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

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.

arXiv commentComment on arXiv:2102.06915

References in corpus (17)

• On representing chemical environments
• Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning
• Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics
• Moment Tensor Potentials: a class of systematically improvable interatomic potentials
• Physics-inspired structural representations for molecules and materials
• Alchemical and structural distribution based representation for improved QML
• Understanding molecular representations in machine learning: The role of uniqueness and target similarity
• On the Completeness of Atomic Structure Representations
• Atom-Density Representations for Machine Learning
• Optimizing many-body atomic descriptors for enhanced computational performance of machine learning based interatomic potentials
• Metrics for measuring distances in configuration spaces
• Feature Optimization for Atomistic Machine Learning Yields A Data-Driven Construction of the Periodic Table of the Elements
• Recursive evaluation and iterative contraction of $N$-body equivariant features
• Comment on "Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning"
• Efficient implementation of atom-density representations
• Manifolds of quasi-constant SOAP and ACSF fingerprints and the resulting failure to machine learn four-body interactions
• Optimal radial basis for density-based atomic representations

Cited by in corpus (3)

• Completeness of Atomic Structure Representations
• A smooth basis for atomistic machine learning
• Spectral Operator Representations