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

TL;DR

This paper provides a rigorous mathematical analysis of striding in CNNs, showing it can be viewed as a form of parameter sharing that reduces training complexity, offering new insights into CNN design.

Contribution

It introduces a theoretical framework demonstrating that striding can be replaced by non-striding CNNs with more filters, clarifying its role as parameter sharing.

Findings

Striding can be mathematically represented by non-striding CNNs with more filters.

Striding acts as a mechanism for parameter sharing among channels.

The framework simplifies future theoretical analysis of CNNs.

Abstract

Since their inception, CNNs have utilized some type of striding operator to reduce the overlap of receptive fields and spatial dimensions. Although having clear heuristic motivations (i.e. lowering the number of parameters to learn) the mathematical role of striding within CNN learning remains unclear. This paper offers a novel and mathematical rigorous perspective on the role of the striding operator within modern CNNs. Specifically, we demonstrate theoretically that one can always represent a CNN that incorporates striding with an equivalent non-striding CNN which has more filters and smaller size. Through this equivalence we are then able to characterize striding as an additional mechanism for parameter sharing among channels, thus reducing training complexity. Finally, the framework presented in this paper offers a new mathematical perspective on the role of striding which we hope shall facilitate and simplify the future theoretical analysis of CNNs.