Unified theory of atom-centered representations and message-passing machine-learning schemes
This provides a foundational theory for machine-learning models in chemistry and materials science, though it is incremental in extending existing frameworks.
The paper tackles the challenge of unifying atom-centered and message-passing machine-learning schemes for molecular and crystal structures by generalizing atom-centered density correlations to include multi-centered information, resulting in a complete linear basis for regressing symmetric functions of atomic coordinates.
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.