials.
This bound is valid for any input dimension, i.e. independently of
the number of variables. The result is obtained by introducing a new
method employing upper bounds on the Vapnik-Chervonenkis dimension
for proving lower bounds on the size of networks that approximate
continuous functions.
Fri, 14 Jan 2000 15:56:59 +0200https://eccc.weizmann.ac.il/report/2000/002