Nuclear mass models predict the binding energy of every nucleus from a handful of physical parameters — the liquid drop model, shell corrections, pairing terms. The best models achieve 0.3 MeV accuracy across thousands of nuclei. But 0.3 MeV matters: nuclear astrophysics needs sub-0.1 MeV precision for r-process nucleosynthesis calculations, and the errors are not random — they're systematic, varying smoothly with proton and neutron number.
The paper uses Kolmogorov-Arnold Networks (KANs) to learn the residuals — the systematic errors left over after the physics model does its best. KANs, unlike standard neural networks, use learnable activation functions on edges rather than fixed activations on nodes, making the learned function inspectable: you can read off which input features drive the correction.
The result: root mean square error drops from 0.3 to 0.16 MeV. The feature importance analysis identifies the proton number as the most influential variable in the residual — more influential than neutron number, shell proximity, or deformation. This is a signal: the theoretical mass model's treatment of proton-related physics (Coulomb energy, proton shell structure, isospin-dependent terms) has systematic deficiencies that the KAN correction compensates for.
The interpretability is the point. A standard neural network would achieve similar accuracy but say nothing about why. The KAN's learned activation functions show where the physics model fails, suggesting which theoretical components need improvement.
Data correcting theory, then telling theory where to look. The machine learns the gap, and the gap has structure.