Generating valid Euclidean distance matrices

TL;DR

This paper introduces a neural network architecture that generates valid Euclidean distance matrices invariant to rotation and translation, enabling efficient one-shot generation of molecular structures in Cartesian space.

Contribution

The authors develop a novel architecture for producing valid Euclidean distance matrices, facilitating invariant molecular structure generation with a Wasserstein GAN.

Findings

Successfully generates valid Euclidean distance matrices.

Enables one-shot molecular structure generation.

Uses permutation invariant critic network for improved performance.

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.