  In this paper, we propose neural networks that tackle the problems of
stability and field-of-view of a Convolutional Neural Network (CNN). As an
alternative to increasing the network's depth or width to improve performance,
we propose integral-based spatially nonlocal operators which are related to
global weighted Laplacian, fractional Laplacian and inverse fractional
Laplacian operators that arise in several problems in the physical sciences.
The forward propagation of such networks is inspired by partial
integro-differential equations (PIDEs). We test the effectiveness of the
proposed neural architectures on benchmark image classification datasets and
semantic segmentation tasks in autonomous driving. Moreover, we investigate the
extra computational costs of these dense operators and the stability of forward
propagation of the proposed neural networks.
