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We derive exact expressions for the probabilities that partly randomhyperplanes separate two Euclidean balls. The probability that a fully randomhyperplane separates two balls turns out to be significantly smaller than thecorresponding probabilities for hyperplanes which are not fully random incertain cases. Our results motivate studying partially random neural networksand provide a first step in this direction.

Separating balls with partly random hyperplanes with a view to partly random neural networks