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arXiv · 1007.1282

A note on sample complexity of learning binary output neural networks under fixed input distributions

Vladimir Pestov
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Abstract

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 superexponential, 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.

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Vladimir Pestov. 2010-07-08. A note on sample complexity of learning binary output neural networks under fixed input distributions. https://doi.org/10.1109/sbrn.2010.10

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