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Neural Computation, Vol 9, 337-348, Copyright © 1997 by The MIT Press

LETTERS

Shattering All Sets of k Points in 'General Position' Requires (k - 1)/2 Parameters

Eduardo D. Sontage

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 slightly weaker result is also proved for piecewise-analytic functions. The special case of neural networks is discussed.




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J COGNITIVE NEUROSCIENCE NEURAL COMPUTATION MIT PRESS JOURNALS
Copyright © 1997 by The MIT Press.