From Regression to Classification: Exploring the Benefits of Categorical Representations of Energy in MLIPs

TL;DR

This paper introduces a categorical, multi-class classification approach for Machine Learning Interatomic Potentials (MLIPs) that matches regression accuracy while providing a way to quantify model uncertainty through distribution entropy.

Contribution

It proposes a novel classification-based formulation for MLIPs that predicts energy and force distributions, enabling uncertainty quantification alongside accurate predictions.

Findings

Categorical approach achieves comparable accuracy to regression models.

Enables quantification of epistemic uncertainty via distribution entropy.

Provides richer supervision through multiple target distributions.

Abstract

Density Functional Theory (DFT) is a widely used computational method for estimating the energy and behavior of molecules. Machine Learning Interatomic Potentials (MLIPs) are models trained to approximate DFT-level energies and forces at dramatically lower computational cost. Many modern MLIPs rely on a scalar regression formulation; given information about a molecule, they predict a single energy value and corresponding forces while minimizing absolute error with DFT's calculations. In this work, we explore a multi-class classification formulation that predicts a categorical distribution over energy/force values, providing richer supervision through multiple targets. Most importantly, this approach offers a principled way to quantify model uncertainty. In particular, our method predicts a histogram of the energy/force distribution, converts scalar targets into histograms, and trains the model using cross-entropy loss. Our results demonstrate that this categorical formulation can achieve absolute error performance comparable to regression baselines. Furthermore, this representation enables the quantification of epistemic uncertainty through the entropy of the predicted distribution, offering a measure of model confidence absent in scalar regression approaches.