Learning derivatives: increasing accuracy and robustness in computer vision tasks

Learning derivatives improves the accuracy of neural networks for a number of low-dimensional tasks. In this paper, this approach is adapted to the model task of machine vision: reconstructing the vertices of a cube from its image. So, learning derivatives by degrees of freedom of a cube allows you to increase the accuracy by 25 times. Derivatives also allow us to solve the problem of robustness, which consists in the presence of two types of vulnerabilities. The first type is small perturbations that dramatically change the network output, and the second is significant image changes that the network mistakenly ignores. Traditionally, robust learning is based on local invariance, which does not allow arbitrary reduction of resistance to both types of perturbations. For this task, knowledge of image derivatives in terms of degrees of freedom allows us to build robust learning without assumptions about local invariance, as a result of which accuracy and resistance to any disturbances are limited only by the size of the network. The prospects of application to real-world tasks of machine vision are discussed.