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Neural Computation

February 15, 1997, Vol. 9, No. 2, Pages 337-348
(doi: 10.1162/neco.1997.9.2.337)
© 1997 Massachusetts Institute of Technology
Shattering All Sets of ‘k’ Points in “General Position” Requires (k — 1)/2 Parameters
Article PDF (153.25 KB)
Abstract

For classes of concepts defined by certain classes of analytic functions depending on n parameters, there are nonempty open sets of samples of length 2n + 2 that cannot be shattered. A slighly weaker result is also proved for piecewise-analytic functions. The special case of neural networks is discussed.