Finiteness Results for Sigmoidal "Neural" Networks

@inproceedings{Krogh1993FinitenessRF,
  title={Finiteness Results for Sigmoidal "Neural" Networks},
  author={Anders Krogh and Richard G. Palmer},
  year={1993}
}
1 1+x 2. This shows that arbitrary (not exp-ra denable) analytic functions may result in architectures with in-nite VC dimension. (Moreover, the architecture used is the simplest one that appears in neural nets practice.) Note that if we wish the x i 's to be bounded, for instance to be restricted to the interval [01; 1], one may replace the above x i 's and w j 's by xi c and cw j , where c = P jx i j. Similarly, if one wants to restrict the weights w j to be bounded, one can use cx i and wj c… CONTINUE READING
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