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Since their inception, CNNs have utilized some type of striding operator toreduce the overlap of receptive fields and spatial dimensions. Although havingclear heuristic motivations (i.e. lowering the number of parameters to learn)the mathematical role of striding within CNN learning remains unclear. Thispaper offers a novel and mathematical rigorous perspective on the role of thestriding operator within modern CNNs. Specifically, we demonstratetheoretically that one can always represent a CNN that incorporates stridingwith an equivalent non-striding CNN which has more filters and smaller size.Through this equivalence we are then able to characterize striding as anadditional mechanism for parameter sharing among channels, thus reducingtraining complexity. Finally, the framework presented in this paper offers anew mathematical perspective on the role of striding which we hope shallfacilitate and simplify the future theoretical analysis of CNNs.

Take it in your stride: Do we need striding in CNNs?