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arXiv · 2204.06062

Local and global topological complexity measures OF ReLU neural network functions

J. Elisenda Grigsby·Kathryn Lindsey·Marissa Masden
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Abstract

We apply a generalized piecewise-linear (PL) version of Morse theory due to Grunert-Kuhnel-Rote to define and study new local and global notions of topological complexity for fully-connected feedforward ReLU neural network functions, F: R^n -> R. Along the way, we show how to construct, for each such F, a canonical polytopal complex K(F) and a deformation retract of the domain onto K(F), yielding a convenient compact model for performing calculations. We also give a construction showing that local complexity can be arbitrarily high.

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BibTeXRIS

J. Elisenda Grigsby, Kathryn Lindsey, Marissa Masden. 2022-04-12. Local and global topological complexity measures OF ReLU neural network functions. https://arxiv.org/abs/2204.06062

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