Title: Generating valid Euclidean distance matrices. Abstract: Generating point clouds, e.g., molecular structures, in arbitrary rotations, translations, and enumerations remains a challenging task. Meanwhile, neural networks
utilizing symmetry invariant layers have been shown to be able to optimize their
training objective in a data-efficient way. In this spirit, we present an architecture
which allows to produce valid Euclidean distance matrices, which by construction are already invariant under rotation and translation of the described object.
Motivated by the goal to generate molecular structures in Cartesian space, we use
this architecture to construct a Wasserstein GAN utilizing a permutation invariant critic network. This makes it possible to generate molecular structures in a
one-shot fashion by producing Euclidean distance matrices which have a three-
dimensional embedding.