  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.
