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On the expressivity of deep Heaviside networks

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arxiv 2505.00110 v1 pith:BBJS5234 submitted 2025-04-30 stat.ML cs.LGcs.NAmath.NA

Insung Kong , Juntong Chen , Sophie Langer , Johannes Schmidt-Hieber This is my paper · ORCID
classification stat.MLcs.LGcs.NAmath.NA
keywords deepheavisidenetworksratesactivationapplicationapproximationbounds
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We show that deep Heaviside networks (DHNs) have limited expressiveness but that this can be overcome by including either skip connections or neurons with linear activation. We provide lower and upper bounds for the Vapnik-Chervonenkis (VC) dimensions and approximation rates of these network classes. As an application, we derive statistical convergence rates for DHN fits in the nonparametric regression model.

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