A budget-dependent crossover between coverage- and response-based training-set selection for machine-learned interatomic potentials

Abstract

Selecting compact training sets for machine-learned interatomic potentials requires deciding whether to preserve structural diversity or target configurations on which models disagree. The better choice can depend on how much data is retained, making a comparison at one training-set size insufficient. Here we link selection criteria to prediction accuracy through a budget-resolved comparison of retrained MACE models on GAP-20 Carbon and pooled revised MD17. Structural coverage is compared with a response-guided selector that targets disagreement between a coverage-trained model and a full-data reference. This retrospective response witness tests the value of model disagreement for compressing an already labelled pool. At 5\%, coverage gives smaller absolute deviations from the full-data error than random sampling across four force endpoints in both datasets. The witness has larger deviations than coverage at 1\% and 5\%, but the ordering reverses at 20\%. At 20\%, witness-selected models also lower direct held-out force errors by 0.46--5.89\% relative to coverage, with all eight paired training-seed intervals favouring the witness. Six errors fall below the full-data reference. Mean force-error reductions are 0.164--0.167~meV~$\text{\AA}^{-1}$, with larger gains for tail and masked endpoints. Complementary analyses show that learned similarity preserves the coverage ranking, while selecting by frozen-model error gives higher error than embedding coverage. These findings establish retained-data budget as a deciding variable in atomistic training-set selection and provide a direct test of when response-guided compression improves on structural coverage.