NeuroCOLT: Neural Networks and Computational Learning Theory

NeuroCOLT

Neural Networks and Computational Learning Theory

1994	1995
1996	1997
1998	1999
2000	2001

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NeuroCOLT Technical Report NC-TR-96-042

Shattering all Sets of k points in `General Position' Requires (k-1)/2 Parameters

Eduardo D. Sontag
Rutgers University
USA

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 which cannot be shattered. A slightly weaker result is also proved for piecewise-analytic functions. The special case of neural networks is discussed.

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