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arxiv:2204.06062

Local and global topological complexity measures OF ReLU neural network functions

Published on Apr 1, 2024
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Abstract

Research applies generalized piecewise-linear Morse theory to define topological complexity measures for ReLU neural networks and constructs canonical polytopal complexes for analysis.

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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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