Shattering All Sets of ‘k’ Points in “General Position” Requires (k — 1)/2 Parameters
- 1 February 1997
- journal article
- Published by MIT Press in Neural Computation
- Vol. 9 (2) , 337-348
- https://doi.org/10.1162/neco.1997.9.2.337
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.Keywords
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