  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.
