Local and global topological complexity measures OF ReLU neural network functions

arXiv:2204.06062v2 Announce Type: replace-cross
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 …

abstract apply arxiv complexity construct cs.cg cs.lg functions generalized global linear math.at network neural network relu show study theory the way type