Unified theory of atom-centered representations and message-passing machine-learning schemes

TL;DR

This paper presents a unified theoretical framework that connects atom-centered density correlations and message-passing schemes, providing a comprehensive basis for machine learning models of molecular and crystal structures.

Contribution

It generalizes the atom-centered density correlation approach to include multi-centered information, unifying different machine learning schemes under a single theoretical foundation.

Findings

Provides a complete linear basis for symmetric functions of atomic coordinates.

Unifies atom-centered and message-passing machine learning schemes.

Lays a foundation for systematic development of structure-property models.

Abstract

Data-driven schemes that associate molecular and crystal structures with their microscopic properties share the need for a concise, effective description of the arrangement of their atomic constituents. Many types of models rely on descriptions of atom-centered environments, that are associated with an atomic property or with an atomic contribution to an extensive macroscopic quantity. Frameworks in this class can be understood in terms of atom-centered density correlations (ACDC), that are used as a basis for a body-ordered, symmetry-adapted expansion of the targets. Several other schemes, that gather information on the relationship between neighboring atoms using "message-passing" ideas, cannot be directly mapped to correlations centered around a single atom. We generalize the ACDC framework to include multi-centered information, generating representations that provide a complete linear basis to regress symmetric functions of atomic coordinates, and provides a coherent foundation to systematize our understanding of both atom-centered and message-passing, invariant and equivariant machine-learning schemes.