Deep Neural Networks and PIDE discretizations
This addresses performance issues in CNNs for computer vision applications like autonomous driving, but appears incremental as it builds on existing neural network paradigms with novel operators.
The paper tackled the stability and field-of-view limitations of CNNs by proposing neural networks inspired by partial integro-differential equations (PIDEs), using integral-based nonlocal operators like global weighted Laplacian, and tested them on image classification and semantic segmentation tasks, showing effectiveness on benchmarks.
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.