Michael Joswig

Michael Joswig, Marek Kaluba, Lukas Ruff

We propose a new geometric method for measuring the quality of representations obtained from deep learning. Our approach, called Random Polytope Descriptor, provides an efficient description of data points based on the construction of random convex polytopes. We demonstrate the use of our technique by qualitatively comparing the behavior of classic and regularized autoencoders. This reveals that applying regularization to autoencoder networks may decrease the out-of-distribution detection performance in latent space. While our technique is similar in spirit to $k$-means clustering, we achieve significantly better false positive/negative balance in clustering tasks on autoencoded datasets.

Michael Joswig, Joe Kileel, Bernd Sturmfels et al.

The multiview variety from computer vision is generalized to images by $n$ cameras of points linked by a distance constraint. The resulting five-dimensional variety lives in a product of $2n$ projective planes. We determine defining polynomial equations, and we explore generalizations of this variety to scenarios of interest in applications.