# Optimal radial basis for density-based atomic representations

arXiv: https://arxiv.org/abs/2105.08717 · HTML: https://mlsanity.com/paper/2105.08717/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 40 references that are in the map.
- First posted on arXiv 18 May 2021.

## Builds on (most cited first, 7 of 7)

- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [DScribe: Library of Descriptors for Machine Learning in Materials Science](https://mlsanity.com/paper/1904.08875/) (2019)
- [Relevance of Rotationally Equivariant Convolutions for Predicting Molecular Properties](https://mlsanity.com/paper/2008.08461/) (2020)
- [Improving Sample and Feature Selection with Principal Covariates Regression](https://mlsanity.com/paper/2012.12253/) (2020)
- [Structure-Property Maps with Kernel Principal Covariates Regression](https://mlsanity.com/paper/2002.05076/) (2020)
- [The role of feature space in atomistic learning](https://mlsanity.com/paper/2009.02741/) (2020)
- [Feature Optimization for Atomistic Machine Learning Yields A Data-Driven Construction of the Periodic Table of the Elements](https://mlsanity.com/paper/1807.00236/) (2018)

## Built on by (most cited first, 4 of 4)

- [The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentials](https://mlsanity.com/paper/2205.06643/) (2022)
- [Tensor-reduced atomic density representations](https://mlsanity.com/paper/2210.01705/) (2022)
- [Wigner kernels: body-ordered equivariant machine learning without a basis](https://mlsanity.com/paper/2303.04124/) (2023)
- [A smooth basis for atomistic machine learning](https://mlsanity.com/paper/2209.01948/) (2022)

## Abstract (arXiv)

The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular representations can be seen as an expansion of the symmetrized correlations of the atom density, and differ mainly by the choice of basis. Considerable effort has been dedicated to the optimization of the basis set, typically driven by heuristic considerations on the behavior of the regression target. Here we take a different, unsupervised viewpoint, aiming to determine the basis that encodes in the most compact way possible the structural information that is relevant for the dataset at hand. For each training dataset and number of basis functions, one can determine a unique basis that is optimal in this sense, and can be computed at no additional cost with respect to the primitive basis by approximating it with splines. We demonstrate that this construction yields representations that are accurate and computationally efficient, particularly when constructing representations that correspond to high-body order correlations. We present examples that involve both molecular and condensed-phase machine-learning models.