arXiv:2512.01160cs.LGq-bio.MN2025-12

用分类法表示能量,让模型不仅能预测还能判断自己有多确定。

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

  • 将能量预测转为多类别分类,用分布代替单一数值
  • 误差与回归方法相当,且能输出不确定性熵
  • 适合需要可信度评估的分子模拟场景

密度泛函理论(DFT)是计算分子能量与行为的常用方法。机器学习原子间势(MLIPs)通过训练逼近DFT级别的能量和力,计算成本大幅降低。现有多数MLIP采用标量回归方式,预测单一能量值并最小化与DFT的绝对误差。本文探索一种多类别分类框架,将能量/力预测转化为对能量分布的分类,提供多目标监督。关键在于,该方法通过预测能量分布直方图,将标量目标转换为分布形式,并使用交叉熵损失进行训练。结果表明,该分类框架在绝对误差上可达到与回归基线相当的性能。更重要的是,其预测分布的熵能有效量化模型的似然性不确定性,为模型置信度提供了回归方法所缺失的衡量标准。

原文摘要 · Abstract (English)

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.

机器学习势不确定性估计分类预测

Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。