The role of feature space in atomistic learning

TL;DR

This paper introduces a framework to compare and analyze different feature spaces used in atomistic machine learning, focusing on how transformations and choices affect information retention and structure.

Contribution

It provides diagnostic tools to evaluate the equivalence and distortion of feature spaces, and assesses the impact of various descriptors, kernels, and metrics in atomistic learning.

Findings

Low-order features lead to information loss.

Non-linear kernels and Wasserstein metrics significantly alter feature space structure.

Basis function choices and hyperparameters impact descriptor effectiveness.

Abstract

Eficient, physically-inspired descriptors of the structure and composition of molecules and materials play a key role in the application of machine-learning techniques to atomistic simulations. The proliferation of approaches, as well as the fact that each choice of features can lead to very different behavior depending on how they are used, e.g. by introducing non-linear kernels and non-Euclidean metrics to manipulate them, makes it difficult to objectively compare different methods, and to address fundamental questions on how one feature space is related to another. In this work we introduce a framework to compare different sets of descriptors, and different ways of transforming them by means of metrics and kernels, in terms of the structure of the feature space that they induce. We define diagnostic tools to determine whether alternative feature spaces contain equivalent amounts of information, and whether the common information is substantially distorted when going from one feature space to another. We compare, in particular, representations that are built in terms of n-body correlations of the atom density, quantitatively assessing the information loss associated with the use of low-order features. We also investigate the impact of different choices of basis functions and hyperparameters of the widely used SOAP and Behler-Parrinello features, and investigate how the use of non-linear kernels, and of a Wasserstein-type metric, change the structure of the feature space in comparison to a simpler linear feature space.