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

Olov Schavemaker

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arXiv · 2505.10470

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

Olov Schavemaker

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Abstract

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

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Olov Schavemaker. 2025-05-15. Separating balls with partly random hyperplanes with a view to partly random neural networks. https://arxiv.org/abs/2505.10470

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