Characterizing generalization and adversarial robustness for set networks

Disobeying the classical wisdom of statistical learning theory, modern deep neural networks generalize well even though they typically contain millions of parameters. Hence, a new generation of learning theory has emerged to explain the characteristics of deep neural networks, such as generalization, overfitting or robustness. Empirical or theoretical, most of the works which prosper in bringing insights to the learning phenomenon, focus on convolutional networks, operating on the image domain. However, a vast majority of the computer vision problems involve either graphs or point clouds which live in unstructured domains. The goal of this project is to first empirically understand the generalization character of point cloud networks. To this end, we will deploy a series of state of the art measures. Guided by this empirical study, we aim to theorize how and why deep sets generalize. In particular, we will focus on topological data analysis as a unifying framework.