Shattering All Sets of ‘k’ Points in “General Position” Requires (k — 1)/2 Parameters
Eduardo D. Sontag · Neural Computation · 1997
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.