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A Note on Sample Complexity of Learning Binary Output Neural Networks under Fixed Input Distributions

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1 Author(s)
Pestov, V. ; Dept. of Math. & Stat., Univ. of Ottawa, Ottawa, ON, Canada

We show that the learning sample complexity of a sigmoidal neural network constructed by Sontag (1992) required to achieve a given misclassification error under a fixed purely atomic distribution can grow arbitrarily fast: for any prescribed rate of growth there is an input distribution having this rate as the sample complexity, and the bound is asymptotically tight. The rate can be super exponential, a non-recursive function, etc. We further observe that Sontag's ANN is not Glivenko-Cantelli under any input distribution having a non-atomic part.

Published in:

Neural Networks (SBRN), 2010 Eleventh Brazilian Symposium on

Date of Conference:

23-28 Oct. 2010