Miloslav Torda

Stochastic relaxation is a well-established technique in machine learning and artificial intelligence used to tackle complex optimization landscapes. Here, we employ stochastic relaxation to address the challenge of discovering the densest packing of closed subsets of n-dimensional Euclidean space, subject to constraints imposed by the Crystallographic Symmetry Group (CSG). To this end, we introduce the Entropic Trust Region Packing Algorithm (ETRPA), which is an instance of the natural gradient learning method with adaptive selection quantile fitness rewriting. Since CSGs induce a toroidal topology on the configuration space, we perform the ETRPA search on a parametric family of probability measures defined on an n-dimensional torus. We examine the information geometry of the ETRPA through its equivalence with the generalized proximal method and characterize the algorithm via local dual geodesic flows that maximize multi-information, a measure of stochastic dependence in complex systems. Therefore, the evolutionary dynamics, statistical physics, and information theoretic background of the ETRPA can be understood in terms of more general graphical interaction models. This work is motivated by the problem of molecular Crystal Structure Prediction, which involves predicting a synthesizable periodic structure based on a molecule's chemical composition and specific pressure-temperature conditions.