(Elsevier, 2023) Rodríguez Martínez, Iosu; Da Cruz Asmus, Tiago; Pereira Dimuro, Graçaliz; Herrera, Francisco; Takáč, Zdenko; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Due to their high adaptability to varied settings and effective optimization algorithm, Convolutional Neural
Networks (CNNs) have set the state-of-the-art on image processing jobs for the previous decade. CNNs work in
a sequential fashion, alternating between extracting significant features from an input image and aggregating
these features locally through ‘‘pooling" functions, in order to produce a more compact representation.
Functions like the arithmetic mean or, more typically, the maximum are commonly used to perform
this downsampling operation. Despite the fact that many studies have been devoted to the development of
alternative pooling algorithms, in practice, ‘‘max-pooling" still equals or exceeds most of these possibilities,
and has become the standard for CNN construction.
In this paper we focus on the properties that make the maximum such an efficient solution in the context
of CNN feature downsampling and propose its replacement by grouping functions, a family of functions that
share those desirable properties. In order to adapt these functions to the context of CNNs, we present (𝑎, 𝑏)-
grouping functions, an extension of grouping functions to work with real valued data. We present different
construction methods for (𝑎, 𝑏)-grouping functions, and demonstrate their empirical applicability for replacing
max-pooling by using them to replace the pooling function of many well-known CNN architectures, finding
promising results.
