Why Dilated Convolutional Neural Networks: A Proof of Their Optimality

Authors

Jonatan Contreras, The University of Texas at El PasoFollow
Martine Ceberio, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

6-1-2021

Comments

Technical Report: UTEP-CS-21-38c

Published in Entropy, 2021, Vol. 23, Paper 767.

Abstract

One of the most effective image processing techniques is the use of convolutional neural networks that use convolutional layers. In each such layer, the value of the output at each point is a combination of input data corresponding to several neighboring points. To improve the accuracy, researchers have developed a version of this technique, in which only data from some of the neighboring points is processed. It turns out that the most efficient case -- called dilated convolution -- is when we select the neighboring points whose differences in both coordinates are divisible by some constant l. In this paper, we explain this empirical efficiency by proving that for all reasonable optimality criteria, dilated convolution is indeed better than possible alternatives.