Comment on "Manifolds of quasi-constant SOAP and ACSF fingerprints and the resulting failure to machine learn four body interactions"

TL;DR

This paper analyzes the origin of quasi-constant SOAP and ACSF fingerprint manifolds, revealing they stem from degenerate configuration pairs and discussing their impact on machine learning models of molecular interactions.

Contribution

It clarifies the cause of quasi-constant fingerprint manifolds and assesses their influence on the accuracy and transferability of machine learning models for high-order interactions.

Findings

Quasi-constant manifolds arise from degenerate configuration pairs.

Singular configurations are finite and discrete, not continuous.

Numerical instabilities near singularities affect model transferability.

Abstract

The "quasi-constant" SOAP and ACSF fingerprint manifolds recently discovered by Parsaeifard and Goedecker are a direct consequence of the presence of degenerate pairs of configurations, a known shortcoming of all low-body-order atom-density correlation representations of molecular structures. Contrary to the configurations that are rigorously singular -- that we demonstrate can only occur in finite, discrete sets -- the continuous "quasi-constant" manifolds exhibit low, but non-zero, sensitivity to atomic displacements. Thus, it is possible to build interpolative machine-learning models of high-order interactions along the manifold, even though the numerical instabilities associated with proximity to the exact singularities affect the accuracy and transferability of such models, to an extent that depends on numerical details of the implementation.