# Manifolds of quasi-constant SOAP and ACSF fingerprints and the resulting failure to machine learn four-body interactions.

@article{Parsaeifard2022ManifoldsOQ, title={Manifolds of quasi-constant SOAP and ACSF fingerprints and the resulting failure to machine learn four-body interactions.}, author={Behnam Parsaeifard and Stefan Goedecker}, journal={The Journal of chemical physics}, year={2022}, volume={156 3}, pages={ 034302 } }

Atomic fingerprints are commonly used for the characterization of local environments of atoms in machine learning and other contexts. In this work, we study the behavior of two widely used fingerprints, namely, the smooth overlap of atomic positions (SOAP) and the atom-centered symmetry functions (ACSFs), under finite changes of atomic positions and demonstrate the existence of manifolds of quasi-constant fingerprints. These manifolds are found numerically by following eigenvectors of the…

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