Linear ACE potentials get calibrated uncertainty: a delete-one-configuration jackknife sets the shape and one conformal quantile the scale, putting most of 20 silicon properties inside 95% intervals
Synopsis
Linear atomic cluster expansion (ACE) potentials are misspecified when trained on deterministic density-functional labels, so Bayesian posterior variances understate their errors. A delete-one-configuration CR3 jackknife covariance supplies the shape and one conformal quantile from held-out data supplies the scale, bringing per-atom force regions close to nominal coverage on held-out silicon and propagating the same parameter distribution through implicit differentiation to 21 silicon properties; of 20 scored properties, 17 fall inside 95% intervals for the smaller model and 15 for the larger, whose intervals are about 4 times tighter.
Interpretation
Per-atom force uncertainty for linear ACE potentials can now be given by one shape times one scale, reaching close to nominal coverage on held-out silicon data. Earlier routes relied on committees of several fits or on combining conformal scaling with a Bayesian posterior, and a single conformal scale guarantees only average coverage while force errors vary strongly between local environments. On 248 test configurations at a nominal 90%, the CR3 shape with one hold-out quantile covers 0.87 of atoms for o3d12 and 0.90 for o4d20; with cracks and screw dislocations removed from training, calibration and test, the same quantile covers 0.86 and 0.93, the cracks are covered, and o3d12's screw dislocations are covered at only 0.77.
The same parameter distribution propagates to derived properties the fit never saw, and the intervals shrink with model accuracy. Per-atom intervals cannot be combined into an interval on a derived property, because such a property depends on every atom and on relaxed geometries. With one global scale fitted to held-out forces and propagated by implicit differentiation through each relaxation, 17 of 20 scored properties fall inside 95% intervals for o3d12 and 15 for o4d20, with median interval widths of 2.52 and 0.64 benchmark tolerances.
The calibrated parameter distribution performs comparably with POPS on these properties, and differs in having an interpretable scale and a numerically well-posed form. POPS targets misspecification directly, but the size of its hypercube is set by a ridge parameter and a leverage cut rather than by held-out errors. At numerically defined ridges POPS covers 15/20 properties for o3d12 and 17/20 for o4d20 at widths close to the headline's; once the defect discrepancy term is added to both, joint evidence favours the CR3 propagation by log Bayes factors of +3.1 for o3d12 and +1.1 for o4d20.
Perspective
The demonstrated setting is two linear ACE models (o3d12 and o4d20) fitted to the GAP-18 silicon database, with per-atom forces evaluated on 248 held-out test configurations and derived properties taken from 20 scored items of a 21-property silicon suite, plus one out-of-distribution test that removes cracks and screw dislocations entirely. The intended readers are researchers and engineers who use linearly parameterized machine-learned potentials and need to report uncertainty.
Calibration assumes the test configurations and the derived-property structures are exchangeable with the training data, which the relaxed point defects show is not always true; the hyperparameters are held fixed in the jackknife, so their own uncertainty is not propagated; 20 properties give a coarse coverage estimate, and 17 of 20 corresponds to a 95% credible interval of 0.65 to 0.96 for the coverage probability; the defect discrepancy term was devised after the property results were seen.